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Beginning Algebra
9780495118077
ISBN:
0495118079
Edition: 8 Pub Date: 2007 Publisher: Thomson Learning
Summary: Easy to understand, filled with relevant applications, and focused on helping students develop problem-solving skills, BEGINNING ALGEBRA is unparalleled in its ability to engage students in mathematics and prepare them for higher-level courses. Gustafson and Frisk's accessible style combines with drill problems, detailed examples, and careful explanations to help students overcome any mathematics anxiety. Their prove...n five-step problem-solving strategy helps break each problem down into manageable segments: analyze the problem, form an equation, solve the equation, state the conclusion, and check the result. Examples and problems use real-life data to make the text more relevant to students and to show how mathematics is used in a wide variety of vocations. Plus, the text features plentiful real-world application problems that help build the strong mathematical foundation necessary for students to feel confident in applying their newly acquired skills in further mathematics courses, at home or on the job
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International Mathematics for the Middle Years has been developed with the international student in mind. This series is particularly beneficial to students studying the International Baccalaureate MYP. All examples and exercises take an international viewpoint, giving students an opportunity to lea South Australia — A Middle Years' Approach is a resource which creates a link between the primary and secondary school approaches to Mathematics. It features a unique and fully integrated textbook/workbook package designed to work in tandem whilst providing a flex...
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This text is a practical course in complex calculus that covers the applications, but does not assume the full rigour of a real analysis background. Topics covered include algebraic and geometric aspects of complex numbers, differentiation, contour more...
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Course Description
(P)
This course covers basic arithmetic, introductory concepts in algebra,
and problem solving techniques. Specific topics include addition,
subtraction, multiplication and division of signed numbers, percentage, and
applications of these skills. The course introduces algebraic concepts,
including algebraic operations of polynomials, solving equations, formulas,
and an introduction to solving word problems. (Prerequisite: MATH C020
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Short Description for An Introduction to the Theory of Numbers The sixth edition of the classic undergraduate text in elementary number theory includes a new chapter on elliptic curves and their role in the proof of Fermat's Last Theorem, a foreword by Andrew Wiles and extensively revised and updated end-of-chapter notes. Full description
Full description for An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers by G.H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D.R. Heath-Brown this Sixth Edition of An Introduction to the Theory of Numbers has been extensively revised and updated to guide today's students through the key milestones and developments in number theory. Updates include a chapter by J.H. Silverman on one of the most important developments in number theory - modular elliptic curves and their role in the proof of Fermat's Last Theorem - a foreword by A. Wiles, and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader The text retains the style and clarity of previous editions making it highly suitable for undergraduates in mathematics from the first year upwards as well as an essential reference for all number theorists.
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Math Reference
WAGmob brings you Simple 'n Easy, on-the-go learning app for Math and Math Formula calculator that is optimized for both phones and tablets. The app helps you understand the basics in a nice and organized manner.
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Math Center
The Math Center is a non-credit, Community Education class which provides assistance
in mathematics as a completely free service. Current Allan Hancock College students
as well as other individuals who are 18 years or older may fill out a simple registration
form and attend as frequently as they want. Registration forms may be found in the
Math Center or at Community Education in Building S.
The goal of the Math Center (sometimes called the Math Lab) is to assist students
in the successful completion of any Allan Hancock College mathematics class by providing
additional instructional resources. The Math Center offers many resources, including
one-on-one, drop-in tutoring by our staff of instructors and student tutors. Please
see the full list of resources below:
Free, drop-in tutoring
A place to study individually or in small groups
In-house loan of current textbooks and solutions manuals
A library of supplemental books, DVDs, and video tapes for check-out
Computers for mathematical purposes
Calculators
Handouts on math topics, including content from various math courses as well as information
on overcoming math anxiety and preparing for and taking math tests
Two private study rooms
Make-up testing
Workshops
Joining the math center group
Current students may access more detailed information by entering their myHancock
portal and joining the Math Center Group. Details may include information such as
the current schedule of instructors and student tutors who work in the Math Center,
a schedule of instructors and tutors who specialize in statistics, upcoming workshops
on selected topics, etc. To join the Math Center Group:
Enter myHancock
Look at the center of the Home page in the box titled "My Groups." Click on "View
All Groups" at the bottom of the box.
STAFF
SPOTLIGHT
Christine Rincon Nursing Student
"At Allan Hancock College, I have a clear path for where I want to go in terms of a career. The classes are really challenging and rewarding. The instructors are really open and willing to share their knowledge with you. They have so much experience to share with us, things that would take years to see in the field." Read More »
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The Complete Idiot's Concise Guide To
Algebra
Edition 2
Published by Alpha Books
Just the facts (and figures) to understanding algebra. The Complete Idiot's Guide to Algebra has been updated to include easier-to-read graphs and additional practice problems. It covers variations of standard problems that will assist students with their algebra courses, along with all the basic concepts, including linear equations and inequalities, polynomials, exponents and logarithms, conic sections, discrete math, word problems
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Algebra World – An Introduction
Algebra World software will turn struggling students into successful math learners and average students into accelerated math learners!
Algebra World teaches and reinforces introductory algebra concepts and meets NCTM standards. Mathematics topics have series of lessons and real world examples that accompany them. Equations and their relationship to word problems are emphasized throughout the program.
The major topics covered in Algebra World are: Expressions, Variables, Algebra Notation, Pattern Recognition, Integers, One Variable Equations, Two Step Equations, Ratio, Proportion and Percent, and Geometry. Each topic has a series of detailed lessons designed to teach key mathematical concepts. The lessons are followed by challenges in three skill levels that assess understanding of the subject and mathematical reasoning ability.
MathRealm's research showed that students are not as responsive to long narrations in software as they are to interactive visuals and audio effects that draw them into the program as active learners, rather than passive listeners.
Hands-on virtual manipulatives with limited text reading and immediate visual feedback will capture your students' attention and help them understand concepts, as well as develop logical reasoning.
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Thinking and Quantitative Reasoning
Designed for the non-traditional Liberal Arts course, Mathematical Thinking and Quantitative Reasoning focuses on practical topics that students need ...Show synopsisDesigned for the non-traditional Liberal Arts course, Mathematical Thinking and Quantitative Reasoning focuses on practical topics that students need to learn in order to be better quantitative thinkers and decision-makers. The author team's approach emphasizes collaborative learning and critical thinking while presenting problem solving in purposeful and meaningful contexts. While this text is more concise than the author team's Mathematical Excursions ((c) 2007), it contains many of the same features and learning techniques, such as the proven Aufmann Interactive Method. An extensive technology package provides instructors and students with a comprehensive set of support toolHide synopsis80618777389-5777372Good. Hardcover. May include moderately worn cover, writing,...Good. Hardcover. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9780618777372Fine. Hardcover. Instructor Edition: Same as student edition...Fine. Hardcover. Instructor Edition: Same as student edition with additional notes or answers. Almost new condition. SKU: 9780618777389-2
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Linear algebra is perhaps the most important field of mathematics for
computations and applications. Linear problems turn up at every step of
every computation and there are well established, powerful methods to
solve them. Linear methods are at the heart of computer graphics, every
form of data analysis, and is the first approximation to every problem
in every field of science. In this course, we will learn the
computational methods, the images and the concepts of linear
algebra.
Grading: Your final grade will be made out of 25% Midterm 1, 25% Midterm 2, 40% Final Exam and 10% Homework.
Reading: I will assign reading in the textbook. You are
responsible for doing this reading in advance of class. This will allow
me to use class time more efficiently to clear up points of confusion
and present alternate perspectives.
Vermeer demonstrates an excellent understanding of
perspective. Did he know that it could be described using matrices?
Homework Policy: You may collaberate on homework, but you must
write up and turn in your own problem set, and you must disclose any
people with whom you worked. Homework is due Wednesdays in
class. If you cannot turn in your homework at that time, you must
contact me in advance to arrange another time.
You are free to seek help from me, from each other (disclosed as
above), and from the tutors at the Mathlab. You
absolutely MAY NOT post homework problems to internet
discussion boards.
If you get help from someone outside this group, it should be limited
in nature, and must be disclosed.
Exams: The first midterm will take place in class on Monday,
October 1. The second midterm will be in class Friday, November 16 9. The
final exam will be Thursday, December 20, 1:30-3:30. If you have a
medical condition requiring special accomodation during exams, please
inform me and provide medical documentation before hand.
Will
Hunting realizes that he can count paths through a
network using matrices. If you want to learn more about this, take
Math 465 or 565.
Syllabus: Readings and problems sets are to be completed before or on the corresponding class date. More details will appear on this calendar as the term progresses.
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You will find 17 videos, 10 practice problems and 1 proof.
Although the page is complete for now, we will continue to watch out for new videos, practice problems and additional discussions that will help you learn this important topic.
We have added a new page containing a quick introduction to linear algebra. We are currently in the process of populating the cross product page and we wanted to make sure you were completely up-to-date on some linear algebra topics that are required to be able to fully understand cross products. So we added a linear algebra page with a quick review of the material you need to know.
This new page is not meant to completely cover linear algebra in detail. It is meant to give you a refresher or to just give you the basic tools you need in order to understand and do cross products.
At this point in time, we have no immediate plans to expand 17calculus to include complete coverage of linear algebra but things could change if we have enough interest. Let us know what you think.
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Course Description: Designed
for those who want to improve their attitude toward mathematics.
Explores feelings & develops strategies to overcome math phobia.
Emphasis will be placed on problem-solving approaches to diagrammed,
descriptive, & symbolic number problems. This course is open to
students at all levels of mathematical skills, whether preparing for a
job, college courses, a test, or living in a world where numbers matter.
One hour lecture/discussion each week.
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What branch of math deals with nonlinear systems?
What branch of math deals with nonlinear systems?
Like linear algebra goes in depth about linear systems, what should I look for to learn about the extension of linear algebra to nonlinear systems? Is there a name of the field of study? If I go into a book store to buy books about it, what should I be looking for?
Abstract Algebra? Complex Analysis? If not, what are those anyway?
Also, I've realised that is cool to know some calculus before linear algebra to relate some topics, but not necessary. Is multivariable calculus and differential equations something I should know before all of this other things? I'm just asking cause most universities have calculus up to differential equations before any of the stuff I'm asking about, including linear algebra. Is that for a particular reason?
I think linear algebra occupies a unique position because even arbitrary transformations can be treated as instantaneously linear and then integrated with respect to some parameter to capture the full, nonlinear effect of the operator. So, some calculus would be helpful there.
Abstract algebra goes into stuff about rings, fields (not fields not a vector space, but fields of numbers), and other general structures which admit an algebra but may be more exotic than the algebra of real numbers. Vector spaces are a topic of study under abstract algebra, too.
Complex analysis is the study of functions of a complex-valued variable, just as real analysis is the study of functions of a real-valued variable. Complex numbers in general are just a way of talking about points or vectors on a 2d plane.
Okay, I've another question related to the subjects we are discussing, but not to my previous question.
If you look at an equation like f(x) = y = x. It has one input and one output, right?
But you can also write it like f(x, y) = 0 = x - y. In which case you have two inputs and one constant output.
In one equation I transform the 1-dimensional vector x into the vector y using the identity function. And in the other case I transform the 2-dimensional vector <x, y> into the the 1-dimensinal vector 0. So <x, y> can be any orthogonal vector to <1, -1>.
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Calculus Terms Flashcards
Enjoy this packet of Introduction to Calculus Terms Flashcards created by the mad scientists at TestSoup. Hopefully you'll learn a thing or two. Calculus is the first advanced math classes for many students. But it has a language that may be unfamiliar to many introductory students. This set of flashcards gives a quick way to learn the basic terms and concepts.
By the way, we've helped thousands of students beat many a standardized exam with our online and mobile study systems using the same system you'll use here. You can customize your practice to focus on weak areas. You can also flag tough concepts for extra review. So, if you are early in your prep, you can practice across all types of math and verbal concepts. If you are far along in your prep, you can focus your practice on the particular section or difficulty level that you care most about. You can also practice with hundreds of example questions customized to simulate the real exam. Our program also allows you to study at your convenience, anytime, anywhere in the world.
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As a community service for those unable to purchase the
book, it is available for free reading in its entirety on
Google Books, but
is not downloadable. If you are benefitting from the free version, please consider
purchasing it on Amazon in Kindle or
paperback format. Please consider posting a review of it on
Amazon or elsewhere, or spreading the word about it to
others who may benefit.
The Math Made a Bit Easier Book Series
The first five books in my self-published Math Made a Bit
Easier book series are now available for purchase exclusively on Amazon.com.
For more information, please see below or
contact me with any
questions about the books. You can use the "Look Inside" and
"Search Inside" functionality on Amazon.
You can also read the books for free in their entirety via Google
Books, but they are not downloadable. If you are
benefitting from the free versions of the books, please consider
purchasing them on Amazon, or writing reviews of them on
Amazon, or at least spreading the word about the books to others who
may benefit.
Books in the Made Made a Bit Easier Series Now
Available
Math Made a Bit Easier: Basic Math Explained in Plain English
This is the first book in the series, and should be your starting
point unless you are absolutely certain that you fully understand
all of the concepts presented. If you do not, later books
in the series will prove to be difficult and frustrating. The book
starts with a review of basic arithmetic, followed by basic
operations, negative numbers, fractions, decimals, percents, and
basic probability and statistics. This is the foundation of all
math. The space devoted to each topic is proportional to how
difficult most students find the topic, as well as how important the
topic is in preparation for later math studies. The material is
explained conversationally and "in plain English" as promised by the
book's subtitle, without talking down to the reader, and without the
use of contrived examples or cartoonish illustrations.
The book concludes with a chapter on how to effectively study
math and improve scores on exams. Like the rest of the book, the
chapter takes a unique standpoint on the matter, and offers
suggestions including how to get oneself into the proper mental
and emotional mindset for being successful with math. Available
exclusively on Amazon.com for $6.50. The book can be read for free in its
entirety on Google Books via
this link.
Basic Algebra and Geometry Made a Bit Easier: Concepts Explained in
Plain English
This is the fourth in the series and the second "main" book. It
covers basic algebra and geometry. The scope of this book should be
sufficient for the algebra and geometry components of exams such as
the GED, (P)SAT, and career-based exams. The book includes some
practice exercises and self-tests, as well as points for review.
Available exclusively on Amazon.com for $5.25. The book can be
read for free in its entirety on Google Books via
this link.
April 2011: Anticipated release of an
independent, self-published weight loss book and companion journal. It
will be extremely practical, and very different than typical books
on the matter. It is my hope that this will be the book that really
gets through to people, and is not "just another weight loss book."
The main book will be available for purchase exclusively on Amazon.com
in paperback for $6.25, with a Kindle edition (no DRM) price of $2.99.
It will be also available for free reading in its entirety on Google
Books. The companion journal will be available in paperback
format for $4.25. Details soon.
June 2011: A test prep review book
covering basic math, algebra, and geometry, intended only for the
purposes of review, and for students who have unfortunately left their studying
for the last minute, and do not have the time to absorb the 450+
pages of material from the first two main books. Estimated price $4.95
July 2011: An 8"x10" book of worksheets
aligned to the Basic Math books of the series, with license to
freely reproduce and distribute for educational purposes. Estimated price $4.95
August 2011: An 8"x10" book of worksheets
aligned to the Basic Algebra and Geometry books of the series, with
license to freely reproduce and distribute for educational purposes. Estimated price $4.95
September 2011: A book focused specifically on
fractions, decimals, and percents, all explained extremely slowly,
targeted at parents, homeschoolers, and older students. Estimated price $5.95
October 2011: A book focused on how to teach math
to young children, targeted at parents and homeschoolers. Estimated price $4.95
November 2011: The third main book in the
series will cover more advanced topics in algebra and geometry. The scope of this book should be more than sufficient for the
algebra and geometry components of exams such as the SAT and high
school exit exams. It will also cover selected topics from the GRE and
GMAT. Not every topic from the aforementioned exams will be covered. The omitted topics will include those which students
typically
have little difficulty with, as well as topics which are considered relatively minor.
The material will be covered at a very fast pace, and will focus on the
concepts themselves, as opposed to rote exercises. Estimated price $6.95
December 2011: A book of lesson plans for
teachers, tutors, parents, and homeschoolers to accompany the third
main book in the series (Topics in Algebra and Geometry). Estimated price $4.95
Early 2012: Future books on
higher level math and/or exam-specific math TBD. The
material covered in the three main books should be more than
sufficient for most standardized exams, and in most cases even the
material in just the first two main books should suffice unless you are
pursuing additional math goals.
About the Author
Larry
Zafran was born and raised in Queens, NY where he tutored and taught
math in public and private schools. He has a Bachelors Degree in
Computer Science from Queens College where he graduated with highest
honors, and has earned most of the credits toward a Masters Degree
in Secondary Math Education.
He is a dedicated student of the piano, and the leader of a large
and active group of board game players which focuses on abstract
strategy games from Europe.
He presently lives in Cary, NC where he works as an independent math
tutor, writer, and webmaster.
Ordering, Shipping, and Returns Information
All orders and returns are fully handled directly by Amazon.com.
The books are part of Amazon's Prime program which means that Amazon
Prime members can order the books with free two-day shipping, and
non-members can get free economy shipping if ordered with $25 worth
of eligible products. The books can be ordered standalone for
Amazon's regular shipping rates.
Online Support for the Books
I provide full, free online support related to my books.
Please contact me via the
Ask a Math
Question page if anything in the books is confusing for you, or
if you would like additional information or help on a topic, or if
you would like to check your understanding of a concept.
Errata for Math Made a Bit Easier
These errors are in the 1st ed. (with leaves on the
cover), but have been fixed in the revised edition
On page 89, "2-to-the-power-of-4" is incorrectly evaluated as 8
due to an editing error. It is equal to 16, making the involved sum
equal to 29 and not 21.
On page 214, the repeating decimal 0.357 incorrectly has a double
bar over it. We always use a single bar over any repeating
decimal digit(s).
Errata for Math Made a Bit Easier Workbook
These errors are in the 1st ed. (with leaves on the
cover), but have been fixed in the revised edition
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I'm not sure if anyone ever wrote about this book on the forums, but I believe it is an absolute must have for anyone studying for the GMAT. It's called "How to solve word problems in Algebra". Let me know what you guys think. Here is a link for the book on Amazon.
Because I'm horrible on the quant section (me and numbers don't usually get along so much), I bought a bunch of the MGMAT section-specific books. I also came across this general math review for graduate entrance exams; so far, it's been pretty good refresher material:
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Standards for Mathematical Practice – High School
The CCR Standards for Mathematical Practices describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. This session will cover what the history of the Mathematical Practices and what the Mathematical Practices look like in High School problem solving experiences. This Webinar specifically focuses on mathematical tasks and how the Mathematical Practices can be integrated through quality mathematical problems.
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Math·U·See provides a firm foundation in mathematics for students of all aptitudes. The mastery-based approach allows students to move at their own pace whether they are naturally gifted in mathematics, struggle with mathematical concepts, or have special needs. Teachers are provided with the tools, skills, and training needed to present an explicit, structured, systematic, and cumulative program using multi-sensory teaching techniques.
Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects.
This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.
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Marvelous Multiplication: Games and Activities that Make Math Easy and Fun
Editorial review
Dazzling Division: Games and Activities that Make Math Easy and Fun
Editorial review
Explorations in College Algebra
Editorial review
Inspired by a desire to reshape the standard college algebra course to make the subject more interesting and relevant to students, shifts the focus from learning a set of discrete mechanical rules to exploring how algebra is used to answe
Very fast receipt, well packaged, very well priced, and everything included. Outstanding service and will definitely consider buying used textbooks from this seller in the future!
Reviewed by a reader
I used the Mathematics for elementary teachers for a college level course. The text is interesting and provides the reader/learner with a solid foundation of Problem solving skills in learning and teaching mathematics. It has several usef
Math Refresher for Scientists and Engineers, 2nd Edition
Editorial review
Reviewed by Duwayne Anderson, (Saint Helens, Oregon)
It's been a few years since I graduated from college, and although I use mathematics every day in my work, I've realized, over the years, that I don't use some aspects of mathematics very much (formal proofs, for example) and that I've be
Reviewed by a reader
ut making the volume too ponderous. Anyone would be hard pressed to find a more concise and useful reference.
Reviewed by a reader
After returning to college after 8 years working I required a review of math concepts. Math Refresher provided all the relevant topics logically laid out in a single volume. The relatively low cost of this book compared to other math refe
Culinary Math
Reviewed by
Reviewed by a reader
Modern Algebra with Applications (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs
Editorial review
Elementary Linear Algebra
Editorial review
This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar
Abstract Algebra
Editorial review
.
Reviewed by "the_incontinent_orson_welles", ("The Minnesota")
quot; (I apologize for using this phrase).One complaint: I can't seem to find a bibliography...
Reviewed by Chan-Ho Suh, (Davis, CA USA)
ncyclopedic but to introduce the reader to the more advanced topics.I've yet to see another book that carries all the topics of this one, and remains fairly reader-friendly (as this one does).
Reviewed by N. Kadambi "Navin", (Gainesville, FL)
long before the student encounters them in the sections.
Reviewed by a reader, (USA)
semester of use. It did see some moderate backpack use but not too much, certainly less than many other books I've had in the past. So take care of it!
Reviewed by Decio Luiz Gazzoni Filho, (Londrina, PR Brazil)
chunk of it yet!
Reviewed by Charlie Johnson, (Minnetonka, MN USA)
Well, I feel that I should add to the long list of affirmative reviews. Why, I don't know? If you want a book that will take you from the basics of Abstract algebra to the advanced level, then buy this book, you won't regret it. It is a l
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PRAXIS II Mathematics 0061From mathematical problem solving to reasoning and proof to use of technology, this comprehensive study guide provides you with the exact material that appears on the actual test. Aligned with current standards, it covers the subareas of Algebra and Number Theory; Measurement; Geometry; Trigonometry; Functions; Calculus; Data Analysis and Statistics; Probability; Matrix Algebra; and Discrete Mathematics. Once you've mastered the core content and competencies, prepare for the real exam with a 50-question practice test that identifies the corresponding skills and question rigor, and includes
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High School Solutions: Think Differently about High School Math
We all know the problem: many students struggle with math—and teaching the same way we always have hasn't worked for all students. Math Solutions professional development offers teachers a different way to view how students learn and shifts teachers' instructional approaches to ensure that all students leave high school college and career ready.
Math Solutions provides teachers with practical tools to help their students make sense of math—and when that happens, engagement and understanding soar. As professional development specialists, we support teachers across the country with hands-on, real-world strategies and tools for teaching:
Logical reasoning and problem solving
Functions and modeling
Numbers and quantity
Algebra and geometry
Our programs are customized to meet your school's needs and devoted to ensuring that all students pass high-stakes exams and leave high school college and career ready.
Ensure Success for High School Teachers and StudentsCourses to Improve High School Math Instruction
The courses described below are just a sample of professional development options for teachers. We will work with you to provide a complete solution to meet your specific needs and goals.
About Teaching Mathematics: Reasoning and Sense Making
Developing students' ability to reason is key to helping them learn and make sense of mathematics. This unique mathematics institute helps high school classroom teachers understand how students learn mathematics, explores ways to make math accessible for students, and focuses on problem solving in the strands of algebra and geometry. Participants engage in problem-solving activities and investigations that develop student understanding, and learn how to use contexts, manipulative materials, and graphing calculator technology to support learning. This course also models a variety of ways to organize the classroom, including whole-class, small-group, and individual learning. Course experiences are based on core student expectations for Algebra I, Geometry, and Algebra II. Grades 9–11.
Goals This course helps participants:
think flexibly about math content knowledge for the purpose of making math accessible for students;
understand how students learn mathematics; and
implement instructional strategies that promote thinking, reasoning, and making sense of mathematics.
focus on problem solving in the strand of algebra with links to geometry;
experience a variety of ways to organize the classroom—whole-class, small-group, and individual learning;
identify and analyze strategies that develop students' ability to reason and make sense of mathematics; and
understand how manipulative materials can be used to support learning.
Resource Materials:Focus on High School Mathematics: Reasoning and Sense Making
Math Solutions for High School Algebra and Geometry Teachers
Introducing teachers to the current guidelines for mathematics instruction, this course presents teachers with the rationale for teaching mathematics through problem solving and using effective instructional strategies that promote thinking and reasoning.
The course focuses on the mathematical content and instructional strategies necessary for developing students' algebraic and geometric thinking. Participants explore what is meant by algebraic and geometric thinking and learn strategies for teaching basic concepts necessary to be successful in Algebra and Geometry. Grades 9–11.
Goals This course helps participants:
strengthen math content knowledge for the purpose of making math accessible for students;
understand how students learn mathematics;
implement effective instructional strategies that promote thinking, reasoning, and making sense of mathematics; and
understand how manipulative materials, contexts familiar to students, and problem-solving experiences can be used to support students' development of algebraic/geometric thinking;
experience a variety of ways to organize the classroom—whole-class, small-group, and individual learning;
identify and analyze strategies to help students see arithmetic, geometry, and algebra as connected topics integral to the study of mathematics; and
experience a classroom atmosphere that stimulates and supports students' learning of algebraic/geometric concepts and skills.
Note: In collaboration with the site host, course experiences will be designed to address specific needs, with appropriate supporting resources and length of the course.The whole experience is amazing. . . . The course presents a feast for your senses, with a variety of different perspectives presented by teachers and instructors from all grades."
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Purpose
This textbook and Internet resource provides introductory information, concept or skill development in Mathematics for grade 8, 9, 10, 11, and 12 students who are at grade level in a single student or whole class situation.
This digital textbook was reviewed for its alignment with the content standards only; California's Social Content Review criteria were not applied.
Districts, schools, and individuals planning to take advantage of this free textbook are reminded to conduct their own review to determine whether this resource meets their instructional needs.
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This edited volume addresses the importance of mathematics for industry and society by presenting highlights from contract research at the Department of Applied Mathematics at SINTEF, the largest independent research organization in Scandinavia. Examples range from computer-aided geometric design, via general purpose computing on graphics cards, to... more...
Based on a teach-yourself approach, the fundamentals of MATLAB are illustrated throughout with many examples from a number of different scientific and engineering areas, such as simulation, population modelling, and numerical methods, as well as from business and everyday life. Some of the examples draw on first-year university level maths, but these... more...
About the Book: This book provides an introduction to Numerical Analysis for the students of Mathematics and Engineering. The book is designed in accordance with the common core syllabus of Numerical Analysis of Universities of Andhra Pradesh and also the syllabus prescribed in most of the Indian Universities. Salient features: Approximate... more...
About the Book: Application of Numerical Analysis has become an integral part of the life of all the modern engineers and scientists. The contents of this book covers both the introductory topics and the more advanced topics such as partial differential equations. This book is different from many other books in a number of ways. Salient Features:... more...
Features contributions that are focused on significant aspects of current numerical methods and computational mathematics. This book carries chapters that advanced methods and various variations on known techniques that can solve difficult scientific problems efficiently. more...
This book, written by two experts in the field, deals with classes of iterative methods for the approximate solution of fixed points equations for operators satisfying a special contractivity condition, the FejÚr property. The book is elementary, self-contained and uses methods from functional analysis, with a special focus on the construction of iterative... more...
The ISAAC (International Society for Analysis, its Applications and Computation) Congress, which has been held every second year since 1997, covers the major progress in analysis, applications and computation in recent years. In this proceedings volume, plenary lectures highlight the recent research results, while 17 sessions organized by well-known... more...
The present collection of four lecture notes.... more...
The eighth edition of this popular book provides a hands-on introduction to MATLAB[registered] that can be used at the undergraduate level. The new edition features the use of MATLAB 8.0, which will be introduced to the market in March 2010. It covers object-oriented programming in MATLAB and the improvements that have been made to the MATLAB desktop... more...
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For Elementary Mathematics Methods or Middle School Mathematics Methods Covers preK-8 Written by leaders in the field, this best-selling book will guide teachers as they help all PreK-8 learners make sense of math by supporting their own mathematical understanding and cultivating effec...
This best-selling writing guide by a prominent biologist teaches students to think as biologists and to express ideas clearly and concisely through their writing. Providing students with the tools they'll ...For courses in Business Statistics. A classic text for accuracy and statistical precision. Statistics for Business and Economics enables students to conduct serious analysis of applied problems rather than running simple "canned" applications. This text is also at a math...
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Geometry: Teaching About Shapes and Their Measures begins February 13, 2012.
Register today to take advantage of this opportunity.
Course registration remains open for the spring offerings of math/numeracy
online professional development courses from
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Geometry: Teaching About Shapes and Their Measures
Adult basic education students need foundational geometry and measurement
skills not only to succeed in GED math, but also in the workplace. In this
course, you will explore key topics in geometry, such as area, perimeter,
and volume, and their importance in everyday life. You'll look at numerous
instructional activities for teaching about angles, spatial relationships,
similarity, and figure transformations on a coordinate graph system.
Course dates: February 13 to March 26, 2012
Full course description: download PDF
<
Registration link:
Course instructor: Barbara Goodridge
Course fee: $179.00
Data: Helping Students Interpret Statistical Representations
Data, or numerical information, can be described, represented, analyzed, and
interpreted in various ways for various purposes. This course looks at some
common uses (and misuses) of data. Learn about the measures of central
tendency statistics, graphs, and probability. Through the course readings,
activities, and discussions, you'll review basic concepts and explore
strategies for introducing and teaching these concepts to your adult
students.
Course dates: March 19 to April 30, 2012
Full course description: download PDF
<
Registration link:
Course instructor: Pam Meader
Course fee: $179.00
Algebra: Introducing Algebraic Reasoning
Research suggests that math topics, including algebra, should be taught at
all levels, not just when a student is ready for GED preparation. In this
course, you'll learn how to introduce algebraic reasoning to your students,
and you'll experiment with strategies for teaching numeric patterns,
relationships, and functions based on real-life situations. You'll also
explore strategies to help students model quantitative relationships using
graphs, tables, words, and equations.
Course dates: April 23 to June 4, 2012
Full course description: download PDF
<
Registration link:
Course instructor: Barbara Goodridge
Course fee: $179.00
Introduction to College Transition Math
Through the readings and activities in this course, you will reflect on your
own and your students' math backgrounds, examine and experience the college
placement test your students take, try out math activities and exercises you
can use in your classrooms, and explore the math knowledge and skills you
will want to present to your own college transition students.
Course Dates: February 27-April 23, 2012
Full Course Description:
Required Text: Unlatching the Gate: Helping Adult Students Learn Mathematics
by Katherine Safford-Ramus (Bloomington, IN: Xlibris Corporation, 2008),
ISBN 978-1-4363-5120-1. Allow at least two weeks for delivery.Bottom of Form
Course Instructor: Pat Fina
Estimated Completion Time: 24 hours/6 weeks
Course Fee: $249.00
Registration:
**********************
Group discounts available! Call (888) 528-2224 ext. 221 or email
prodev at proliteracy.org <mailto:%20prodev at proliteracy.org> for more
information.
Questions? Please e-mail prodev at proliteracy.org
<mailto:%20prodev at proliteracy.org>
ProfessionalStudiesAE.org is a partnership of World Education, Inc., and
ProLiteracy/New Readers Press. Visit
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professionalstudiesae.org&srcid=4593&srctid=1&erid=443971>
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Kaye
Kaye Beall
Project Director
World Education
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TI-89 Graphing Calculator For Dummies
Do you own a TI-89, TI-89 Titanium, TI-92 Plus, or a Voyage 200 graphing calculator? If you do, or if you need to get one for school or your job, then you need to know how it works and how to make the most of its functions.
TI-89 For Dummies is the plain-English nuts-and-bolts guide that gets you up and running on all the things your TI-89 can do, quickly and easily. This hands-on reference guides you step by step through various tasks and even shows you how to add applications to your calculator. Soon you'll have the tools you need to:
Solve equations and systems of equations
Factor polynomials
Evaluate derivatives and integrals
Graph functions, parametric equations, polar equations, and sequences
Create Stat Plots and analyze statistical data
Multiply matrices
Solve differential equations and systems of differential equations
Transfer files between two or more calculators
Save calculator files on your computer
Packed with exciting and valuable applications that you can download from the Internet and install through your computer, as well as common errors and messages with explanations and solutions, TI-89 For Dummies is the one-stop reference for all your graphing calculator questions!
Customer Reviews:
Good and bad
By Fred K. Johnson - November 11, 2006
This book is very good at what it does cover and very bad at what it doesn't cover. It's clear it was written by a mathematician. The topics and tricks dealing with functions and graphing are great. Anyone taking a math class such as Algebra, Trig or Calculus will be helped. It doesn't cover certain important topics at all or very lightly. There is nothing on programming. Two pages are dedicated to writing your own functions with nothing on how you can use a user defined function in a formula. While the book carefully explains how to make sure if variables are defined or not there is nothing on folders which would be a great help as the scope of a variable is a folder. By organizing folders you can keep things seperated and track when variables are defined. There is nothing on units of measure which is a strong point of this machine. That would be important in say a physics or EE class. It has very little on statistics for someone in a statistics class.
Unlocking the Power of the TI-89
By Naut Gauss - September 30, 2005
"TI-89 ...For Dummies" has unlocked for me many useful features of this powerful calculator. The TI-89 is required for a sequence of classes I am taking. The TI supplied manual reads like some poor engineer was asked to spruce up the notes from designing the thing. But CC. Edwards presents essential features in a clear, fun, and readable manner. I wanted skills that would help me quickly perform needed operartions and understand how to get out of quirky modes that you can blunder into. Thanks, C.C., you did it! She is a good writer.
The book that should come with the calculator
By Robert L. Wilson "lifelong student" - March 14, 2006
When you purchase a TI-89, you should be either directed to purchase the Dummies book for it, or it should be included with the device. More informative (and easier reading than the dry manual included) the Dummies book is excellent to assist you in the learning curve and get your money's worth out of the device.
My opinion is that the only dummies are those who do not make use of their Dummies books. Well written by knowledgable professionals who have a sense of humor.
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*While many lesson plan sites have a subscription fee or otherwise sell their lesson plans (that is an additional feature of some of the sites found here) all lesson plans and collections of lesson plans listed here are free.
Cool math Lessons - Trigonometry - The Pythagorean Identities __ "This page shows the derivations of the three Pythagorean Identities. A "derivation" means that we need to create this from scratch - or, at least, from other things that we know." - From coolmath.com -
Inverse Trig Function Lesson Plan __ "(Generalization of a Concept) To find the single valued inverse function of a periodic trigonometric function, the original function's domain must be restricted on an interval so we have a new one-to-one function that fully encompasses the range of the trigonometric function. Thus, the range of the inverse
function is equivalent to the domain of the new one-to-one function." I haven't the slightest idea of what this means. Goals, procedure - From scribd.com -
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Algebraic conventions
You can use these techniques and examples when planning lesson sequences on
algebraic conventions.
Pupils need to be as familiar with the conventions of algebra as they are with those
of arithmetic. Algebraic conventions should become a routine part of algebraic
thinking, allowing greater access to more challenging problems.
It is a common error to deal with these conventions rather too quickly.
How pupils understand and manipulate algebraic forms is determined by their
mental processing of the meaning of the symbols and the extent to which they can
distinguish one algebraic form from another.
A goal is to develop pupils' mental facility to recognise which type of algebraic form
is presented or needs to be constructed as part of a problem. Some time spent on
this stage of the process can reduce misconceptions when later problems become
quite complex.
For example, in the equation p+7=20 the letter p represents a
particular unknown number, whereas in p+q=20, p and q can each
take on any one of a set of different values and can therefore be called variables.
Equations, formulae and functions can describe relationships between variables. In
a function such as q=3p+5 we would say that 3p was a variable term,
whereas 5 is a constant term.
Be precise and explicit in using this vocabulary and expect similar usage by pupils.
Progression
Representing an unknown value in equations with a unique solution:
3x+5=11
Representing unknown values in equations with a set of solutions:
p+q=20
Representing variables in formulae:
2l+2b=p
Representing variables in functions:
y=x2-7
Identifying equivalent terms and expressions
It is often the case that pupils do not realise when an equation or expression has
been changed, or when it looks different but is in fact still the same. The ability
to recognise and preserve equivalent forms is a very important skill in algebraic
manipulation and one in which pupils need practice.
One way of approaching this is to start with simple cases and generate more
complex, but equivalent, forms. This can then be supported by tasks involving
matching and classifying.
Progression
Simple chains of operations, for example 2x+x+5
Some with unknown coefficients, for example ax+5
Linear brackets, for example 7(x+2)
Quadratic brackets, for example (x+2)(x+5)
Positive indices, for example x3×x.
Identifying types and forms of formulae
This will build on the understanding of equivalence and will rely on knowledge of
commutativity and inverse.
Encourage pupils to see general structure in formulae by identifying small collections
of terms as 'objects'.
These objects can then be considered as replacing the numbers in 'families of facts',
such as 3 + 5 = 8, 5 + 3 = 8, 3 = 8 – 5, 5 = 8 – 3. The equations are then more easily
manipulated mentally.
For example, consider these equivalent formulae:
ab=l
a=l×b
To develop pupils' understanding of the dimensions of a formula, make explicit
connections between the structure of the formula and its meaning. Consider the
units associated with each variable and how these build up, term by term.
For example, consider the dimensions of these formulae:
a=l×b
2l+2b=p
Involve pupils in generating and explaining non-standard formulae, for example, for
composite shapes.
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Calculus For Biologists: A Beginning - Getting Ready for Models and Their Analysis
This book tries to show beginning biology majors
how mathematics, computer science and biology can
be usefully and pleasurably intertwined.
After the necessary start up costs to develop some
essential calculus tools, we use a few select models to illustrate how these three fields influence each other in interesting and useful ways. Indeed, we believe that the three must be considered as part of a larger whole and that the use of these ideas is perhaps best described as an emergent phenomena! And we must always be careful to make sure our use of mathematics gives us insight. This fourth edition again adds a bit more biology and polishes the mathematical and numerical discussions. In addition,more exercises have been added and additional typographical errors have been found and corrected.
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The Chapter 1 Test is postponed, until after I return from my absence. Please make sure that you retain all of the knowledge and understanding you have worked so hard to acquire!
If you have hand held technology device on which you can access our text book, please bring it to class this week!
Tuesday 9/25/2012
No HW
Thursday 9/27/2012
Practice Constructions.
RTN & GP Lesson 2.1
Monday 10/1/2012
Prepare for Unit 1 Test: Sections 1.1 - 1.5 and 2.1
Tuesday 10/2/2012
The take home portion (constructions) of your Test is due on Thursday
RTN & GP Lesson 2.2 and page 86 (Symbolic Notation)
Wednesday 10/3/2012
Page 74: #3, 5, 6, 7, 8, 9, 10, 25, 26, 27, 29, 35. If you did not finish Journal #2 Entry #2 in class, finish it at home (it is on today's work sheet). Review the RTN & GP for this section and page 86. The take-home portion (constructions) of your Unit 1 test is due at the beginning of class tomorrow.
Thursday 10/4/2012
Homework: Page 75: #19 – 24, 31, 32.
Finish class work sheets from Lesson 2.2 day 1 and day 2.
RTN & GP Lesson 2.3
Friday 10/5/2012
Review the RTN for lesson 2.3. Stretch your logic and reasoning abilities by completing as many of the logic puzzles and sudoku puzzles as you can!
Monday 10/8/2012
Page 82: #1, 5, 7, 9, 13, 17, 21, 22, 25, 26, 27, 28. Check out the e-textbook animation that goes with this lesson, to help you learn the law of syllogism!
RTN & GP Lesson 2.4 – Please note: you are not expected to memorize postulate numbers or the exact wording of the Point, Line, and Plane Postulates!
Wednesday 10/10/12
Journal #2 is due tomorrow. Retest of the Take home portion of chapter 1 test is due Monday. Finish the 2.4 sheet from class today. RTN & GP Lesson 2.5 - Study the examples very carefully. You will be expected to know the names of all of the properties, and use them to justify each step of an algebraic process. Also notice how Geometric properties are also named as reasons.
Thursday 10/11/12
Lesson 2.5 Day 1 worksheet. Remember to go back to your text book and review the examples in 2.5 that use the segment addition postulate and the angle addition postulate.
Friday 10/12/12
Study the example(s) completed in class, on the Lesson 2.5 Day 2 work sheet. On the back of the sheet, do the proof using different logic, using the hints provided. Carefully read the Chapter 2 project sheets, to decide which project you want to do. Test on Lessons 2.2 - 2.5 on Tuesday 10/16. The retest of the take home portion of the unit 1 test is due on Monday.
Monday 10/15/12
Prepare for Test on Lesson 2.2 - 2.5 tomorrow. Practice! Finish or redo any worksheets from class. Use the on-line text book resources!
Try the proofs on the Lesson 2.6 Day 2 packet - remember to solve the problem in your head first, and developing an overall stategy before you write anything down! If you find some of the proofs frustrating or difficult, don't panic - we'll take care of it in class. However, if you are struggling, do some problems from the text book and check your answers.
Finish any proofs your were not able to complete in class. Test on 2.6 and 2.7 on Friday. RTN & GP Lesson 3.1. All of the highlighted vocabulary terms on page 141 should be familiar to you. Make sure that you realize that these are angle relationship names based on position only, and do not tell you anything about congruence or measures! The two new postulates should make intuitive sense to you.
Thursday 10/25
Prepare for test on 2.6 and 2.7.
Friday10/26/12
Page 142: #3, 4, 5, 6, 15, 16, 17, 28, 29, 30, 31, 32
RTN & GP Lesson 3.2
Monday 10/29/12
Page 150: #22 – 36. For each problem (except #34), copy the diagram, set up an equation and state the postulate or theorem that justifies it, using the acceptable abbreviation.
RTN & GP Lesson 3.3
Monday 11/12/12
WELCOME BACK FROM HURRICATION 2012! No HW
Tuesday 11/13/12
Do pages 1 & 2 ONLY of the 3.2/3.3 packet
RTN & GP Lesson 3.3
Wednesday 11/14/12
Page 150: #22 – 36. For each problem (except #34), copy the diagram, set up an equation and state the postulate or theorem that justifies it, using the acceptable abbreviation.
Practice the 3 constructions on pages 190 & 191, until you can do them neatly, accurately and without looking at the instructions.
RTN & GP Lesson 3.4. Please make note, for each vocabulary term, key concept, postulate and example, which ones you already know, which are new, and which simply need a refresher. PLEASE BRING YOUR TEXT BOOK, or personal technology to access to class on Monday!
Monday 11/19/12
Study for Chapter Test on sections 3.1 – 3.3.
11/20/12 Tuesday
RTN & GP Lesson 3.5. Please make note, for each vocabulary term, key concept, postulate and example, which ones you already know, which are new, and which simply need a refresher.
11/21/12 Wednesday
Have a nice break!
11/26/12 Monday
Finish the 3.4/3.5 intro sheet from class.
Page 167: #11, 12, 13, 14, 34, 39, 40, 42
Review your RTN & GP for lesson 3.5
11/27/12 Tuesday
Page 176: #19, 21, 25, 27, 29, 31, 35, 47, 48, 59.
If you were not able to do #42 from yesterday's HW, try again!
11/28/12 Wednesday
Finish the 3.4/3.5 sheets from class.
RTN & GP for lesson 3.6. Notice that the first three theorems don't have names. If you were a math teacher, what do you think would be the best name for each? You should have the next 2 theorems already proven in your notebook. Know how to measure the distance between a point and a line and the distance between parallel lines. Carefully study example #4.
11/29/12 Thursday
Finish the 3.6 sheet from class.
11/30/12 Friday
Page 186: #13, 14, 25, 26, 27.
Test on 3.4 – 3.6 and Constructions on Tuesday 12/4
12/3/12 Monday
Prepare for Test on 3.4 – 3.6 and Constructions.
12/4/12 Tuesday
RTN & GP Lessons 1.6 and 4.1. Know all highlighted vocabulary terms.
12/5/12 Wednesday
Page 44: #8 – 14, 18 - 27
Page 211: #1 - 6, 29 – 37
12/6/12 Thursday
RTN & GP Lesson 8.1
Lesson 8.1 Packet pages 2 & 3. If you are struggling or unsure, try some similar problems in the text book and check the answer key.
12/7/12 Friday
10 point graded HW on sections 1.6, 4.1, & 8.1 should be completed this weekend, but will not be collected until Wednesday. If you are not able to complete the sheet by Monday's class, I will expect you to come in for extra help on Monday or Tuesday! RTN & GP Lesson 4.2.
Complete the coordinate proof from today's activity, two different ways. Do your best to follow the conventions of a "formal coordinate proof" given in the example and notes on Monday.
1/10/13 Thursday
Page 300: #15 – 19, 29, 30
RTN & GP Lesson 5.2
1/11/13 Friday
RTN & GP Lessons 5.3 and 5.4. Review lesson 5.2 and make note of the 4 types of Centers of Triangles including the names and what type of segments create them and any special properties they have. We will be doing constructions next week, so make sure you know where your compass and straight edge are!
1/14/13 Monday
Finish Page 2 ONLY of the construction packet (the 4 centers of acute triangles). Inspect your constructions as you reread lessons 5.2 - 5.4, with a focus on securing the vocabulary and developing an understanding of the properties of each type of center.
1/15/13 Tuesday
Finish the rest of the construction packet. Remember to construct the circle that circumscribes the triangle, with its center at the circumcenter. Remember to construct the circle that inscribes the triangle, with its center at the incenter. Make sure you know how to construct each type of segment, and which type of segment is constructed to find each type of center of a triangle.
1/16/13 Wednesday
Redo any constructions that you are struggling with. Make a graphic organizer to help you know all of the vocabulary and concepts associated with each of the 4 centers.
1/17/13 Thursday
Carefully review the Points of Concurrency Project requirements sheet. The project is due Tuesday 1/29. Put together a plan with your partner, so that you are prepared to review each other's work by the middle of next week. DO NOT treat this like a "divide & conquer" and just put 2 half-projects together at the last minute! LOOKING AHEAD: Plan on a test or quiz on either Tuesday or Friday next week, covering midsegment theorem, coordinate proofs and centers of triangles.
1/18/13 Friday
Work on your Points of Concurrency Project Due Tuesday 1/29. Work on the packet from class today (problems from 5.2 – 5.4). You are not required to complete the packet! Choose several problems from each section that stimulate and challenge you.
Reread the description and examples of indirect proofs in your text book.
Page 340: #11, 12, 13
Work on your Points of Concurrency Project Due Tuesday 1/29.
Start reviewing for your chapter 5 test. Do you know how to use distance formulate, midpoint formula and slope formula in a Midsegment Theorem Verification or any coordinate proof?
1/24/13 Thursday
Prepare for your Chapter 5 Test
IMPORTANT NOTICE:As discussed in class today, tomorrow's test only covers sections 5.1, 5.5 and 5.6. Study the class handouts! Sections 5.2, 5.3 and will be assessed as a partners quiz (multiple choice and short answer, on Tuesday 1/29.
ANOTHER IMPORTANT NOTICE: The Review Guide for the Marking Period 2 Quarterly Assessment is now posted on this website. See the menue on the left side of my homepage.
1/25/13 Friday
Work on your Points of Concurrency Project Due Tuesday 1/29.
RTN & GP Lesson 8.2
1/28/13 Monday
Your project is due tomorrow!
Partner Quiz on 5.2-5.4 tomorrow!
Page 512: #7, 11, 15, 31, 33
RTN & GP Lesson 8.3 – Know the 5 new theorems, and how they differ from the theorems in 8.2. These will be justifications you can use if you already know relationships involving angles, sides and/or diagonals and you are concluding that the figure is a parallelogram. Study the examples carefully.
1/29/13 Tuesday
Bring in any questions you have about the Quarterly Assessment.
1/30/13 Wednesday Page 521 #15, 16, 17, 34, 35, 36
********************************
1/31/13 Thursday
Period 6 – finish preparing for tomorrow's quarterly. (The HW listed below for period 8 will be your HW tomorrow night!)
Period 8 – finish the 8.2 and 8.3 sheets from class. RTN & GP Lesson 8.4 – Know the formal definitions of a rhombus, rectangle and square. Notice how the Venn diagram presented is justified by the definitions. Notice that the corollaries on page 527, restate the definitions, without having to mention anything about parallelograms! The three new theorems on page 529 pack a lot of information about rectangles and rhombuses. Since they are biconditionals, you should write each of the 3 theorems as two separate conditionals that are converses of each other. Then reread each one, and create a diagram that allows you to see what it is actually telling you about the figure.
********************************
2/1/13 Friday
Period 6 – finish the 8.2 and 8.3 sheets from class. RTN & GP Lesson 8.4. See yesterday's period 8 HW posting for RTN details. (The HW listed below for period 8 will be your HW Monday night!)
Period 8 – Page 531: #25, 27, 29, 33, 35, 39, 41, 45, 47, 49
********************************
2/4/13 Monday
Period 6 – Page 531: #25, 27, 29, 33, 35, 39, 41, 45, 47, 49
Period 8 – finish preparing for tomorrow's quarterly.
********************************
2/5/12 Tuesday
Period 6 & 8 are back in sync NOW! Complete as much as you can in the 8.4 packet. ALL problems must be at least reasonably attempted!
2/6/12 Wednesday
Complete the 8.4 packet.
RTN & GP Lesson 8.5. Know the formal definition of a trapezoid, isosceles trapezoid and a kite. The first two theorems about isosceles trapezoids make sense if you see that is like an isosceles triangle with the top sliced off! Notice that the third theorem makes sense when you look at the symmetry. There is not much to know about trapezoids that are not necessarily isosceles, except for which pairs of angles must be supplementary, and that the midsegment is parallel to the bases, and its length is the average of the length of the bases. The kite theorems should be very clear and intuitive if you look at the symmetry of a kite in one direction, and from the other direction look at it as two non-congruent isosceles triangles. You can also see it as 4 right triangles.
Page 586: 19, 21, 26 (do this twice – once with compass and straight edge and once with ruler and protractor)
Review for Quiz tomorrow on 4.3, 4.9, 9.1, 9.3, 9.4.
3/1/13 Friday
No new HW. Self assess, regarding Friday's quiz. What do you need to review, practice and/or reinforce? Choose problems appropriately. Also review/practice/reinforce Thursday's lesson, performing reflections with a compass and straight edge, as well as performing them with a ruler and protractor. Consider the advantages and disadvantages of each.
3/4/13 Monday
Complete the 9.5 compositions packet. RTN & GP Lesson 9.5.
3/5/13 Tuesday
Complete the 9.5 Day 2 compositions packet.
3/6/13 Wednesday
Page 604: #13 - 22
Go to the online text book. In Chapter 9 go to the Videos & Activities tab and find the Animated Math section. Do the Activity for Extension 9.5: Tessellations
3/7/13 Thursday
Use the square template and the class handout to create a unique shape that tessellates. This is just practice, so don't get too complicated, but do not copy the author's seahorse. You do not have to fill the page, but you should show 8 – 10 interlocking copies of your figure.
3/8/13 Friday
Use the equilateral triangle and/or regular hexagon template, today's handouts and tracing paper to practice a different method for creating a unique shape that tessellates. You do not have to fill the page, but you should show 8 – 10 interlocking copies of your figure.
Finish the Law of Cosines sheet started in class today. Use the Law of Cosines to find each missing value. Then use the triangle sum theorem to check your angle measures, and then check using the Law of Sines.
If you had 2 congruent cookies named A and B, and you cut A into congruent halves named 1 and 2 , and you cut B into congruent halves 3 & 4, you KNOW (and you CAN prove!!!) that 1 & 4 are congruent and 2 & 3 are congruent. Its just a bit of delightfully tediaous algebra.
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The chapter begins with an exploratory problem designed to introduce the concept of linear programming with an objective function to maximize profits by optimizing a company's product mix. The problem context involves assembling two types of computers with different profit margins and labor requirements. Students are led through a graphical solution to a two decision variable problem involving two constraints.The second product mix example involves a detailed totally worked-out example involving the manufacture of skateboards. Students are shown step-by-step how to formulate and solve this two decision variable problem graphically. A third decision variable is then added to motivate the need for EXCEL to solve larger problems. Students are taught how to use SOLVER as standard add-in to EXCEL to solve linear programming problems. This section also discusses how to use the linear programming output to perform sensitivity analysis. There is also an optional section that discusses the Simplex algorithm that is the basis for computational solution of LP problems. The third example is a sports shoe company and focuses on interpretation of results. The text presents a fully formulated and solved problem involving six decision variables and six constraints. The emphasis is on interpreting the output from SOLVER and answering a variety of what-if questions.
Binary programming is a form of integer programming. The word "binary" refers to the decision variables. When decision variables are binary, this means that they can only take on the values of either 0 or 1. That might seem overly restrictive, but there are many situations that can easily be modeled using binary decision variables. For example, the following decisions could be modeled with binary decision variables:
- Should we located a new automobile dealership at this location?
- Should I choose to apply to this college?
- Should I invest in this stock?
We all make decisions everyday in our lives that involve uncertainty. Decision Trees is the first chapter in the Probabilistic material and introduces the concept of making decisions under uncertainty and risk. The decision tree methodology involves accounting for every possible decision and random event. The best alternative generally maximizes the expected value of profit or minimized the expected cost, however, other non-financial variables are also considered. Expected value does not also capture an individual's risk tolerance. This risk aversion is the foundation for the insurance industry. The final problem in this chapter follows Jee Min a high school junior as he tries to determine how much collision insurance he needs.
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Mathematics - Geometry (533 results)
Hence, with a very large proportion of beginners in Geometry, it depends mainly upon the form in which the subject is presented whether they pursue the study with indifference, not to say aversion, or with increasing interest and pleasure. In compiling the present treatise, the author has kept this fact constantly in view. All unnecessary discussions and scholia have been avoided; and such methods have been adopted as experience and attentive observation, combined with repeated trials, have shown to be most readily comprehended. No attempt has been made to render more intelligible the simple notions of position, magnitude, and direction, which every child derives from observation; but it is believed that these notions have been limited and defined with mathematical precision. A few symbols, which stand for words and not for operations, have been used, but these are of so great utility in giving style and perspicuity to the demonstrations that no apology seems necessary for their introduction. Great pains have been taken to make the page attractive. The figures are large and distinct, and are placed in the middle of the page, so that they fall directly under the eye in immediate connection with the corresponding text. The given lines of the figures are full lines, the lines employed as aids in the demonstrations are shortdotted, and the resulting lines are long-dotted.
A Course of Mathematics: Containing the Principles of Plane Trigonometry, Mensuration was written by Jeremiah Day in 1853. This is a 263 page book, containing 72393 words and 31 pictures. Search Inside is enabled for this title.
It has been urged that the investigation and progress that have characterized other branches of the school curriculum have been lacking in so far as mathematics is concerned, especially in the case of mathematics as applied to secondary schools. This is doubtless due largely to the fact that mathematics, as a pure science, is not so susceptible to theory as is a subject whose limitations are not so closely drawn, and whose subject matter is more open to speculation. In spite of this fact, however, educators have dreamed of a more ideal course in mathematics; a course which would give better and larger returns for the time spent in study, and a course which would remove from mathematics the stigma which it so often bears, of being the bite noir of the average high school student. #The teacher of secondary mathematics has his choice between what might be called the natural and the artificial incentives. Under the natural incentives fall the following: a the uses of mathematics in the activities of life; bthe charm of achievement which comes with the solving of problems; cthe gain of mental power, of the ability to reason clearly to a definite conclusion. Among the artificial incentives, the following are the most usual and most powerful: a graduation from the high school; bpreparation for college; cthe winning of some special prize or honor; dthe avoiding of suspicion of mental weakness.
The object and plan of this book are explained in the Introduction (page16). I had hoped to give some account of the recent literature, but this would have delayed work that has already taken several years. I have prepared a list of technical terms as found in a few of the more familiar writings, very incomplete, and, I fear, not without errors. The list may be of service, however, to those who wish to consult the authors referred to; it will also indicate something of the confusion that exists in a subject whose nomenclature has not become fixed. It has been necessary for me to introduce a considerable number of terms, but most of these have been formed in accordance with simple or well-established principles, and no attempt has been made to distinguish them from the terms that have already been used. I am indebted to the kindness of Mr. George A. Plimpton of New York for an opportunity to examine his copy of Rudolphs Coss referred to on page 2. I am also under many obligations to Mrs. Walter C.Bronson of Providence, to Mr. Albert A. Bennett, Instructor at Princeton University, and to my colleagues, Professors R.C. Archibald andR. G.D. Richardson, from all of whom I have received valuable criticisms and suggestions. Many of the references in the first four pages were found by Professor Archibald; several of these are not given in the leading bibliographies, and the reference to Ozanam I have not seen anywhere. Henry P.Manning. Providence, July, 1914.
This book is the outgrowth of an experience of many years in the teaching of mathematics in secondary schools. The text has been used by many different teachers, in classes of all stages of development, and under varying conditions of secondary school teaching. The proofs have had the benefit of the criticisms of hundreds of experienced teachers of mathematics throughout the country. The book in its present form is therefore the combined product of experience, classroom test, and severe criticism. The following are some of the leading features of the book: Tke student is rapidly initiated into the subject. Definitions are given only as needed. The selection and arrangement of theorems is such as to meet the general demand of teachers, as expressed through the Matiiematical Associations of the country. Most of the proofs have been given in full. Proofs of some of the easier theorems and constiTictions are left as exercises for the student, or are given in an incomplete form; but in every case in which the proof is not complete, the incompleteness is specifically stated. The authors believe that the proofs of most of the propositions should be complete, first, in order to serve as models for the handling of exercises; second, to prevent the serious error of making the student feel contented with loose and slipshod reasoning which defeats the main purpose of instruction in geometry; and third, as an excellent means of reviewing the previous theorems on which they depend. The indirect method of proof is consistently applied. The usual method of proving such propositions as Arts.
As a result of the widespread discussion during recent years on the improvement of our courses in elementary geometry, the majority of thoughtful teachers appear to have reached substantial agreement on at least one point: To begin the course in plane geometry in the traditional formal manner is pedagogically irrar tional and scientifically unnecessary. There has accordingly arisen an increasing demand for a textbook which will supply a pedagogically rational approach to the study of Plane Geometry, without sacrificing the logical structure of the subject. The present text aims to supply this demand. The beginning should be thoroughly concrete, informal, and to the pupil natural and interesting. More formal methods should be introduced gradually at a time when the pupil can understand their significance and value. These ends we have sought to attain by making a systematic study of geometric drawing the basis of the first chapter. Throughout this chapter points, lines, etc., are concrete things to be drawn with a pencil or a piece of chalk; the reasoning involved is couched in easy, natural language, without any of the stiffness of a formal arrangement. While the development of the subject matter of this chapter is wholly systematic, the emphasis is intended to be placed on the exercises which have been carefully selected both with respect to interest and for drill in developing the power of making inferences. The study of this first chapter will, we confidently believe, accomplish two ends:(1) It will lead the pupil to gain a thorough understanding of the fundamental notions of geometry;(2) it will develop in him the power of attack and insight into the spirit of a geometric problem.
Most persons do not possess, and do not easily acquire, the power of abstraction requisite for apprehending geometrical conceptions, and for keeping in mind the successive steps of a continuous argument. Hence, with a very large proportion of beginners in Geometry, it depends mainly upon the form in which the subject is presented whether they pursue the study with indifference, not to say aversion, or with increasing interest and pleasure. Great care, therefore, has been taken to make the pages attractive. The figures- in small italics, immediately following the statement. This prevents the necessity of interrupting the logical train of thought by turning to a previous section, and compels the learner to become fanQlar with a large number of geometrical truths by constantly seeing and repeating them. This help is gradually discarded, and the pupil is left to depend upon the knowledge already acquired, or to find the reason for a step by turning to the given reference. It must not be inferred, because this is not a geometry of interrogation points, that the author has lost sight of the real object of the study.
One of the most desirable attainments of the mathematician is the ability to form a mental picture of three dimensional systems with ease and perspicuity, an ability which cannot better be developed than by a course of Descriptive Geometry. It is a singular and regrettable fact that in most British Universities, Descriptive Geometry has hitherto been omitted from the regular mathematical curriculum and studied only in the technical classes. The tendency of recent years, however, is towards a recognition of its unique value, both from the educational and from the practical point of view. The present tract embodies the course which is given to the non-technical students in the Mathematical Laboratory of the University of Edinburgh. In its compilation I have consulted from time to time the works of Catalan, Antomari, and Gino Loria, and, above all, the Gdomitrie Descriptive of Monge, which has been a never-failing source of inspiration. I cannot bring this Preface to a conclusion without expressing my sense of deep obligation to Professor Whittaker for his invaluable suggestions and criticism, both during the compilation of the tract and during its passage through the press. E.L. I. The Mathematioal Laboratory, University of Edinburgh, 23 rd June 1916.
Scarcely any department of Mathematics is more important, or more extensive in its applications, than Trigonometry. By it the mariner traces his path on the ocean; the geographer determines the latitude and longitude of places, the dimensions and positions of countries, the altitude of mountains, the courses of rivers, c., and the astronomer calculates the distances and magnitudes of the heavenly bodies, predicts the eclipses of the sun and moon, and measures the progress of light from the stars. The section on right angled triangles in this treatise, may perhaps be considered as needlessly minute. The solutions might, in all cases, be effected by the theorems which are given for oblique angled triangles. But the applications of rectangular trigonometry are so numerous, in navigation, surveying, astronomy, fec., that it was deemed important, to render familiar the various methods of stating the relations of the sides and angles; and especially to bring distinctly into view the principle on which most trigonometrical calculations are founded, the proportion between the parts of the given triangle, and a similar one formed from the sines, tangents, fec., in the tables. As this treatise is intended to form a part of Day and Thomsons Course of Mathematics for the use of Schools and Academies, the references to Algebra are made to Thomsons Abridgment; and the references to Geometry, to Thomsons Legendre, as well as to Euchd sElements.
Most persons do not possess, and do not easily acquire, the power of atstraction requisite for apprehending geometrical conceptions, and for keeping in mind the successive steps of a continuous argument. Hence, with a very large proportion of beginners in Geometry, it depends mainly upon the form in which the subject is presented whether they pursue the study with indifference, not to say aversion, or with increasing interest and pleasure. Great care, therefore, has been taken to make the pages attractive. The iigm es ui small italics, immediately following the statement. This prevents the necessity of interrupting the logical train of thought by turning to a previous section, and compels the learner to become familiar with a large number of geometrical truths by constantly seeing and repeating them. This help is gradually discarded, and the pupil is left to depend upon the knowledge already acquired, or to find the reason for a step by tiirning to the given reference. It must not be inferred, because this is not a geometry of interrogation points, that the author has lost sight of the real object of the study.
Lib. Qa This book has been prepared primarily for the use of the students in the Massachusetts Institute of Technology, but it is hoped that it will be found adapted to the needs of other technical schools and colleges. While the authors have restricted themselves to subjectmatter properly belonging to a first course, they have, nevertheless, endeavored to give a complete and rigorous treatment of all questions discussed. The memorizing of a mass of formulas has been discouraged, the attention of the student being directed rather to the methods employed. At the end of the book a collection of formulas has been made, which, it is believed, is sufficient for all needs of the student. In the Plane Geometry considerable space has been devoted to the general forms of the equations. In particular, the equation of the circle is treated in its most general form. The conies have been approached from tlieir general definition, and the student is led to discuss the general equation of the second degree in which the xy term is missing, and to find the equations of the tangent, the normal, and the polar for the equation of this form. By this method of procedure much time is gained when the special equations of the parabola, the ellipse, and the hyperbola are discussed, and it is believed that the students grasp of the subject is thereby strengthenedOx account of the present disturbed state of public afairs, the publication of the Mathematical Monthly will be discontinued until further notice. Electrotyped md Printed by Welch, Bigelow, md Company.
Entered according to Act of Congress, fn the year 1860, by J.D. Runkle, in the Clerks Office of the District Court of the District or Massachusetts. Untrenity Prwm, Cambridge: Btectrotyped and Printed by Welch, Bigeiow, ft Co.
In this book I have attempted to follow a middle course between the treatise which fully proves the propositions of elementary geometry and the syllabus which contains no proofs whalever. The early propositions are proved at length in order to make clear the form of geometrical demonstration and the details of proof are gradually removed in order to throw the pupil on his own resources. It hardly needs argument to show the wisdom of retaining and intensifying the pupils interest in the study, and many teachers are convinced that this is best done by expecting easy original work very early and by making the exercises an integral part of the course. How far I have succeeded in giving just the right amount of assistance of course depends on the character of the class. The teacher should be ready to supplement and expand the hints to meet the need of students. This requires judgment, as all teaching does. I shall be especially grateful for criticism and suggestion on this feature of the book. The order of propositions in Plane Geometry is nearly the conventional order of American text-books, but 1 have placed in Book I the elementary relations of rectilinear figures and of the circle; in Book II proportional line segments including similar and regular figures; in Book III the relations of areas, and measurement. The constructions are established before they are used in demonstration.
Modern Geometry is to present to the more advanced students in public schools and to candidates for mathematical honours in the Universities a concise statement of those propositions which I consider, to be of fundamental importance, and to supply numerous examples illustrative of them. Results immediately suggested by the propositions, whether as particular cases or generalized statements, are appended to them as Corollaries. The Examples are printed in smaller type, and are classified under the Articles containing the principal theorems required in their solution. The more difficult ones are fully worked out, and in most cases hints are given to the others. The reader who is familiar with the first six books of Euclid with easy deductions and the elementary formulae in Plane Trigonometry will thus experience little difficulty in mastering the following pages. I have dwelt at length in Chap. II. on the Theory of Maximum and Minimum. Chap. III. is devoted to the more recent developments of the geometry of the triangle, initiated 21 1873 by Lemoine spaper entitled Sur quelques propride sd un point remarquable du triangle.
One of the main purposes in writing this book has been to try to present the subject of Geometry so that the pupil shall understand it not merely as a series of correct deductions, but shall realize the value and meaning of its principles as well. This aspect of the subject has ben directly presented in some places, and it is hoped that it pervades and shapes the presentation in all places. Again, teachers of Geometry generally agree that the most diflBcult part of their work lies in developing in pupils the power to work original exercises. The second main purpose of the book is to aid in the solution of this difficulty by arranging original exercises in groups, each of the earlier groups to be worked by a distinct method. The pupil is to be kept working at each of these groups till he masters the method involved in it. Later, groups of mixed exercises to be worked by various methods are given. In the current exercises at the bottom of the page, only such exercises are used as can readily be solved in connection with the daily work. All difficult originals are included in the groups of exercises as indicated above.
The pedagogy of Geometry is divisible into three parts, the Science of Geometry (the facts), the Logic of Geometry (the framework), and the Art or Technique of Geometry. The Science and Logic of Geometry are presented in the current text-books. The Art of Geometry is given in the following pages. One of the great causes of complaint among students of Geometry is the lack of a systematic course of procedure. The student has no guide as to what to do next, and is generally unable to give any reason for the different steps he takes, except that they are logically correct and that they produce an answer. On the other hand, he ought to know why each step in the proof is taken. Only thus can he proceed with real understanding and be prepared to attack intelligently a new and unknown problem. Thus in the problem. To compute the length of the bisector of the angle of a triangle, the first step given by all the text-books is, draw the circumscribing circle. But why? What suggests such a step? What preparation has been given to the student to lead him to such a construction? No text-book has yet answered the question. The following pages will show not only what suggests the circle, but will provide the student with such a course of procedure (technique) that he could not miss it if he would. The current text-books supply the student with propositions and a logical proof of their correctness, but they do not put him in a position to deduce his own propositions nor to build a proof independently for himself.
This book is intended as a sequel to the First Lessons in Geometry, and, tlierefore, presupposes some acquaintance with that little treatise. I think it better, however, that some interval should elapse between the study of that book and of this, during which time the child may be occupied in the study of Arithmetic. Geometrical facts and conceptions are easier to a child than those of Arithmetic, but arithmetical reasoning is easier than geometrical. The true scientific order in a mathematical education would therefore be, to begin with the facts of Geometry, then take both the facts and reasoning of Arithmetic, and afterwards return to Geometry, not to its facts only, but to its proofs. The object of Firat Lessons in Geometry is to develop the childs powers of imagination; the object of this book is to develop his powers of reasoning. That book I consider adapted to children from six to twelve years of age, this to childreu from thu-teen to eighteen years old.
In this little treatise on the Geometry of the Triangle are presented some of the more important researches on the subject which have been undertaken during the last thirty years. The author ventures to express not merely his hope, but his confident expectation, that these novel and interesting theorems some British, but the greater part derived from French and German sources will widen the outlook of our mathematical instructors and lend new vigour to their teaching. The book includes some articles contributed by the present writer to the Educational Times Reprint, to whose editor he would offer his sincere thanks for the great encouragement which he has derived from such recognition. He is also most grateful to Sir George Greenhill, Prof. A.C. Dixon, Mr. V.R. Aiyar, Mr. W.F. Beard, Mr. R.F. Davis, and Mr. E.P. Rouse for permission to use the theorems due to them. W.G.
This text presents a course in elementary mathematics adapted to the needs of students in the freshman year of an ordinary college or technical school course, and of students in the first year of a junior college. The material of the text includes the essential and vital features of the work commonly covered in the past in separate courses in college algebra, trigonometry, and analytical geometry. The fundamental idea of the development is to emphasize the fact that mathematics cannot be artificially divided into compartments with separate labels, as we have been in the habit of doing, and to show the essential unity and harmony and interplay between the two great fields into which mathematics may properly be divided; viz., analysis and geometry. A further fundamental feature of this work is the insistence upon illustrations drawn from fields with which the ordinary student has real experience. The authors believe that an illustration taken from life adds to the cultural value of the course in mathematics in which this illustration is discussed. Mathematics is essentially a mental discipline, but it is also a powerful tool of science, playing a wonderful part in the development of civilization. Both of these facts are continually emphasized in this text and from different points of approach. The student who has in any sense mastered the material which is presented will at the same time, and without great effort, have acquired a real appreciation of the mathematical problems of physics, of engineering, of the science of statistics, and of science in general. A distinctly new feature of the work is the introduction of series of timing exercises in types of problems in which the student may be expected to develop an almost mechanical ability. The time which is given in the problems is wholly tentative; it is hoped, in the interest of definite and scientific knowledge concerning what may be expected of a freshman, that institutions using this text will keep a somewhat detailed record of the time actually made by groups of their students.
In annouacing the commencement of a new series, the Editors desire to explain the modifications which will distinguish it from the former series. The Messenger of Mathematics was projected about ten years ago, chiefly with the view of encouraging original research in the three Universities, among junior graduates and others. It was thought that through the Messenger many valuable papers might be made public which their authors would not have deemed of sufficient interest to communicate to Scientific Societies. An examination of the Five Volumes already published will make it evident that the Editors have throughout endeavoured to keep their original purpose steadily in view. While feeling, however, that they have every reason to be satisfied with the success achieved by the Messenger regarded as a stimulus to original research in junior students, they have also great satisfaction in acknowledging that no inconsiderable proportion of its contents have been supplied by writers of established reputation, who rank amongst the foremost mathematicians of the age; and it is this fact in particular which now induces them to appeal directly to the mathematical world at large, and to remove from their title-page any words which might be supposed to limit the sphere of usefulness of the Messenger.
Mathematical- cr I Screnees yI Library Wi. J2I lPREFACE. This book contains some matter not heretofore foiTnd in works upon Analytical Geometry. As it is designed as a text-book, care lias been taken to separate the different subjects so that they may be studied advantageously, each by itself. The Cartesian system will naturally, if not necessarily, be studied first, for it is not only the most common, but is the leading system used in the Calculus. The matter pertaining to the conic sections is considerably condensed, compared with most other works which treat of the subject. This has been accomplished by treating of the several curves under one head when discussing a property which is common to all of them. By this arrangement we trust that some time will be saved to the student in this part of the work, and thus enable him to give more time to advanced portions of the subject. The subject of Quaternions is treated in the most elementary manner, and the examples are of the simplest kind, the object being to explain and illustrate the principles and the character of the operations without taxing the ingenuity of the student in the mere solution of problems. One cannot form a correct judgment of the power of this analysis from these examples, but to attempt to explain its higher processes would be equivalent to excluding it from our courses of study. If the presentation here made of the subject succeeds in creating an interest in it, and of establishing a correct foundation for its future study, all will be accomplished that was intended. The English works upon the subject are not numerous.
This Book of Mathematical Problems consists, mainly, of questions either proposed by myself at various University and College Examinations during the past fourteen years, or communicated to my friends for that purpose. It contains also a certain number, (between three and four hundred), which, as I have been in the habit of devoting considerable time to the manufacture of problems, have accumulated on my hands in that period. In each subject I have followed the order of the Text-books in general use in the University of Cambridge; and I have endeavoured also, to some extent, to arrange the questions in order of diflBculty. I had not sufficient boldness to seek to impose on any of my friends the task of verifying my results, and have had therefore to trust to my own resources. I have however done my best, by solving anew every question from the proof sheets, to ensure that few serious errors shall be discovered. I shall be much obliged to any one who will give me infoimation as to those which still remain. I have, in some cases, where I thought I had anything serviceable to communicate, prefixed to.
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Intermediate worktext format for basic college math or arithmetic courses including lecture-based, self-paced, and modular classes. John Tobey and Jeff Slater are experienced developmental math authors and active classroom teachers. The Tobey approach focuses on building skills one at a time by breaking math down into manageable pieces. This building block organization is a practical approach to basic math skill development that makes it easier for students to understand each topic, gaining confidence as they move through each section. Knowing students crave feedback, Tobey has enhanced the new edition with a "How am I Doing?" guide to math success. The combination of continual reinforcement of basic skill development, ongoing feedback and a fine balance of exercises makes the fifth edition of Tobey/Slater Basic College Mathematics even more practical and accessible.
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Prealgebra and IntroductoryElayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief. Prealgebra& Introductory Algebra, Third Edition was written to help students effectively make the transition from arithmetic to algebra. The new edition offers new resources like the Student Organizer and now includes Student Resources in the back of the book to help students on their quest for success.
3.2 Solving Equations: Review of the Addition and Multiplication Properties
Integrated Review–Expressions and Equations
3.3 Solving Linear Equations in One Variable
3.4 Linear Equations in One Variable and Problem Solving
4. Fractions and Mixed Numbers
4.1 Introduction to Fractions and Mixed Numbers
4.2 Factors and Simplest Form
4.3 Multiplying and Dividing Fractions
4.4 Adding and Subtracting Like Fractions, Least Common Denominator, and Equivalent Fractions
4.5 Adding and Subtracting Unlike Fractions
Integrated Review–Summary on Fractions and Operations on Fractions
4.6 Complex Fractions and Review of Order of Operations
4.7 Operations on Mixed Numbers
4.8 Solving Equations Containing Fractions
5. Decimals
5.1 Introduction to Decimals
5.2 Adding and Subtracting Decimals
5.3 Multiplying Decimals and Circumference of a Circle
5.4 Dividing Decimals
Integrated Review–Operations on Decimals
5.5 Fractions, Decimals, and Order of Operations
5.6 Solving Equations Containing Decimals
5.7 Decimal Applications: Mean, Median, and Mode
6. Ratio, Proportion, and Percent
6.1 Ratio and Proportion
6.2 Percents, Decimals, and Fractions
6.3 Solving Percent Problems with Equations
6.4 Solving Percent Problems with Proportions
Integrated Review–Ratio, Proportion, and Percent
6.5 Applications of Percent
6.6 Percent and Problem Solving: Sales Tax, Commission, and Discount
6.7 Percent and Problem Solving: Interest
7. Graphs and Triangle Applications
7.1 Reading Pictographs, Bar Graphs, Histograms, and Line Graphs
7.2 Reading and Drawing Circle Graphs
Integrated Review–Reading Graphs
7.3 Square Roots and the Pythagorean Theorem
7.4 Congruent and Similar Triangles
7.5 Counting and Introduction to Probability
8. Geometry and Measurement
8.1 Lines and Angles
8.2 Perimeter
8.3 Area, Volume, and Surface Area
Integrated Review–Geometry Concepts
8.4 Linear Measurement
8.5 Weight and Mass
8.6 Capacity
8.7 Temperature and Conversions Between the U.S. and Metric Systems
9. Equations, Inequalities, and Problem Solving
9.1 Symbols and Sets of Numbers
9.2 Properties of Real Numbers
9.3 Further Solving Linear Equations
Integrated Review–Real Numbers and Solving
Linear Equations
9.4 Further Problem Solving
9.5 Formulas and Problem Solving
9.6 Linear Inequalities and Problem Solving
10. Exponents and Polynomials
10.1 Exponents
10.2 Negative Exponents and Scientific Notation
10.3 Introduction to Polynomials
10.4 Adding and Subtracting Polynomials
10.5 Multiplying Polynomials
10.6 Special Products
Integrated Review–Exponents and Operations on Polynomials
10.7 Dividing Polynomials
11. Factoring Polynomials
11.1 The Greatest Common Factor
11.2 Factoring Trinomials of the Form x2+ bx + c
11.3 Factoring Trinomials of the Form ax2 + bx + c
11.4 Factoring Trinomials of the Form ax2 + bx + c by Grouping
11.5 Factoring Perfect Square Trinomials and the Difference of Two Squares
Integrated Review–Choosing a Factoring Strategy
11.6 Solving Quadratic Equations by Factoring
11.7 Quadratic Equations and Problem Solving
12. Rational Expressions
12.1 Simplifying Rational Expressions
12.2 Multiplying and Dividing Rational Expressions
12.3 Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator
12.4 Adding and Subtracting Rational Expressions with Different Denominators
12.5 Solving Equations Containing Rational Expressions
Integrated Review–Summary on Rational Expressions
12.6 Rational Equations and Problem Solving
12.7 Simplifying Complex Fractions
13. Graphing Equations and Inequalities
13.1 The Rectangular Coordinate System
13.2 Graphing Linear Equations
13.3 Intercepts
13.4 Slope and Rate of Change
13.5 Equations of Lines
Integrated Review–Summary on Linear Equations
13.6 Introduction to Functions
13.7 Graphing Linear Inequalities in Two Variables
13.8 Direct and Inverse Variation
14. Systems of Equations
14.1 Solving Systems of Linear Equations by Graphing
14.2 Solving Systems of Linear Equations by Substitution
14.3 Solving Systems of Linear Equations by Addition
Integrated Review–Summary on Solving Systems of Equations
14.4 Systems of Linear Equations and Problem Solving
15. Roots and Radicals
15.1 Introduction to Radicals
15.2 Simplifying Radicals
15.3 Adding and Subtracting Radicals
15.4 Multiplying and Dividing Radicals
Integrated Review–Simplifying Radicals
15.5 Solving Equations Containing Radicals
15.6 Radical Equations and Problem Solving
16. Quadratic Equations
16.1 Solving Quadratic Equations by the Square Root Property
16.2 Solving Quadratic Equations by Completing the Square
16.3 Solving Quadratic Equations by the Quadratic Formula
Integrated Review–Summary of Solving Quadratic Equations
16.4 Graphing Quadratic Equations in Two Variables
Appendices
Appendix A. Tables
1. Geometric Figures
2. Percents, Decimals, and Fraction Equivalents
3. Finding Common Percents of a Number
4. Squares and Square Roots
Appendix B. Factoring Sums and Differences of Cubes
Appendix C. Mixture and Uniform Motion Problem Solving
Appendix D. Systems of Linear Inequalities
Appendix E. Geometric Formulas
Student Resources
Study Skills Builders
Bigger Picture—Study Guide Outline
Practice Final Exam
Answers to Selected Exercises
An award-winning instructor and best-selling author, Elayn Martin-Gay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association's Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators.
Prior to writing textbooks, Elayn developed an acclaimed series of lecture videos to support developmental mathematics students in their quest for success. These highly successful videos originally served as the foundation material for her texts. Today, the videos are specific to each book in the Martin-Gay series. Elayn also pioneered the Chapter Test Prep Video to help students as they prepare for a test–their most "teachable moment!"
Elayn's experience has made her aware of how busy instructors are and what a difference quality support makes. For this reason, she created the Instructor-to-Instructor video series. These videos provide instructors with suggestions for presenting specific math topics and concepts in basic mathematics, prealgebra, beginning algebra, and intermediate algebra. Seasoned instructors can use them as a source for alternate approaches in the classroom. New or adjunct faculty may find the videos useful for review.
Her textbooks and acclaimed video program support Elayn's passion of helping everystudent to succeed.
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Mathematics Course Descriptions
Algebra I
Algebra I is the study of mathematical patterns and ideas. It is balanced between learning skills, exploring concepts, and solving problems. Technology is used to gather, interpret, and represent data from real-world situations. Creating and using mathematical models is a theme throughout. Algebra is integrated with geometry, probability, and statistics. Topics covered include equations-linear, quadratic, and exponential-as well as systems of equations and inequalities, functions, and fractals.
Geometry
This course is investigation-driven and activity-based. It covers topics of Euclidean Geometry such as deductive proof, properties of polygons, circles, similar/congruent triangles, parallel lines, area and volume, the Pythagorean Theorem, basic concepts of right triangle trigonometry, and general ideas of transformations. Computer technology and traditional Geometry tools are used in the investigations. Applications of Geometry concepts to various arts areas are incorporated within the course.
Algebra II
Algebra II is primarily the study of functions-linear, exponential, polynomial, and parametric-through the use of data. Introductory trigonometry, statistics, and probability topics are also explored. Students use calculators, computers, and data gathering devices to investigate all topics. Throughout the course students discover the sense behind the mathematics, rather than simply learn steps for solving problems. Small group work, discussion, and the real world interpretation of the mathematics are stressed. Applications to the arts are woven throughout the curriculum.
Advanced Mathematics
This course is designed to serve students who are preparing for Calculus or further work in mathematics. As a pre-calculus course, it offers an analytical, graphical and numerical approach to understanding polynomials, exponential functions, logarithms, and a wide variety of trigonometry topics. Additional topics may include polar graphs, conic sections, matrices, sequences, and series. Real life applications and data interpretation are integral parts of this course of study.
Advanced Placement Statistics
This course introduces the students to the basic concepts of one of the most important fields of mathematics most people ever encounter. Statistics is about data, and data are numbers with a context. Students learn to make statements of facts and inferences and to state a level of confidence in their inferences. They become proficient in accurately communicating statistical concepts, including methods of data collection and valid interpretations of data. The course follows the topics outlined in the Advanced Placement curriculum in preparation for the AP Test in May.
Advanced Placement Calculus
This course covers approximately one and one-half semesters of college calculus. Students completing the course successfully are prepared to take the AP Calculus AB exam. Topics include limits, continuity, differentiability; optimization, related rates, separable differential equations, and slope fields; indefinite integrals, Riemann Sums, definite integrals, the Fundamental Theorem of Calculus, and applications of the definite integral. The course material is explored through class discussions, small group activities and investigations, sample exam questions, and individual study of problems.
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Choose a format:
Paperback
Overview
Book Details
Algebra, Grades 6-8
English
ISBN:
0769663060
EAN:
9780769663067
Publisher:
Carson-Dellosa Publishing, LLC
Release Date:
05/26/2012
Age Range:
11-14
Synopsis:
Spectrum Algebra helps students from sixth through eighth grade improve and strengthen their math skills in areas such as factors and fractions; equations and inequalities; functions and graphing; rational numbers; and proportion, percent, and interest.
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Computers and math are a natural, after all, computers
were developed to solve complex math problems for the military,
industry, and academia. Spreadsheets, such as Microsoft
Excel, help organize and analyze information, especially information involving numbers.
We can use this technology to review and apply algebra.
There is also a great amount of information on the
Web. The "Quick Links" on the right all contain more
information about any topic we discuss in class. Below are
links to some of the resources I have created for this class. Each
reviews important concepts and recommends useful Web resources.
Interactive
Activity: Number Types. I created this MS Excel
spreadsheet to review different number types (Natural, Whole, Integer,
Rational, Irrational, and Real). To use it, you will need to have
EXCEL 2000 or greater. The spreadsheet will pop up in a new browser
window. Simply close that window when you are done.
Interactive
Activity: Divisibility Rules. Let's review when
numbers are divisible by 2, 3, 4, 5, 6, 9, & 10. The rules are
listed. The first 3 are done for you as an example. The spreadsheet will pop up in a new
browser window. Simply close that window when you are done.
Interactive
Activity: Beginning Algebra Vocabulary. The
algebraic terms and concepts from each chapter are presented here is a
"matching" format. Read the short definitions and select
the appropriate term for each from pull-down menus. The spreadsheet will pop up in a new
browser window. Simply close that window when you are done.
Integrated Math Projects
Fall
Semester MS Excel Review This interactive presentation introduces the
basics of spreadsheets and MS Excel. Please follow the navigation
directions at the bottom of each slide.
Spring
Semester MS Excel Review Another interactive presentation, with
a springtime theme, introduces the
basics of spreadsheets and MS Excel. Please follow the navigation
directions at the bottom of each slide.
Algebra
and Excel. Working with a math teacher, I created this
handout to introduce the concept of formulas in Excel and review some
basic algebraic concepts. We use the formula for the perimeter of
a rectangle to illustrate this. (Click HERE
for printable, .pdf version)
Story Problems: Percents. Problem solving is all about
understanding a situation and systematically setting up a strategy to
provide a solution. We will use MS Excel to set up a spreadsheet
to solve different types of percentage problems. (Click HERE
for printable, .pdf version)
Mile Per
Gallon. I try to keep all of my computer activities
focused on problem solving and "real-world" skills. (Click
HERE for
printable, .pdf version)
Virtual
Dice. I wrote this activity to introduce basic concepts of
probability, review Excel functions, and have some fun in class.
(Click HERE for
printable, .pdf version)
Free Web Space -
StuStorage. I want my students to take advantage of the
technology support that is available on campus. Here are
directions for signing up for and using the student storage accounts at
UW-Whitewater. (Click HERE for
printable, .pdf version)
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The HillSchool mathematics department's primary focus is to challenge its students to learn mathematics as deeply and thoroughly as possible.Through courses carefully designed at the regular and honors level, all Hill School students have the opportunity to take four full years or more of stimulating and demanding mathematics classes.Our curriculum supports our belief that a quality education in mathematics is necessary for all people in the 21st century, and our program seeks to develop a broad foundation of core knowledge, an ability to use practical skills, a universal base for further study in mathematics and an appreciation of the contributions made by mathematics to the progress of our culture.
Students new to The Hill are placed in mathematics classes based on previous study. While some new students enroll in Algebra 1 first, the most common class for new third form students is geometry, with some advanced students entering at even higher levels.At the upper end of our course offerings, classes are structured to challenge the most talented students at the level of first-year and sophomore-level college mathematics, including courses in Advanced Placement Calculus, Advanced Placement Statistics, Multivariable Calculus, Graph Theory, and Stochastic Processes.
Our students participate in the Pennsylvania Mathematics League six times per year.Typically about one-third of our students sit for at least one of these contests.Also, every February almost 100 selected students take the American Mathematics Contest (AMC).High scores on that test allow our students to then take the American Invitational Mathematics Examination (AIME) and sometimes even the U. S. A. Mathematical Olympiad (USAMO).
If you have any questions about mathematics at The Hill School, please contact the department chair, Elizabeth Dollhopf at edollhopf@thehill.org.
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Applications of Trigonometry Lesson 2: Vector Applications lesson is an extension of Vectors in the Plane for added emphasis toward Common Core Standards and solving real-world applications. The lesson contains an eight-page "Bound Book style Foldable," a Smart Notebook lesson, the *.pdf completed lesson and solutions.
Compressed Zip File
Be sure that you have an application to open this file type before downloading and/or purchasing.
1423.3
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intro tensors book
intro tensors book
Being educated as a physicist, I understand many people who complain about "bourbaki" style of writing math textbooks, and I would not recommend to read the books by F. Warner and M. Spivak as a first introductory reading in modern geometry. (Spivak is only good to understand the historical line of development, but you have to have some background and being familiar with modern terminology for that.) In my opinion more or less suitable book, written by mathematicians for physicists and engineers, is
Dubrovin, Novikov, Fomenko, Modern Geometry v. 1,2,3.
This is three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics.
Topics of 1st volume starts from curves and surfaces and include tensors and their differential calculus, vector fields, differential forms, the calculus of variations in one and several dimensions, and even the foundations of Lie algebra. So, the first volume would be enough for start. I looked in 2 and 3 v. and think its close to the front of modern geometry and definitly prepares for the reading more special books...
The material of books is explained in simple and concrete language that is in terminology acceptable to physicists. There are some exercises, but should be more to get practical skills. If I will find the special problem book on modern geometry to accompanying this textbook, it would be excellent pair for any beginner.
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Natural Science Division
Course Descriptions: Math (MATH)
MATH 99. Intermediate Algebra (4) A study of the algebraic operations related to polynomial, exponential, logarithmic, rational and radical functions, systems of equations, inequalities, and graphs. Designed for students who have had from one to two years of high school algebra, but who are unprepared for MATH 103/104 (College Algebra/Trigonometry). Grades are A, B, C, NC. The course grade is not calculated into the student's GPA and does not count toward fulfilling any requirements for a degree, including total units for the degree.
MATH 103. College Algebra (3) A study of the real number system, equations and inequalities, polynomial and rational functions, exponential and logarithmic functions, complex numbers, systems of linear and nonlinear equations and inequalities, matrices, and introduction to analytic geometry. The emphasis of this course will be on logical implications and the basic concepts rather than on symbol manipulations. Prerequisite: MATH 99 or appropriate score on math placement exam.
MATH 120. The Nature of Mathematics (3) An exploration of the vibrant, evolutionary, creative, practical, historical, and artistic nature of mathematics, while focusing on developing reasoning ability and problem-solving skills. Core material includes logic, probability/statistics, and modeling, with additional topics chosen from other areas of modern mathematics. (GE)
MATH 130. Colloquium in Mathematics (1) Designed to introduce entering math majors to the rich field of study available in mathematics. Required for all math majors during their first year at Pepperdine. One lecture period per week. Cr/NC grading only.
MATH 140. Calculus for Business and Economics (3) Derivatives: definition using limits, interpretations and applications such as optimization. Basic integrals and the fundamental theorem of calculus. Business and economic applications such as marginal cost, revenue and profit, and compound interest are stressed. Prerequisites: Two years of high school algebra and appropriate score on math placement exam, or Math 103. (GE)
Math 270. Foundations of Elementary Mathematics I (4) This course is designed primarily for liberal arts majors, who are multiplesubject classroom teacher candidates, to study the mathematics standards for the Commission on Teacher Credentialing. Taught from a problem-solving perspective, the course content includes sets, set operations, basic concepts of functions, number systems, number theory, and measurement. (GE for liberal arts majors.)
Math 271. Foundations of Elementary Mathematics II (3) This course includes topics on probability, statistics, geometry, and algebra. The course is part of the liberal arts major in continuing study to meet mathematics standards for the Commission on Teacher Credentialing. (Students who have previous approved math courses or who select the math concentration must check with the liberal arts or math advisor for course credit.)
MATH 317. Statistics and Research Methods Laboratory (1) A study of the application of statistics and research methods in the areas of biology, sports medicine, and/or nutrition. The course stresses critical thinking ability, analysis of primary research literature, and application of research methodology and statistics through assignments and course projects. Also emphasized are skills in experimental design, data collection, data reduction, and computer-aided statistical analyses. One two-hour session per week. Corequisite: MATH 316 or consent of instructor. (PS, RM)
MATH 320. Transition to Abstract Mathematics (4) Bridges the gap between the usual topics in elementary algebra, geometry, and calculus and the more advanced topics in upper division mathematics courses. Basic topics covered include logic, divisibility, the Division Algorithm, sets, an introduction to mathematical proof, mathematical induction and properties of functions. In addition, elementary topics from real analysis will be covered including least upper bounds, the Archimedean property, open and closed sets, the interior, exterior and boundary of sets, and the closure of sets. Prerequisite: MATH 151. (PS, RM, WI)
MATH 325. Mathematics for Secondary Education. (4) Covers the development of mathematical topics in the K-12 curriculum from a historical perspective. Begins with ancient history and concludes with the dawn of modern mathematics and the development of calculus. Considers contributions from the Hindu-Arabic, Chinese, Indian, Egyptian, Mayan, Babylonian and Greek people. Topics include number systems, different number bases, the Pythagorean Theorem, algebraic identities, figurate numbers, polygons and polyhedral, geometric constructions, the Division Algorithm, conic sections and number sequences. Course also covers the NCTM standards for K-12 content instruction and how to build mathematical understanding into a K-12 curriculum. Prerequisite: MATH 320 or concurrent enrollment.
MATH 335. Combinatorics (4) Topics include basic counting methods and theorems for combinations, selections, arrangements, and permutations, including the Pigeonhole Principle, standard and exponential generating functions, partitions, writing and solving linear, homogeneous and inhomogeneous recurrence relations and the principle of inclusion-exclusion,. In addition, the course will cover basic graph theory, including basic definitions, Eulerian and Hamiltonian circuits and graph coloring theorems. Throughout the course, learning to write clear and concise combinatorial proofs will be stressed. Prerequisite: MATH 151 and MATH 320 or concurrent enrollment in MATH 320 or consent of the instructor.
MATH 355. Complex Variables (4) An introduction to the theory and applications of complex numbers and complex-valued functions. Topics include the complex number system, Cauchy-Riemann conditions, analytic functions and their properties, complex integration, Cauchy's theorem, Laurent series, conformal mapping and the calculus of residues. Prerequisite: MATH 250 and MATH 320 or concurrent enrollment in MATH 320 or consent of the instructor.
MATH 370. Real Analysis I (4) Rigorous treatment of the foundations of real analysis; metric space topology, including compactness, completeness and connectedness; sequences, limits, and continuity in metric spaces; differentiation, including the main theorems of differential calculus; the Riemann integral and the fundamental theorem of calculus; sequences of functions and uniform convergence. Prerequisites: MATH 250 and MATH 320 or consent of the instructor.
MATH 470. Real Analysis II (4) Convergence and other properties of series of real-valued functions, including power and Fourier series; differential and integral calculus of several variables, including the implicit and inverse function theorems, Fubini's theorem, and Stokes' theorem; Lebesgue measure and integration; special topics (such as Hilbert spaces). Prerequisite: MATH 370.
MATH 490. Research in Mathematics (1-4) Research in the field of mathematics. May be taken with the consent of a selected faculty member. The student will be required to submit a written research paper to the faculty member.
In The News
Pepperdine Named to the 2013 President's Higher Education Community Service Honor Roll: Pepperdine University was recently named to the President's Higher Education Community Service Honor Roll for... more
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Saxon
Saxon Math has a proven record of success among schools and homeschools. As a result, Saxon is a top math choice from kindergarten through high school.
Saxon's approach to math is to focus on individual skills and essential concepts rather than classroom interaction. Therefore, with Saxon, each concept is introduced and then reviewed and expanded on consistently throughout the school year. Students gain new concepts, practice them and build on them incrementally as they learn new concepts that apply to the old.
When used in its entirety, Saxon's innovative approach ensures that students gain and retain critical math skills, ensuring success in more complex skills.
Topics and concepts are never taught and then dropped to be reviewed next year. Instead, more complex concepts build on the old as students practice them every day.
Saxon does not provide colorful textbooks; instead it provides a step-by-step proven approach to math that leads to math success.
Buying your Saxon Curriculum, home school supplies and other homeschooling curriculum at Curriculumexpress.com can be done with confidence because our home education materials, science kits, home schooling curriculum, books and more are backed by our 30 day money back guarantee.
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Elementary And Intermediate Algebra For College Students - 4th edition
Summary: Today's students are visual learners, and Angel/Runde offers a visual presentation to help them succeed in math. Visual examples and diagrams are used to explain concepts and procedures. New Understanding Algebra boxes and an innovative color coding system for variables and notation keep students focused. Short, clear sentences reinforce the presentation of each topic and help students overcome language barriers to learn math.
Hardcover Fair 0321620925 Student Edition. Missing up to 10 pages. Light wrinkling from liquid damage. Does not affect the text. Light wear, fading or curling of cover or spine. May have used stick...show moreers
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MS Mathematics
It is the goal of the mathematics department that every student will develop a competence in fundamental mathematical processes and a foundation for logical thinking. In accordance with the National Council of Teachers of Mathematics Standards, an emphasis is placed on problem-solving techniques. In our highly technological society, all young women must increase their mathematical sophistication so that their future career options will be kept open.
The mathematics department places a student in the course and level most appropriate to her aptitude and preparation. Placement in all Math Classes is based on recommendation of the department and not determined by the grade level of a student alone. Final placement depends on the successful completion of the level before so may not be finally determined until the conclusion of the year.
Courses in this department:
Math
Foundations of Mathematics
Students will explore practical as well as theoretical mathematics. Basic math and computational skills, problem solving, patterns, estimating and mental math are emphasized. Topics include decimals, integers, fractions, exponents, ratios, rates, proportions, percents, measurement, graphing in the coordinate plane and an introduction to variables, equations, inequalities and geometry.
Algebra I
Credit: 1 (if taken in 9th grade or above)
Students entering this class are expected to have already studied positive and negative numbers, the basic properties of numbers, and simple equations. The course covers all topics of elementary algebra, including verbal problems, factoring, graphing of linear equations, radicals, solving linear and quadratic equations, and linear systems.
Honors Algebra I
Credit: 1 (if taken in 9th grade or above)
This course is for students who have a strong background in arithmetic facts and skills and in elementary algebra, including positive and negative numbers, the basic properties of numbers, and simple equations. They must have demonstrated a good aptitude for mathematical reasoning. The course covers all topics of elementary algebra, including verbal problems, factoring, algebraic fractions, graphing of linear functions, radicals, solving linear and quadratic equations, systems of equations, variations, and the quadratic formula.
Pre-Algebra
This course is for students who have completed Foundations of Mathematics or an equivalent course. Topics include further exploration of decimals, factors, fractions, integers, exponents, ratios, proportions, and percents, as well as algebraic expressions and integers, linear equations, and solving equations and inequalities.
Reunion 2013
Meet Heejin, '14
Favorite class:
My favorite class was public speaking, which I took during my freshman year. Although it was the most stressful course of my life, the reason why this class became my favorite is because it helped me to overcome my drawback and to be more confident.
- Heejin, '14
South Korea
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Algebra tutorials and lessons
Shmoop.com Prealgebra
Free learning guides (tutorials) for all prealgebra topics with interactive practice problems, step-by-step examples, graphs, and real-world applications. This can be used for an online pre-algebra textbook.
Algebra-Class.com
A website with some simple algebra lessons for typical Algebra 1 class. Each lesson has a brief introduction followed by several examples with detailed explanations, and then a few practice problems.
Virtual Nerd
Video tutorials for prealgebra, algebra 1, algebra 2, and intro physics. This will also include practice problems and quizzes sometime during 2010-2011 school year. Includes both a free and paid (premium) versions. virtualnerd.com
MathTV.com
Over 6,000 free, online video lessons for basic math, algebra, trigonometry, and calculus. Videos also available in Spanish. Also includes online textbooks. I've written a review of MathTV lessons when they used to be offered on CDs.
BrightStorm Math
Over 2,000 free videos covering all high school math topics from algebra to calculus. Registration required (free).
Khan Academy
Possibly the web's biggest and free site for math videos. What started out as Sal making a few algebra videos for his cousins has grown to over 2,100 videos and 100 self-paced exercises and assessments covering everything from arithmetic to physics, finance, and history.
High School Operations Research
Series of 10 tutorials (modules) that illustrate how mathematics is used in real-world applications. The student tutorials are printable and ready-to-use pdf-files. The teacher resources have background info, case studies of real companies, homework exercises, and more. For those who want to know where mathematics is actually used, and how. Topics include systems of inequalities, probability & simulation, and finding shortest route among others.
Algebra word problem resources
Algebra word problems generators from Math Celebrity
This site has automated quiz and word problem generators for these types of common algebra word problems: two-number problems (sum & product known), consecutive integers, distance/time/rate, average/count, sum, markup, markdown, percent, percentage, two coins, and work word problems. You can generate just one practice problem and then see its step-by-step solution, or generate an online quiz that will be graded.
Save Our Dumb Planet
Defend Earth from deadly meteorites using missiles. A team of dumb scientists are on hand to suggest possible trajectories. Practice drawing lines, quadratic curves, and some harder curves using their equations. The game has many levels, and you can stay at the easier levels if you so wish. Don't listen to the dumb scientists' talk - they mislead you!
Dr. Math Gets You Ready For Algebra
and
Dr. Math Explains Algebra
By The Math Forum, Drexel University. Read my review of these two refreshing algebra companions. These books are meant for pre-algebra and algebra students, respectively. Both are written in a warm, easy-reading style, with some cartoons in between and clear layout. Dr. Math® books are compiled from the best answers that real math teachers and tutors have written to students' questions over the years at the popular Dr. Math® website.
Algebra Unplugged
This is not a textbook, nor does it have any exercises, but instead contains verbial, often humorous explanations of algebra 1 concepts for those who would rather hear or read math explained in many words, instead of in a few symbols. Algebra Unplugged also often explains the reasons behind some peculiar mathematical notations or terminology, and in general, tells the students WHY things are done the way they are done in your "Real Algebra Book". I enjoyed reading through it (read my review).
Real World Algebra By Edward Zaccaro - who has also written several excellent problem solving books. With his algebra book, you can understand algebra with the help of real-world examples, and realize that mathematics is more than basic facts and memorized procedures. It includes cartoons and little stories that help you remember the rules of algebra.
Art of Problem Solving: Introduction to Algebra
A good textbook for the mathematically inclined students. For each topic, there are many example problems with detailed solutions and explanations, through which algebraic techniques are taught. The explanations often highlight ideas on best problem solving approaches, which is something you don't usually see in regular algebra textbooks.
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Feeling free by Mary Beth Sullivan(
Book
) 4
editions published
between
1979
and
1985
in
English
and held by
405
libraries
worldwide
Children with learning problems and physical disabilities talk about their handicaps.
Against all odds inside statistics(
Visual
) 6
editions published
between
1988
and
1989
in
English
and held by
241
libraries
worldwide
Twenty-six programs on 13 videocassettes, each cassette running ca. 30 minutes, explain the principles of statistics using real-world situations. Originally developed as a public television series.
For all practical purposes(
Visual
) 3
editions published
in
1986
in
English
and held by
129
libraries
worldwide
A series which stresses the connections between contemporary mathematics and modern society. Presents a great variety of problems that can be modeled and solved by quantitative means.
College algebra in simplest terms(
Visual
) 4
editions published
in
1991
in
English
and held by
125
libraries
worldwide
Presents the role of algebra in daily life and demonstrates practical applications in the workplace. Uses symbols, charts, pictures, and state-of-the-art computer graphics to illustrate basic algebraic techniques. Reviews problems step-by step, focusing on the methods students find most difficult to grasp.
Statistics(
Visual
) 5
editions published
between
1987
and
1988
in
English
and held by
57
libraries
worldwide
Sol Garfunkel takes the viewer on an exploration of statistics and their related display and interpretative disciplines. Methods of gathering useable reliable data, such as randomization, and sampling are discussed. Methods of graphical displaying data from histograms to three dimensional computer arrays are shown. Statistics are shown to be useful when patterns of events are more important than individual events themselves. Finally the methods for stating the reliability of the results are explored.
Race for the top(
Visual
) 4
editions published
between
1990
and
1993
in
English
and held by
50
libraries
worldwide
Shows the competition between Fermilab in the United States and CERN in Europe to discover the "top quark" (the predicted, but not yet detected fundamental subatomic particle).
Normal calculations ; Time series(
Visual
) 1
edition published
in
1989
in
English
and held by
50
libraries
worldwide
Normal calculations covers standardization and calculation of normal relative frequencies from tables and assessment of normality by normal quantile plots. Time series deals with distribution of a single variable, change over time, seasonal variation, inspecting time series for trends, and smoothing by averaging. Uses animated graphics, on-location footage, and interviews.
An Astronaut's view of earth(
Visual
) 4
editions published
between
1991
and
1992
in
English
and held by
49
libraries
worldwide
Film footage on the earth shot aboard the Space Shuttle.
What is statistics? ; Picturing distributions(
Visual
) 1
edition published
in
1989
in
English
and held by
45
libraries
worldwide
Presents the why as well as the how of statistics using computer animation, colorful on-screen computations, and documentary segments.
Algebra in simplest terms(
Visual
) 3
editions published
in
1991
in
English
and held by
43
libraries
worldwide
This is an instructional series of 26 half-hour programs for high school, college, and adult learners, or for teachers seeking to review the subject matter. Host Sol Garfunkel explains concepts that may baffle many students, while graphic illustrations and on-location examples demonstrate how algebra is used for solving real-world problems. Algebra is important in today's world, used in such diverse fields as agriculture, sports, genetics, social science, and medicine. This series helps students connect algebra's mathematical themes and applications to daily life.
For all practical purposes. Statistics(
Visual
) 5
editions published
in
1988
in
English
and held by
31
libraries
worldwide
These five programs from the series For All Practical Purposes explore the nature and use of statistics in the modern world.
For all practical purposes. Social choice : #15 prisoner's dilemma(
Visual
) 1
edition published
in
1986
in
English
and held by
26
libraries
worldwide
Program 15 discusses the human problem of making decisions, such as in business and politics. Partial conflict results in these situations and cooperation for mutual benefit is shown to be the best solution for these games of partial conflict.
For all practical purposes. Statistics : #8 organizing data. #9 probability(
Visual
) 1
edition published
in
1986
in
English
and held by
24
libraries
worldwide
Program 8 focuses on exploratory data analysis, emphasizing that the human eye and brain are the best known devices to see and recognize patterns. Introduces histograms, medians, quartiles, scatterplots and boxplots. Program 9 analyzes how we can predict long-term patterns of chance events by looking at the operation of a gambling casino. Introduces elementary probability concepts along with an analysis of normal curves, standard deviation and expected value.
For all practical purposes. Statistics : #6 overview. #7 collecting data(
Visual
) 1
edition published
in
1986
in
English
and held by
23
libraries
worldwide
Program 6 introduces the major themes of statistics, collecting data, organizing and picturing data and drawing conclusions from data. Program 7 looks at data collection and explores how surveys and public opinion polls actually work. Discusses the difference between a survey and an experiment and considers why and how chance is used in random sampling to make our confidence in our findings more certain.
Overview(
Visual
) 10
editions published
between
1985
and
1987
in
English
and held by
22
libraries
worldwide
Introduces the major themes of statistics, collecting data, organizing and picturing data and drawing conclusions from data.
For all practical purposes. Computer science : #25 computer graphics / #26 conclusion(
Visual
) 1
edition published
in
1987
in
English
and held by
22
libraries
worldwide
Program 25 shows how computer art, graphics and animation is created. Explains pixels and how their collective image can represent a picture or any graphic symbol. Program 26 sums up the key points in the series and emphasizes the real-world applications of mathematics in today's society and the mathematical models that can be built from them.
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Build your confidence and ability in algebraic methods of problem solving. Learn how algebra can be applied in ways that are both contemporary and representative of a wide range of disciplines. Explore expressions, equations, fractions, exponents, radicals, matrices, trigonometric functions, geometry, graphing and more. Also see our distance education course.
Note(s):
A final grade of C (63%) or better in this course meets the mathematics admission requirement of most full-time programs at George Brown.
Equivalent:
MATH 1034, MATH 1112
Prerequisites:
You must have completed Grade 10 math or MATH 1080 (Math Essentials) . If you do not meet the prerequisite requirement, you must complete the General Math Assessment and score high enough to be assigned to Mathematics. Proof must be presented at the first class
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Stony Brook
Second Year Mathematics Courses
Multi-variable calculus
First year calculus develops the basics of one variable calculus --
but describing most real-life situations requires more than one
variable. You usually need at least three dimensions to describe
situations in physics, while movements in systems like the stock
market depend on many more variables. Other sciences such as biology and
chemistry regularly require functions of several variables. Calculus
III studies calculus in spaces of two and three dimensions. It
develops the fundamental concepts needed to understand movement in
three dimensions, three dimensional geometry, electricity, the motion
of fluids, probability, volume, and the maximization of quantities
such as profit, which depend on many variables. There are two versions of
Calculus III. Either version is acceptable for the
mathematics major, although some other
departments require one rather than the other.
This version of Calculus III is recommended for those students who would like a deeper understanding of the underlying mathematical concepts. We highly recommend that students take MAT211 either before, or while, taking MAT205.
(3 credits)
Linear Algebra
Linear algebra is an essential tool for studying situations that depend on many variables. It provides important insights into solving simultaneous equations, and shows how these solutions may be described in terms of certain fundamental algebraic ideas, like bases and eigenvalues, which are themselves used to help understand more complicated phenomena such as the resonance of vibrating systems or
fluctuations in populations.
AMS210: Linear Algebra
This course is taught in the Applied Mathematics and Statistics department, and has an applied focus.
(3 credits)
MAT211: Linear Algebra
This course spends more time discussing the theoretical foundations of linear algebra. Besides being required for the major, MAT 211 is a prerequisite for many 300 level MAT classes. We strongly encourage mathematics majors to take it early on. It can be taken in the first year together with MAT132 and provides a helpful background for MAT 205.
(3 credits)
General
MAT260: The Problem Seminar
This course is intended for students who are interested in developing both their mathematical intuition and their ability to express mathematical ideas, while having fun solving problems. It can be taken repeatedly for credit. Students have the opportunity to sign up for the Putnam exam, a competitive national mathematics exam for undergraduates, held each December.
(1 credit)
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Calculus: Concepts & Connections follows a relatively standard order of presentation, while integrating technology and thought-provoking applications, examples, and exercises throughout the text. Wherever practical, concepts are developed from graphical, numerical, algebraic, and verbal perspectives (the "Rule of Four") to give students a complete understanding of calculus. The text contains more than 7000 exercises, found at the end of each section, as well as review exercises at the end of each chapter.
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MAT
495
- Middle Grades Mathematics
This course is the mathematics capstone course for Middle School Mathematics Education majors. Students will spend time reflecting on the mathematics learned in previous courses through rich problems that draw on concepts from multiple disciplines in mathematics. The course will help students develop a deeper and more connected understanding of middle school mathematics content while continuing to develop their mathematical habits of mind and problem-solving strategies. Students will also spend time connecting their knowledge of mathematics education to national and state standards and policies regarding the mathematical education of students.
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Basic Math:
This course focuses on the basic arithmetic skills of operations with
whole numbers, fractions, decimals, percents, ratio and proportion in
a problem-solving context. Emphasizes improved study skills including
time management, not taking, test preparation and other skills that
will improved study skills including time management, not taking, test
preparation and other skills that will help students successful in future
mathematics courses.
Elective: 2 credits
Pre-Algebra:
This course provides the opportunity to apply arithmetical and mathematical
principles and develop and maintain basic arithmetic and pre-algebra
skills. The course content is a review of arithmetic skills including
whole numbers, positive and negative numbers, fractions, decimals, percents,
ratio and proportion, plus computation of perimeters, areas, volumes
associated with triangles, rectangles, circles, rectangular prisms,
cylinders, cones and metric system applications. It is an in depth pre-algebra
course.
Elective: 2 credits
Consumer and Career
Math Prerequisite General Math; students who have passed Algebra
1A/1R are not eligible for this class The student will study mathematics through application problems
that relate to business and home environments. The student will be required
to work on a variety of mathematical problems including computing with
whole numbers, decimals, and fractions, solving problems involving equations,
proportions, percent, perimeter, area and volume and applying methods
of probability and statistics. The student will apply mathematical techniques
to solving consumer problems involving gross and net income, buying
foods and goods, budgeting, personal banking, car buying and car buying
and car operating expenses general travel expenses, renting or decorating
a home, state and federal income tax, and insurance.
Elective: 2 credits
Algebra 1A
This is the first year of a two-year sequence in algebra. Topics included
are properties of real numbers, solving simple equations and inequalities,
positive and negative numbers, formulas, factoring, graphing, solving
two equations, fractions, decimals and percents; squares and square
roots relations and functions. This course is followed by Algebra 1B.
The second semester of this course builds upon the first. Therefore,
students must successfully complete the first semester prior
to enrolling in the second semester.
Elective: 2 credits
Algebra 1B
Prerequisite Algebra 1A: This is the second year of the two- year sequence in algebra.
It is designed to prepare all students for success in mathematics. Topics
include data analysis, communicating mathematics, drawings and patterns,
equations, spatial relations, ratio and proportion, probability and
decision making, and functions. This two- year sequence could be followed
by a year of Regular Geometry, followed by Alegbra 2.
Elective: 2 credits
Algebra & Geometry
Concepts
Prerequisite Algebra 1A and Algebra 1B
Students receiving a "C" or better in Algebra 1R are not eligible
for this class. This course includes a semester study of concepts of Euclidian
Geometry including logic and proofs, as well as applications of area
and distance calculations. Also included is a semester of algebra concepts
including linear and quadratic equations. Introductory trigonometry
is also included in the algebra portion of this course. This course
is designed to prepare students for the work force, military, or two-year
technical school.
Elective: 2 credits
Algebra 1 The study of algebra will prepare students to continue their
studies in mathematics, and it will help them to organize their thoughts
to solve mathematical problems that everyone meets from day to day.
In Algebra students will be working with directed numbers, solving linear
and quadratic equations, working with polynomials, factoring, working
with fractions, solving inequalities, working with functions, solving
systems of linear equations, working with rational and irrational and
irrational numbers, graphing in 1 and 2 dimensions, and solving algebraic
word problems.
Elective: 2 credits
Geometry Regular
Prerequisite Algebra 1 or Algebra 1A and 1B
The study of geometry is interesting and rewarding in the field of mathematics.
Geometry is an entrance requirement for admission to most colleges and
is a prerequisite for Advanced Algebra and Trigonometry. The objectives
are as follows: (1) strengthen the student's understanding of algebra
and geometry (2) develop powers of spatial visualization while building
a knowledge of the relationships among geometric figures (3) introduce
the elementary methods of inductive and deductive reasoning and increase
the student's appreciation of the need for precision of the language
(4) develop some understanding of the methods to coordinate geometry
and of the way in which algebra and geometry complement each other (5)
provide the opportunity, stimulation and guidance for creative thinking.
The course content is operations with real numbers; ratio and proportion;
measurement of geometric figures; equalities; inequalities; logic, inductive
and deductive reasoning; proofs; properties of points, lines, planes,
triangles, quadrilateral circles and spheres; area and volume of plane
and solid figures; coordinate geometry, and locus. The second semester
of this course builds upon the first. Therefore, students must successfully
complete the first semester prior to enrolling
in the second semester.
Elective: 2 credits
Modern Geometry/ Algebra
2
Prerequisite Algebra 1 This course is a prerequisite for students planning to take
Calculus as seniors. The successful completion of the Algebra 1 - Modern
Geometry - Advanced Math - Pre calculus and Statistics - Calculus sequence
will provide the student with the equivalent of five years of college
preparatory mathematics. The Modern Geometry course is similiar to Regular
Geometry, but more emphasis is placed on study transformations and isometries.
The isometries (reflections, rotations, translations, and glide reflections)
will be used to study parallel lines, congruence of figures, area, volume,
etc. Approximately fifty percent of the course will be devoted to Geometry,
and the remainder will focus on Algebra 2/Trigonometry.
Elective: 2 credits
Technical Math
Prerequisite Algebra 1A/1B , Algebra & Geometry Concepts, OR Algebra
1R and Geometry 1R This course is ideal for a student who wants to learn a technical
skill and is planning to enter one or two year technical or trade program.
Algebra, geometry, probability and statistics, discrete math, calculator
and computer skills are reinforced. The problems are geared to a large
number of applications emphazing skills needed by persons entering many
technical fields including agriculture, architecture, chemistry, computer
science, construction, electronics, engineering, physics, and mechanics.
A student receiving a "C" or better in Algebra 2 should consider
taking Advanced Math, not Technical Math.
Elective: 2 credits
Algebra 2
Prerequisite Algebra 1 and Geometry: This course is intended primarily for students planning to
attend college or a technical school. It builds on sequential approaches
to content and learning from preceding courses. Geometric and algebraic
concepts are extended and connected to topics in probability and statistics,
trigonometry, and discrete mathematics. The course content consists
of linear functions, linear functions, linear systems and inequalities,
applying exponents and logarithms, trigonometry, discrete mathematics
and models. A student receiving a "C" or better in this course
should consider taking Advanced Math.
Elective: 2 credits
Advanced Math
Prerequisite Modern Geometry or Algebra 1, Geometry, and Algebra 2 It includes extensive work with the graphing calculator, linear
functions, exponential and log functions, trigonemetric functions and
PreCalculus concepts. It is a prerequisite for students planning to
take PreCalculus and Calculus. Students planning to take College Statistics
second semester should take this class first semester.
Elective: 2 credits
College Statistics*
Prerequisite One semester of Advanced Math or (1 year Algebra 2 with
instructor's permission) This course, taught at Atlantic High School, is taken for dual
high school credit and Iowa Western Community College credit. The college
credit will transfer to most major colleges and universities. This is
an excellent course for college-bound students who desire a better mathematics
background but do not plan to specialize in courses requiring a lot
of mathematics. The course will include a wide range of applications
in economics, social sciences, biological sciences, education, medicine,
industry and business. Topics include numerical methods of analyzing
data, rules of probability, binomial and normal distributions, sampling,
estimation, hypothesis testing and linear correlation1 credit
PreCalculus*
Prerequisite: "C" or better grade in Advanced Math This course, taught at Atlantic High School, is taken for high
school credit and Iowa Western Community College credit. The college
credit will transfer to most major colleges and universities. This course
continues the work from Advanced Math. It is an intensive review of
College Algebra and Trigonometry and prepares students for Calculus.
Topics include functions, logarithms, systems of equations, matrices,
polynomials, conic sections, trigonometric functions, graphs, identifies,
equations, complex numbers, and polar coordinates 2 credits
Calculus
Prerequisite Modern Geometry/Algebra 2, Advanced Math, and a "C"
or better grade in PreCalculus This course, usually offered only in college, provides the
high school student with the opportunity to apply the advanced mathematics
to solve complex practical problems encountered daily by mathematicians,
engineers, and scientists. Students take this class for dual high school
and college credit. The objectives of the course are as follows: (1)
enable the student to grasp historical significance and present day
importance of calculus as the foundation for most other branches of
mathematics, engineering and science (2) provide the student with an
abundance of application problems from mathematics, chemistry, physics,
biology and economics. The course content includes a brief review of
functions, analytic geometry and trigonometry; a general method for
graphing all functions; the derivative; limits; continuity; the integral;
applications to problems involving slope; maximum-minimum; rates of
change; area; volume; and velocity, motion, forces and work
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Math Made Easy has helped over 1 million students worldwide significantly improve their math skills.
Description
Parents, is your son or daughter struggling with Intermediate Algebra and Pre-Calculus? Then the Intermediate Algebra & Pre-Calculus DVD courseware created by Math Made Easy can help your child get an A in this very difficult course!
Educators around the world consider this intricate mathematics as the gateway to college math. This tutorial program is indispensable for students who need a detailed review to make this complex and often confusing math less intimidating and easy to learn and remember.
Intermediate Algebra & Pre-Calculus covers material generally taught in high school and college math classes. In just 4-12 weeks, your son or daughter can become proficient in Intermediate Algebra and Pre-Calculus. Especially in the days leading up to a math test or an achievement exam, the easy-to-use Intermediate Algebra & Pre-Calculus DVD series will help your child succeed as it helps keep the math material fresh in his or her mind.
The software was developed by Dr. Meryl Kohn, Math Chairperson Emeritus at one of America's top universities. If your son or daughter has been having a hard time with Intermediate Algebra and Pre-Calculus, then the dynamic and simple to follow lessons along with the many interactive do-it-yourself exercises in this software will help make this complex math easy!
Special Bonus: If you order the Intermediate Algebra & Pre-Calculus software from Sam's Club, your son or daughter will get a free 2 month membership to Tutorial Channel. Once a week for 20 minutes, he or she will work with a live tutor on any math related questions.
The Math Made Easy track record speaks for itself. Our programs have been used successfully in over 10,000 K-12 schools and colleges, including the NYC school system and Bowling Green University. Plus, we have already helped over 1,000,000 students worldwide to significantly improve their math skills.
The Intermediate Algebra & Pre-Calculus software makes intricate and complex concepts less intimidating and easy to learn. The program consists of several hours of comprehensive step-by-step reviews that offer clear and concise instruction using real life-examples. The software's many interactive do-it-yourself exercises help students build self-confidence and math proficiency.
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Discrete Mathematics And Its Application By Susanna S.epp Manual
On this page you can read or download Discrete Mathematics And Its Application By Susanna S.epp Manual in PDF format. We also recommend you to learn related results, that can be interesting for you. If you didn't find any matches, try to search the book, using another keywordsDiscrete Mathematics and Its Applications Fifth Edition Kenneth H. Rosen AT&T Laboratories Boston .. Much of discrete mathematics is devoted to the study of discrete structures, which are used to represent discrete objects. Many important discrete structures are built. study of discrete mathematics with an introduction to logic. In addition to its importance in understanding niathematical reasoning, logic has numerous applications in. the study of mathematics are: (1) When is a mathematical argument correct? (2) What methods can be used to construct mathematical arguments? This. include axioms or postulates, which are the underlying assumptions about mathematical structures, the hypotheses of the theorem to be proved, and. they are used to prove mathematical theorems, but also for their many applications to computer science. These applications include verifying that computer programs., understanding the techniques used in proofs is essential both in mathematics and in computer science. RULES OF INFERENCE We will now.
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This unique book places emphasis on the understanding of the material presented by adopting a reflective approach towards the scientific method used. Knowledge of algebra, geometry and trigonometry is required however, the authors introduce more advanced mathematical methods in the context of the physical problems which are used for analysis. Modern physics topics, including quantum mechanics and relativity are introduced early and are integrated with more "classical" material from which they have evolved.
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The calculus of differential forms has significant advantages over traditional methods as a tool for teaching electromagnetic (EM) field theory. First, films clarify the relationship between field intensity and flux density, by providing distinct
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AMC Archives
Your browser does not appear to support JavaScript, or you have turned JavaScript off. You may use unl.edu without enabling JavaScript, but certain functions may not be available.
Art of Problem Solving
A site developed to help students learn how to solve the puzzling problems --
The creators of AoP were this student once. They were the kids who wanted to win the trophies. They worked hard and became the kids who won the trophies. The trophies are in attics now. The problem-solving skills, the love of mathematics, and the friendships forged with peers with similar interests remain. They've applied the skills we've developed through mathematics to a variety of fields in college, then in the professional world.
"Now we've returned to our starting point - the student in a room, chewing on a pencil, staring at a question, giving up, reading the answer, and thinking. . . How would I have thought of that?
"This time you are the student. We are building this site for you, to provide a resource you can turn to.
"You're stuck on a problem, so you write friends on our Forum. You hang out in our Math Jams. You take an online class. You don't give up. You learn how to think of the solution. You solve the problem. Then you think..........Next problem.
Awesome Math
AwesomeMath consists of three major intiatives.
The AwesomeMath Summer Program is a three-week camp designed to hone high school students' mathematical problem-solving skills up to the Olympiad level.
The AwesomeMath Year-round program is an effort to continue students' enrichment during the school year through a series of correspondence lectures and problem sets.
Mathematical Reflections is an online journal that presents students with quality mathematical writing and gives them the opportunity to formally publish their own exceptional work.
Bay Area Mathematical Olympiad (BAMO)bamo.org
The Bay Area Mathematical Olympiad (BAMO) consists of three annual competitions:
Two exams, each taken by about 200 students, with 4 or 5 proof-type math problems to be solved in 4 hours. One exam is for students in 8th grade and under, and the other for students in 12th grade and under. They are held on the last Tuesday of every February, at schools and several open sites around the Bay Area. There is also an exam offered for teachers, giving an opportunity to show how to use deeper mathematical knowledge to be more successful in the classroom. Typically held on the Sunday immediately preceding the student exam, teachers come together for a social event as well as an exam.
Calculus the Musical
Matheatre is an educational performance duo.-- touring our original production of "Calculus: The
Musical!," a comic "review" of the concepts and history
of Calculus. Created by a licensed math teacher and a professional
theatre artist, Matheatre strives to put the "edge" back in "education!" For services contact
us at calculusthemusical@gmail.com. All materials on our website are free for use by any student, educator
or fan of mathematics!
Circus of Patterns
This site is a product of a mathematicians research in mathematics number patterns for 25 years. He has developed a series of mathematical charts for teachers and those students who do not like math, so they become involve in mathematics and having "FUN". The series of math charts are in, whole number, fraction, and decimals. Students are draw to the board searching for numerical and geometric patterns, as they are having "FUN" to doing the math.
Convergence mathdl.maa.org/convergence/1
An online magazine of the Mathematical Association of America which provides a wealth of resources to help teach mathematics using its history.
Cut the Knot
The site, among others, is the winner of the MERLOT Classics 2004 award and a 2003 selection of the Scientific American. It's a big site with more than 500 Java illustrations. Topics covered are drawn from Arithmetic, Algebra, Geometry, Probability, Calculus, Social Sciences, Logic and more.
Dolciani
The Mary P. Dolciani Halloran Foundation has provided funding for the Mathematical Association of America (MAA) to award grants for projects designed to develop mathematical enrichment programs for talented students in middle school or high school. The goal of the program is to interest students who are ready for more challenge in the study of mathematics and encourage them to further their mathematical studies.
Grants will be up to $6000 and will be made to the college or university of the project director for a one-year project. An institution is expected to supply in-kind support as an indication of commitment to the project; these grants will not support any institutional indirect costs or provide fringe benefits. Any matching funds available should be described in the proposal and included in the budget. To provide maximum flexibility, unexpended funds may be carried forward. Some grants may be renewed up to a maximum of three years. Projects that have received previous funding must include a report on outcomes of the project.
Global Institute of Mathematics
GIOM offers highly interactive courses from Algebra through Calculus in
real time. Students can interact with the instructor as lessons are
taking place. Lessons are also archived for future viewing. Students
have unlimited email access to the instructor outside of lesson time.
IDEA Math
IDEA MATH brings together students who take pleasure in tackling difficult math problems. We believe that mathematics is a field that demands not only flexibility with numbers, symbols, and geometric objects, but also the patience to be exposed to something which is completely new and different, eventually integrating it into an ever-widening but coherent body of knowledge; in our classes, students will expand their knowledge and develop techniques towards approaching and effectively applying their skills to solve difficult problems, alongside the opportunity to form friendships with students who, like themselves, enjoy math.
IDEAMath offers courses for able students of all skill levels, including a wide variety of problem solving courses and summer math camps which draw from topics found on contests such as the AMC 8/10/12, AIME and USA Math Olympiad. Offerings including:
Weekend classes at Lexington High School during the school year
AMC123 in the Bay Area, California during winter break
Summer Programs on both coasts
IMO - Official Site
There is a lot of information from the previous IMOs on this site, but
a lot of the data is still missing. Please take some time and send
the missing results for the competitors from your country to the webmaster at webmaster@imo-official.org
IMO Compendium
This website is dedicated to mathematical olympiads, and we hope it will be of use to all those who prepare for math competitions or simply love problem mathematics.
International Mathematics Project Competition (IMPC)
We honorably inform that the seventh International Mathematics Project Competition (IMPC-2005) will be held between 17-21 May 2005 in Almaty, the old capital city of Kazakhstan. The competition aims at inspiring and motivating mathematically talented high school students by exposing them to the beauty and variety of mathematics with technological application.
Kiran Kedlaya's Math Related Web Sites Listing unl.edu/amc/a-activities/a4-for-students/K-links.html
This directory is intended to catalog resources on the Web of possible use to mathematically motivated students, their parents and teachers.
Math Forummathforum.com/mam/00/612/index.html
This page was designed for Mathematics Awareness Month. It is ranked as one of the best. It contains links to mathematicians who have made significant contributions to mathematics and its applications.
MathCounts
A national math competition for Jr. High Students (6-8th graders) -- it has been around for more than 20 years. Is held regionally, state wide, and then nation wide.
Math Is Power
Contains Problems of the Week relating elementary and middle school mathematics in geometry, algebra, discrete mathematics, trigonometry and calculus.
Math Meet math.uww.edu/mathmeet
A free, on-line, team mathematics competition for middle and high school teams. Held Mid April, sponsored by CLARC.
Mathworks
Mathworks runs the Junior Summer Math Camp (JSMC) and Honors Summer Math Cap (HSMC) in Texas. The JSMC is a 2-week camp for middle school students, developing their skills in problem solving and mathematical investigations. The HSMC is a 6-week residential camp for high school students, who take college-level math courses, as well as participate in original math research projects.
National Association of Math Circles (NAMC) mathcircles.org
The association is an MSRI sponsored organization that provides a support structure for Math Circles and similar programs. The NAMC has an extensive website that includes: the Circle in a Box wiki, contacts for Math Circles throughout North America, the Math Circle Problem Collection, and a forum for discussion of Math Circles and related issues among NAMC members. We are adding new features and content to the website. The association also sponsors math circle training workshops and has a math circle grant program.
Nick's Mathematical Puzzles
A collection of more than 100.
Online Companion to the Special Interfaces Issue
A forthcoming special issue of Interfaces on OR/MS applied to e-business is now freely available. Its seven papers collectively demonstrate that decision technology is becoming a powerful adjunct to information technology as the digital economy matures.
QuestBridge
Pairs outstanding low-income stuents with full four-year scholarships to 12 QuestBridge partner colleges. Qualified students can apply for admission to any or all of our partner schools through the College Match using our free online application. A pdf with more information.
Swarthmoreforum.swarthmore.edu
A must page for students and teachers of mathematics K-12. This site contains many useful links and features a Problem of the Week.
Terry Wesner's page
An author for William C. Brown/McGraw Hill Publishers for 25 years. "I feel it is time to start giving back to the educational community that has supported me for all of those years. As time and resources allow, I will be providing all of my books and the teacher's resource materials for free download.
The site < has been designed so that users with modem connections can download all of the material.
THEA practice tests
These are online THEA (Texas Higher Education Assessment) practice tests at no charge. The site in general also has a wide variety of other practice tests.
USA Mathematical Talent Search (USAMTS) usamts.org
The USA Mathematical Talent Search (USAMTS) is a free mathematics competition open to all United States middle and high school students. Different from most mathematics competitions, the USAMTS allows students a full month to work out their solutions. Carefully written justifications are required for each problem. The problems range in difficulty from being within the reach of most high school students to challenging the best students in the nation. Students may use any materials - books, calculators, computers - but all the work must be their own. The USAMTS is run on the honor system - it is an individual competition, whose competitive role is very secondary.
Valentin Vornicu
A former Romanian IMO Team Member, currently an undergraduate student in Mathematics at University of Bucharest. He thought that the site he had forged would fit in quite nicely.
The site's address would be and it has a math forum, with a lot of users, most of them being former, current or future IMO contestants, download problems section and also a weekly contest - similar with USAMO in difficulty. It is not as big as the mathforum (yet :-) ).
Wolframmathworld.wolfram.com
A free service for the mathematical community provided by Wolfram Research, makers of Mathematica, with additional support from the National Science Foundation Includes all sorts of problem solving pages.
World of Mathematical Equationseqworld.ipmnet.ru
The EqWorld website presents information on solutions to various classes of algebraic, ordinary differential, partial differential (mathematical physics), integral, and other mathematical equations. It also outlines some methods for solving equations, includes interesting articles, lists, useful handbooks, and "monographs," etc. More advanced than most high school math levels, but included here for reference.
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Tag Archives: Algebra and Functions
After writing yesterday's post on the connections between polar and Cartesian graphs, I realized that I hadn't said anything about how easy it is to start from scratch and create a polar graph in Sketchpad, so I decided to write … Continue reading →
The May 2013 Mathematics Teacher has an excellent article by Jonathan F. Lawes ("Graphing Polar Curves") on the value of plotting the same function in both polar and rectangular coordinates. Doing so not only helps students understand how polar coordinates … Continue reading →
Last week was the fourth session of my spring Advanced Secondary Math Methods class at the University of Pennsylvania. Each year I assign a semester project in which groups of three students use lesson-study techniques—on a small scale—to create, test,"What do you like about working here?" I asked during my interview to work at KCP Tech. I was rather struck by Vishakha's response that she liked being able to help people learn math. She thought that it was completely … Continue reading →
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Past Courses
All programmes at Wizard Education aim to help students work towards the new OCR GCSE Maths B course which includes four key areas: Number, Algebra, Geometry and Measures and Statistics. This award is externally assessed at the end of the course. Ultimately we aim to help develop learners' mathematical understanding, familiarise them with problem solving and teach maths that is appropriate to their individual needs. Functional Skills and Entry Level Maths will also be offered as appropriate. On joining Wizard, students will be set an assessment to identify strengths and areas for improvement whilst also gain an indication of the current level of performance. An appropriate program will then be agreed for the individual.
Sessions will mainly be in group format with additional individual support available as required within the group and further one to one sessions where this is beneficial.
Maths will also be embedded into individual projects, enterprise duties and other activities for instance: Costings, bookkeeping, spreadsheets, assessing break even points for product or service pricing, analysis etc are all used in enterprise whilst using measurements, shapes, angles, fractions and simple physics are all used in the workshops.
Practical application will be used to reinforce learning wherever possible
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Full-time Courses: A Level Mathematics
Mathematicians are always in demand to solve problems and help make the right decisions. That's why those with a Mathematics A level earn on average £5,000 more than those with other qualifications in each year of their career.
You will have access to the multitude of university courses which require an A level Maths qualification. You will continue to use and enjoy maths because it is the language we use to describe and model the world in physical and social science.
If you would like to add an A Level onto your Level 3 study programme, then please include this on your application form.
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MAT
362
- Algebra for Teachers
This course will examine concepts in algebra including: Patterns, arithmetic sequences, geometric sequences, arithmetic and algebra of the integers, least common multiple and greatest common divisor, The Fundamental Theorem of Arithmetic, The Division Algorithm and Euclidean Algorithm, modular arithmetic and systems of numbers, properties of groups and fields, the field of complex numbers, polynomial arithmetic and algebra, The Fundamental Theorem of Algebra, linear equations, matrix algebra determinants, and vectors. Students will engage with these concepts through proofs, problem solving and through activities used in middle school mathematics. Throughout the course students will be given opportunities to relate the mathematical concepts studied to the mathematical concepts they will be teaching.
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Core Mathematics involves building on ideas studied at GCSE level. The one new topic of calculus is very useful in the analysis of practical problems.
Mechanics is the study and application of Newton's discoveries concerning the effect of forces on bodies at rest or in motion. It suits students interested in Sciences, Engineering, Geography, Design and PE.
Statistics builds upon ideas in data handling and probability studied at GCSE level. It is useful for students interested in other subjects that require the handling and analysis of numerical data (Psychology, Economics, Accounts, Business, Geography, Biology, and Law).
Entry Requirements
Minimum grade B in GCSE Maths at Higher Level. Conscientious work ethic and the ability to study independently. Previous study of Maths at AS/A/HE level is preferable.
Course Delivery
Students attend classes on two evenings per week (usually Wednesday and Thursday). Assessment is by six modular, externally assessed examinations. Further details supplied at interview.
Course Progression
Successful students often progress to HE, teacher training or employment.
Additional Information
Students are advised to purchase the relevant modular textbooks. Details supplied at interview.
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This course is designed for the enhancement of algebraic skills and introduction of trigonometry through calculators and computers.With particular emphasis placed on trigonometry, graphs and inverses of trigonometric functions, trigonometric identities and equations, vectors, relations with advanced functions and graphing.
Course Purpose:
This is an advanced mathematics course taught for one semester. Its purpose is to provide a strong foundation for higher mathematics, whether in high school or college.
Objectives:
1.Students will use the real and complex number systems.
2.Students will investigate vectors.
3.Students will perform basic operations with matrices and use them to formulate
and solve problems.
4.Students will understand and use arithmetic and geometric sequences and series.
5.Students will understand and apply probability and statistics.
6.Students will recognize, analyze, and graph the equations of the conic sections.
7.Students will recognize, analyze, and graph functions
8.Students will define and apply the trigonometric ratios to right triangles and the
unit circle.
9.Students will define and apply trigonometric identities and equations to solve
problems.
Grading Scale:
The students will be evaluated with the following grading scale.Progress reports given every 3 weeks with a report card given out at the end of the semester.
Unit Assessments (Common/Summative)50%
Tests and Quizzes (Formative) 25%
Daily Assignments (Homework, Classwork, and Tasks)10%
Final Exam15%
Make-up Work:
If you are out for any reason it is your responsibility to get the notes from someone the day you come back and make-up any assignments from that day(s) within 3 days of returning to school.If you are out on the day of a test, it is your responsibility to setup a time to make the test up.If you do not make-up your assignment or test within the 3 days you will be assigned 5th block.
Calendar:
Unit assessments will be given every 4½ weeks and tests will be given every 3-5 days.Quizzes will be announced 2-3 days in advanced.
Class Rules
1.Class Expectations:
Be respectful
Listen to understand
Include yourself
Set aside judgment
Stay focused
2.Come to class on time and be in your seat when the bell rings.
3.Obey all school rules.
4.Bring materials to class everyday.
Exam Exemption Policy:
The only students that may earn exemption from final exams are seniors.
Tutoring:
I will be available for extra help in the mornings from 7:00am until 7:20am.I will be available on Monday and Wednesday afternoons during 5th block from 2:30pm – 3:15pm.Please do not hesitate to come in for help any time.
Note:
5th block is every Monday and Wednesday from 2:30 – 3:15 and transportation is provided by the school on these days.If you sign up and do not come to 5th block then you will be given two more opportunities to come before further action is taken.
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Alexa
Blog Archive
Total Pageviews
>> Sunday, January 23, 2011
When students get to the more advanced math classes in their high school careers, they are typically required to purchase a graphing calculator. These calculators are unlike any tool they have used before, and can truly be compared to handheld computers. Before it becomes too overwhelming, students should consider a few tips for using their graphing calculator. Before getting started with the graphing calculator, students should understand that this piece of equipment is far more advanced than what they have previously used. They will use it to solve entire problems and will spend a great deal of time staring at the screen. That is why they should first set the brightness and contrast settings to a level that will be comfortable for their eyes.
The most important thing a student can do to be successful with their new graphing calculator is to read the manual. There are many more keys on this calculator than the average model, and it is important to be familiar with them all. If this seems like too much to handle, they may want to make a cheat sheet with the most important key functions on it. All of the keys on the graphing calculator are very useful in math class, but there are a few that will be used on a regular basis. The first key to become familiar with is the exponent key, which quickly solves any number to any exponent. When a student first purchases a graphing calculator for math class, they may be overwhelmed by everything it is capable of doing. The best way to become comfortable with it is by reading the manual and understanding all of the functions.
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Algebra by Design Series: Algebra II Topics by Design
By Russell E. Jacobs
Employs a search-and-shade technique that rewards students for their efforts and allows for self-check. Each page contains exercises with shading codes that students use to shade a grid labeled with the answers. If the answers are correct, a symmetrical design emerges. Reproducible for classroom use. Answer key is provided.
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A Level mathematics isn't all about differentiation, integration and volumes of revolution. The fact that one third of the total marks available at A Level are made up of the two applied modules (whether they be Statistics, Mechanics or the ever popular Decision) is a bonus for many students who often find these modules far more accessible than their Core cousins - especially the notorious black sheep of the family, Core 3! Time pressures often dictate that the Applied modules, much like the Core, have to be taught in a traditional, teacher-led way. The danger here, of course, is that might not be appropriate for all students and some may find themselves left behind. This collection of resources is designed to throw up a few new ideas for tackling the Applied modules
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Upper School Classrooms
Math
6th Grade
Mastery of skills and number sense related to multiplication and division with fractions, decimals, and percents; exploring topics in measurement, geometry, and probability; pre-algebra topics including proportions, algebraic notation, solving equations, and integers.
7th Grade
Pre-algebra; use of algebraic formulas, graphs, and tables to represent patterns and functions, both abstract and applied; use of decimals and fractions in algebraic equations; applying algebra to percent and proportion problems; properties of real numbers; extension of geometry and measurement to three-dimensional shapes.
8th Grade
Algebra; formal work with algebraic notation; solving and graphing equations and systems of equations of different forms; solving and graphing inequalities; polynomials and rational expressions; quadratic equations; use of the quadratic formula; radical expressions and equations.
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Description of this Book
The second edition of the reference text for primary and intermediate school students. Designed to help students improve their understanding of mathematical concepts, it is also a useful reference for teachers and parents. The six sections cover; numbers, geometry, statistics, algebra, measurement and a dictionary of mathematical terms.
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Compositions of Functions
In this lecture you will learn about Compositions of Functions in Calculus. Our instructor will walk you through Alternative Notation in Compositions as well as reviewing several functions before our five video examples.
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Compositions of Functions
This topic is very
important in preparation for the Chain Rule for differentiation!
You can informally
think of this as involving an "outer function" and an "inner
function."
Some functions
involve a composition of three of more functions.
You will be using
function compositions throughout the rest of calculus!
Compositions of Functions
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
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This is a book about real analysis, but it is not an ordinary real analysis book. Written with the student in mind, this text incorporates pedagogical techniques not often found in books at this level. The book is intended for a one-year course in real analysis at the graduate level or the advanced undergraduate level. The text material has been class tested several times and has been used for independent study courses as well. This book contains many features that are unique for a real analysis text. Here are a few. Motivation of key concepts. Detailed theoretical discussion. Illustrative examples. Abundant and varied exercises. Applications. The text offers considerable flexibility in the choice of material to cover. \par
Chapters 1 and 2 (set theory, real numbers, and calculus) present prerequisite material that provides a common ground for all readers. Chapters 3 and 4 present the elements of measure and integration by first discussing the Lebesgue theory on the line (Chapter 3) and then the abstract theory (Chapter 4). This material is prerequisite to all subsequent chapters. Chapter 5 provides an introduction to the fundamentals of probability theory, including the mathematical model for probability, random variables, expectation, and laws of large numbers. In Chapter 6 differentiation is discussed, both of functions and of measures. Topics examined include differentiability, bounded variation, and absolute continuity of functions, and a thorough discussion of signed and complex measures, the Radon-Nikodým theorem, decomposition of measures, and measurable transformations. Chapter 7 provides the fundamentals of topological and metric spaces. In addition to topics traditionally found in an introduction to topology, a discussion of weak topologies and function spaces is included. Completeness, compactness, and approximation comprise the topics for Chapter 8. Examined therein are the Baire category theorem, contractions of complete metric spaces, compactness in function and product spaces, and the Stone-Weierstrass theorem. Presented in Chapter 9 are Hilbert spaces and the classical Banach spaces. Among other things, bases and duality in Hilbert space, completeness and duality of ${\cal L}^p$-spaces, and duality in spaces of continuous functions are discussed. The basic theory of normed and locally convex spaces is given in Chapter 10. Topics include the Hahn-Banach theorem, linear operators on Banach spaces, fundamental properties of locally convex spaces, and the Krein-Milman theorem. Chapter 11 provides applications of previous chapters to harmonic analysis. We examine the elements of Fourier series and transforms and the ${\cal L}^2$-theory of the Fourier transform. In addition, an introduction to wavelets and the wavelet transform is presented. Chapter 12 examines measurable dynamical systems. This chapter requires the one on probability (Chapter 5) and discusses ergodic theorems, isomorphisms of measurable dynamical systems, and entropy.
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Mathematics Course Descriptions
MATH 0013
Pre-Intermediate Algebra - A course to teach the basic ideas in theory and
application of several areas of mathematics. The student will be prepared to
complete Intermediate Algebra. Course covers real numbers, simple algebraic
expressions, linear equations in one variable and consumer multiplication. This
course does not count as a degree requirement.
MATH 0123 Intermediate Algebra - A course designed to meet the curriculum
deficiency for beginning freshmen or transfer students. The course includes
elementary algebra to give the student an adequate mathematical background. This
course does not count as degree a requirement.
MATH 1313 Statistics - Designed to introduce the non mathematics student to the
techniques of experimental statistics, to furnish the background necessary to
conduct research, and to read and evaluate associated literature. Will not
satisfy general education requirements.
MATH 1403 Contemporary Mathematics - Offers an overview of traditional algebraic
topics using an applied format. An alternative to College Algebra, Contemporary
Mathematics will satisfy the general education mathematics requirement. Students
planning to take courses that have MATH 1513 College Algebra as a prerequisite
SHOULD NOT TAKE CONTEMPORARY MATHEMATICS since it WILL NOT SATISFY ANY
COLLEGE ALGEBRA PREREQUISITES.
MATH 1513 College Algebra - Designed to provide techniques and concepts
necessary to study applications in various fields. Course fulfills general
education requirement. Pre: Curricular requirements from high school.
MATH 2215 Analytic Geometry and Calculus I - Introduction to theory and
applications of elementary analytical geometry and calculus including theory of
limits, differentiation and integration. Pre: MATH 1613 or permission of the
mathematics department.
MATH 2315 Analytic Geometry and Calculus II - A continuation and extension of
2215 including techniques of integration, infinite sequences and series, and
parametric and polar coordinates. Pre: MATH 2215 or permission of the
mathematics department.
MATH 3013 Linear Algebra - Fundamental concepts of the algebra of matrices,
including the study of matrices, determinants, linear transformations, and
vector spaces. Pre: MATH 2315 and MATH 3513 or permission of the mathematics
department.
MATH 3033 Theory of Probability and Statistics I - Probability as a mathematical
system with associated applications to statistical inference. Pre: MATH 2315 or
permission of the mathematics department.
MATH 3041 Mathematics Technology - This course will introduce students to
several types of mathematics technology. In particular, students will be
introduced to the TI-92™ Graphing calculator and computer software such as
Mathematica, Derive, and Equation Editor. The course is designed to help
students learn and understand mathematics with the aide of technology. The
technology will be used to help illustrate various applications of mathematics,
including solving equations, graphing equations, trigonometry, elementary
statistics, and calculus. Prerequisites: MATH 2215 Calculus I or permission of
the department.
MATH 3323 Multivariable Calculus - A continuation and extension of Calculus I
and II to Euclidean 3-space. Pre: MATH 2315 or permission of the mathematics
department.
MATH 3353 Introduction to Modern Algebra - Fundamental concepts of the
structure of mathematical systems. Group, ring, and field theory. Pre: MATH 2315
and MATH 3513 or permission of the mathematics department.
MATH 4533 Mathematics Models and Applications - A study
of the foundations of model building. Applications of advanced mathematics.
Computer algorithms and practical evaluation of models. Pre: MATH 2315 or
permission of the department.
Mathematics Area of Concentration for
Elementary Teachers (These classes will NOT satisfy general education
requirements and will NOT count as electives for math majors)
MATH 2233 Structural Concepts in Arithmetic - A modern
introduction to the real number system and its subsystems.
MATH 3203 Structural Concepts in Mathematics - A modern
introduction to probability, statistics, geometry and other related topics. Pre:
MATH 2233 or permission of the mathematics department.
MATH 3223 Geometry for Elementary Teachers - Introduction to geometric concepts to provide a superior mathematical
background for elementary teachers. A generalization and extension of intuitive
Geometry studied in MATH 2233 and MATH 3203. Pre: MATH 3203 or permission of the
mathematics department.
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More About
This Textbook
Overview
media and technology products for successful teaching and learning.
Related Subjects
Meet the Author
Dr. Ron Larson is a professor of mathematics at The Pennsylvania State University where he has taught since 1970. He received his Ph.D. in mathematics from the University of Colorado and is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson conducts numerous seminars and in-service workshops for math educators around the country about using computer technology as an instructional tool and motivational aid. He is the recipient of the 2012 William Holmes McGuffey Longevity Award for PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE and the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS (a complete text on CD-ROM that was the first mainstream college textbook to be offered on the Internet.)
Bruce Edwards has been a mathematics professor at the University of Florida since 1976. Dr. Edwards majored in mathematics at Stanford University, graduating in 1968. He then joined the Peace Corps and spent four years teaching math in Colombia, South America. He returned to the United States and Dartmouth in 1972, and he received his PhD. in mathematics in 1976. Dr. Edwards' research interests include the area of numerical analysis, with a particular interest in the so-called CORDIC algorithms used by computers and graphing calculators to compute function values. His hobbies include jogging, reading, chess, simulation baseball games, and travelStill One of the Best Out There
I found my old Calculus Book in the garage and decided to flip through it to see if I could refresh my memory. Still, after all of these years, this is still one of the best Calculus books ever made. It has plenty of great examples and tons of practice problems that focus on a very important comcept of math that most professors take for granted: Repetition is the key to understanding math.
Every school should use this book. It just doesn't make sense not to.
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Aidda
Posted August 17, 2009
Very Well Structured
I got this book to accompany an online Calculus class I was taking and I fine it very useful. It has many problems you can work out on your own and it's very nicely structured.
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Anonymous
Posted July 5, 2002
Made calclulus easy to understand
This is the book that I used in Calculus class when I was an exchange student in High School. It has great examples and is easy to work with. A must have.
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Anonymous
Posted May 6, 2002
Use it
This is a very easy-to-understand book in most of its application. It highlights the important things and goes through each step of each type of problem in detail, a number of times. I highly recommend its use to any serious Calculus teacher and student.
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Anonymous
Posted January 4, 2001
Great Application Problems
This book has many practical application problems along with great examples as it introduces the materials. Also, the illustrations and colorful drawings are a big plus.
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Anonymous
Posted August 18, 2000
An Excellent Calculus Book
This was a very good book. My calculus teacher said it is the best she has ever seen. It was easy to follow (unlike some other math books that I have had experience with), so thus is wasn't difficult to unserstand.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
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Book Description: Hungerford integrates graphing technology into the course without losing sight of the fact that the underlying mathematics is the crucial issue. Mathematics is presented in an informal manner that stresses meaningful motivation, careful explanations, and numerous examples, with an ongoing focus on real-world problem solving. The concepts that play a central role in calculus are explored from algebraic, graphical, and numerical perspectives. Students are expected to participate actively in the development of these concepts by using graphing calculators (or computers with suitable software), as directed in the Graphing Explorations, either to complete a particular discussion or to explore appropriate examples.
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The Student Support Edition of Intermediate Algebra: An Applied Approach, 7/e, brings comprehensive study skills support to students and the latest technology tools to instructors. In addition, the program now includes concept and vocabulary review material, assignment tracking and time management resources, and practice exercises and online homework to enhance student learning and instruction. With its interactive, objective-based approach, Intermediate Algebra provides comprehensive, mathematically sound coverage of topics essential to the intermediate algebra course. The Seventh Edition features chapter-opening Prep Tests, real-world applications, and a fresh design--all of which engage students and help them succeed in the course. The Aufmann Interactive Method (AIM) is incorporated throughout the text, ensuring that students interact with and master concepts as they are presented.
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Algebra I am getting ready to start an Algebra class for the first time and I was wondering what challenges people have with learning and using algebra concepts. Also what are the best ways to over come math anxiety? The best way? Learn the language of algebra.
Tuesday, March 20, 2007 at 9:02am by jeff
SHAY THE MATH QUESTION IS IT ALGEBRA , PRE ALGEBRA' OR GEOMETRY? Quadriatic functions. so algebra i think.
Wednesday, January 17, 2007 at 7:09pm by ROSA
College Algebra is this really algebra, im doing this now in freshman year algebra 2
Monday, February 21, 2011 at 1:06am by BOSSAlgebra This site has excellent explanations of both terms.
Monday, September 14, 2009 at 1:53pm by Ms. Sue
Algebra 1A How is algebra a useful tool? what concepts investigated in algebra can be apply to personal and professional life? I need help answering this question. Please help?
Sunday, November 30, 2008 at 7:34pm by Julissa
algebra 2 thats part of algebra 2 thats easy were doing that now in pre algebra
Wednesday, April 29, 2009 at 1:14pm by Tanisha
what does pre-algebra mean?? pre algebra is like a bunch of math that comes before algebra in middle school.
Monday, August 25, 2008 at 9:11pm by Grace
Algebra (Intermediate) Tutors can better help you when they know they're working with the same student. You might try something like this: Algebra (1), Algebra (2), and so on. Also -- you are more likely to get assistance if you tell us what you know and what you don't understand about your ...
Monday, October 11, 2010 at 12:26pm by Ms. Sue
algebra Once again did you click on the "answer" part of examples #6 and #7 ?
Tuesday, December 1, 2009 at 10:30pm by Reiny
Algebra 2 In Kentucky, where i am from, we do algebra and algebra two before pre-cal and calculus. I didnt realize that the problem could be solved in multiple ways and i apologise. But the solution should be done without calculus.
Thursday, February 24, 2011 at 10:33pm by Anon
7th grade There are at least 5 more than twice as many students taking algebra 1 than taking algebra 2. If there are 44 students taking algebra 2, what is the least number of students who could be taking algebra 1. Show all work
Thursday, November 20, 2008 at 8:37pm by lee
algebra 1 at a certain high school,350 students are taking algebra. the ratio of boys to girls taking algebra is 33:37. How many more girls are taking algebra than boys? - How can you write a system of equations to model the situation? - Which equation will you solve for a variable in ...
Sunday, January 27, 2013 at 3:24pm by lucy
Algebra-still need some help Homework Help Forum: Algebra Posted by Jena on Thursday, February 3, 2011 at 7:32pm. Find the domain of the function. f(x)=(sqrt x+6)/(-2x-5) Write your answer as an interval or union of intervals. Algebra - David, Thursday, February 3, 2011 at 7:42pm (-6,-5/2)and(-5/2,...
Thursday, February 3, 2011 at 8:43pm by Jena
Algebra Nor was I in my algebra class of 1943. This COULD be a case of changing the rules (as has been done with all the SI units). A micron isn't a micron anymore (:(]. In fact my algebra teachers said, "DON'T forget there is a negative root of the square root of 4."
Sunday, January 4, 2009 at 5:46pm by DrBob222
Algebra The average mark on a test in an algebra class is 80. If the two lowest scores of 34 and 48 are not counted, the remaining scores would average 83. How many students are in the algebra class?
Thursday, October 28, 2010 at 7:52pm by Rocky
algebra x = 4 is the answer, if you take the positive square roots. There may be other answers if you take the negative square root on one or both sides. I got that by trial and error, not by using algebra. The algebra got too messy.
Tuesday, July 22, 2008 at 11:00pm by drwlsCollege Algebra Thank you very much. I'm not doing very good understanding this algebra right now so I will definately have other questions tonight. I'm working on getting a tutor here in my town because right after this class is over Sunday, I go into Algebra two.
Wednesday, November 18, 2009 at 7:41pm by LeAnn/Please help me
algebra An algebra book weighs 6 oz less than twice as much as a grammar book. If 5 algebra books weigh the same as 8 grammar books, how much does an algebra book weigh?
Wednesday, October 19, 2011 at 12:00am by AnonymousAlgebra I am having a problem with solving a composite function in Algebra 1 How do I solve f(x) = -2x + 1 and g(x) = 4x? Don't I need more info? No, that is all you need. I it unclear what you want to do here. see
Wednesday, July 18, 2007 at 9:45pm by Alec
Algebra ello i need help factoring I haven't had factorin sense Algebra one and now am in Algebra two and our school is screwed up were they shove in a year of Euclidean Geometry and Basic Trig inbetween first two years of Algebra... so i need to factor X^2-12X+35 I can sit there ...
Sunday, December 7, 2008 at 8:34pm by Algebra
collage algebra 1 no need to throw a hissy-fit. I also wondered why somebody claims to have a "college Algebra" question and can't spell 'college' Besides, this is at most a grade 9 type algebra question. Anyway, why don't you substitute the value of x given in the ...
Monday, January 5, 2009 at 10:55pm by Reiny
algebra X=2 Is that right Ms. Sue? I will spell Algebra correctly from now on thanks for your help.
Tuesday, March 26, 2013 at 5:03pm by Eric
algebra You'll find out after you complete your algebra assignment.
Friday, February 8, 2013 at 11:57am by Ms. Sue
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Book Description: Ensure top marks and complete coverage with Collins' brand new IGCSE Maths course for the Cambridge International Examinations syllabus 0580. Provide rigour with thousands of tried and tested questions using international content and levels clearly labelled to aid transition from the Core to Extended curriculum. * Endorsed by University of Cambridge International Examinations * Ensure students are fully prepared for their exams with extensive differentiated practice exercises, detailed worked examples and IGCSE past paper questions. * Stretch and challenge students with supplementary content for extended level examinations and extension level questions highlighted on the page. * Emphasise the relevance of maths with features such as 'Why this chapter matters' which show its role in everyday life or historical development. * Develop problem solving with questions that require students to apply their skills, often in real life, international contexts. * Enable students to see what level they are working at and what they need to do to progress with Core and Extended levels signalled clearly throughout. * Encourage students to check their work with answers to all exercise questions at the back (answers to examination sections are available in the accompanying Teacher's Pack).
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accompanying CD
A feature of the accompanying CD is our new 'self-tutoring' software where
a teacher's voice explains each step in every worked example in the book. Click anywhere on
any worked example where you see the
icon to activate the self-tutoring software.
The CD is ideal for independent study and revision. It also contains the full text of the
book so that if students load it onto a home computer, they can keep the textbook at school
and access the CD at home.
Table of contents
Symbols and notation used in this book
6
Graphics calculator instructions
11
A
Basic calculations
12
B
Basic functions
13
C
Secondary function and alpha keys
17
D
Memory
17
E
Lists
19
F
Statistical graphs
21
G
Working with functions
22
H
Two variable analysis
26
Assumed Knowledge (Number)
29
A
Number types
CD
B
Operations and brackets
CD
C
HCF and LCM
CD
D
Fractions
CD
E
Powers and roots
CD
F
Ratio and proportion
CD
G
Number equivalents
CD
H
Rounding numbers
CD
I
Time
CD
Assumed Knowledge (Geometry and Graphs)
30
A
Angles
CD
B
Lines and line segments
CD
C
Polygons
CD
D
Symmetry
CD
E
Constructing triangles
CD
F
Congruence
CD
G
Interpreting graphs and tables
CD
1
Algebra (expansion and factorisation)
31
A
The distributive law
32
B
The product (a+b)(c+d)
33
C
Difference of two squares
35
D
Perfect squares expansion
37
E
Further expansion
39
F
Algebraic common factors
40
G
Factorising with common factors
42
H
Difference of two squares factorisation
45
I
Perfect squares factorisation
47
J
Expressions with four terms
48
K
Factorising x2+bx+c
49
L
Splitting the middle term
51
M
Miscellaneous factorisation
54
Review set 1A
55
Review set 1B
56
2
Sets
57
A
Set notation
57
B
Special number sets
60
C
Interval notation
61
D
Venn diagrams
63
E
Union and intersection
65
F
Problem solving
69
Review set 2A
72
Review set 2B
73
3
Algebra (equations and inequalities)
75
A
Solving linear equations
75
B
Solving equations with fractions
80
C
Forming equations
83
D
Problem solving using equations
85
E
Power equations
87
F
Interpreting linear inequalities
88
G
Solving linear inequalities
89
Review set 3A
91
Review set 3B
92
4
Lines, angles and polygons
93
A
Angle properties
93
B
Triangles
98
C
Isosceles triangles
100
D
The interior angles of a polygon
103
E
The exterior angles of a polygon
106
Review set 4A
107
Review set 4B
109
5
Graphs, charts and tables
111
A
Statistical graphs
112
B
Graphs which compare data
116
C
Using technology to graph data
119
Review set 5A
120
Review set 5B
122
6
Exponents and surds
123
A
Exponent or index notation
123
B
Exponent or index laws
126
C
Zero and negative indices
129
D
Standard form
131
E
Surds
134
F
Properties of surds
137
G
Multiplication of surds
139
H
Division by surds
142
Review set 6A
143
Review set 6B
145
7
Formulae and simultaneous equations
147
A
Formula substitution
148
B
Formula rearrangement
150
C
Formula derivation
153
D
More difficult rearrangements
155
E
Simultaneous equations
158
F
Problem solving
164
Review set 7A
166
Review set 7B
167
8
The theorem of Pythagoras
169
A
Pythagoras' theorem
170
B
The converse of Pythagoras' theorem
176
C
Problem solving
177
D
Circle problems
181
E
Three-dimensional problems
185
Review set 8A
187
Review set 8B
188
9
Mensuration (length and area)
191
A
Length
192
B
Perimeter
194
C
Area
196
D
Circles and sectors
201
Review set 9A
206
Review set 9B
207
10
Topics in arithmetic
209
A
Percentage
209
B
Profit and loss
211
C
Simple interest
214
D
Reverse percentage problems
217
E
Multipliers and chain percentage
218
F
Compound growth
222
G
Speed, distance and time
224
H
Travel graphs
226
Review set 10A
228
Review set 10B
229
11
Mensuration (solids and containers)
231
A
Surface area
231
B
Volume
239
C
Capacity
245
D
Mass
248
E
Compound solids
249
Review set 11A
253
Review set 11B
254
12
Coordinate geometry
255
A
Plotting points
256
B
Distance between two points
258
C
Midpoint of a line segment
261
D
Gradient of a line segment
263
E
Gradient of parallel and perpendicular lines
267
F
Using coordinate geometry
270
Review set 12A
272
Review set 12B
273
13
Analysis of discrete data
275
A
Variables used in statistics
277
B
Organising and describing discrete data
278
C
The centre of a discrete data set
282
D
Measuring the spread of discrete data
285
E
Data in frequency tables
288
F
Grouped discrete data
290
G
Statistics from technology
292
Review set 13A
293
Review set 13B
295
14
Straight lines
297
A
Vertical and horizontal lines
297
B
Graphing from a table of values
299
C
Equations of lines (gradient-intercept form)
301
D
Equations of lines (general form)
304
E
Graphing lines from equations
307
F
Lines of symmetry
308
Review set 14A
310
Review set 14B
311
15
Trigonometry
313
A
Labelling sides of a right angled triangle
314
B
The trigonometric ratios
316
C
Problem solving
322
D
The first quadrant of the unit circle
327
E
True bearings
330
F
3-dimensional problem solving
331
Review set 15A
336
Review set 15B
337
16
Algebraic fractions
339
A
Simplifying algebraic fractions
339
B
Multiplying and dividing algebraic fractions
344
C
Adding and subtracting algebraic fractions
346
D
More complicated fractions
348
Review set 16A
351
Review set 16B
352
17
Continuous data
353
A
The mean of continuous data
354
B
Histograms
355
C
Cumulative frequency
359
Review set 17A
364
Review set 17B
365
18
Similarity
367
A
Similarity
367
B
Similar triangles
370
C
Problem solving
373
D
Area and volume of similar shapes
376
Review set 18A
380
Review set 18B
381
19
Introduction to functions
383
A
Mapping diagrams
383
B
Functions
385
C
Function notation
389
D
Composite functions
391
E
Reciprocal functions
393
F
The absolute value function
395
Review set 19A
398
Review set 19B
399
20
Transformation geometry
401
A
Translations
402
B
Rotations
404
C
Reflections
406
D
Enlargements and reductions
408
E
Stretches
410
F
Transforming functions
413
G
The inverse of a transformation
416
H
Combinations of transformations
417
Review set 20A
419
Review set 20B
420
21
Quadratic equations and functions
421
A
Quadratic equations
422
B
The Null Factor law
423
C
The quadratic formula
427
D
Quadratic functions
429
E
Graphs of quadratic functions
431
F
Axes intercepts
438
G
Line of symmetry and vertex
441
H
Finding a quadratic function
445
I
Using technology
446
J
Problem solving
447
Review set 21A
451
Review set 21B
453
22
Two variable analysis
455
A
Correlation
456
B
Line of best fit by eye
459
C
Linear regression
461
Review set 22A
466
Review set 22B
467
23
Further functions
469
A
Cubic functions
469
B
Inverse functions
473
C
Using technology
475
D
Tangents to curves
480
Review set 23A
481
Review set 23B
481
24
Vectors
483
A
Directed line segment representation
484
B
Vector equality
485
C
Vector addition
486
D
Vector subtraction
489
E
Vectors in component form
491
F
Scalar multiplication
496
G
Parallel vectors
497
H
Vectors in geometry
499
Review set 24A
501
Review set 24B
503
25
Probability
505
A
Introduction to probability
506
B
Estimating probability
507
C
Probabilities from two-way tables
510
D
Expectation
512
E
Representing combined events
513
F
Theoretical probability
515
G
Compound events
519
H
Using tree diagrams
522
I
Sampling with and without replacement
524
J
Mutually exclusive and non-mutually exclusive events
527
K
Miscellaneous probability questions
528
Review set 25A
530
Review set 25B
531
26
Sequences
533
A
Number sequences
534
B
Algebraic rules for sequences
535
C
Geometric sequences
537
D
The difference method for sequences
539
Review set 26A
544
Review set 26B
545
27
Circle geometry
547
A
Circle theorems
547
B
Cyclic quadrilaterals
556
Review set 27A
561
Review set 27B
562
28
Exponential functions and equations
565
A
Rational exponents
566
B
Exponential functions
568
C
Exponential equations
570
D
Problem solving with exponential functions
573
E
Exponential modelling
576
Review set 28A
577
Review set 28B
578
29
Further trigonometry
579
A
The unit circle
579
B
Area of a triangle using sine
583
C
The sine rule
585
D
The cosine rule
588
E
Problem solving with the sine and cosine rules
591
F
Trigonometry with compound shapes
593
G
Trigonometric graphs
595
H
Graphs of y=asin(bx) and y=acos(bx)
599
Review set 29A
601
Review set 29B
602
30
Variation and power modelling
605
A
Direct variation
606
B
Inverse variation
612
C
Variation modelling
615
D
Power modelling
619
Review set 30A
622
Review set 30B
623
31
Logarithms
625
A
Logarithms in base a
625
B
The logarithmic function
627
C
Rules for logarithms
629
D
Logarithms in base 10
630
E
Exponential and logarithmic equations
634
Review set 31A
636
Review set 31B
637
32
Inequalities
639
A
Solving one variable inequalities with technology
639
B
Linear inequality regions
641
C
Integer points in regions
644
D
Problem solving (Extension)
645
Review set 32A
647
Review set 32B
648
33
Multi-Topic Questions
649
34
Investigation and modelling questions
661
A
Investigation questions
661
B
Modelling questions
669
Answers
673
Index
752
Using the interactive CD
The interactive Student CD that comes with this book is designed for those
who want to utilise technology in teaching and learning Mathematics.
The CD icon that appears throughout the book denotes an active link on the
CD. Simply click on the icon when running the CD to access a large range of
interactive features that includes:
spreadsheets
printable worksheets
graphing packages
geometry software
demonstrations
simulations
printable chapters
SELF TUTOR
For those who want to ensure that they have the prerequisite levels of
understanding for this new course, printable chapters of assumed knowledge
are provided for Number (see p. 29) and Geometry and Graphs (see
p. 30).
SELF TUTOR is an exciting feature of this book.
The icon on each worked example denotes an
active link on the CD.
Simply 'click' on the
(or anywhere in the example box) to access the worked example, with a
teacher's voice explaining each step necessary to reach the answer.
Play any line as often as you like. See how the basic processes come alive
using movement and colour on the screen.
Ideal for students who have missed lessons or need extra help.
Graphics calculators
The course assumes that each student will have a graphics calculator. An
introductory section 'Graphics calculator instructions' appears
on p. 11. To help get students started, the section includes some basic
instructions for the Texas Instruments TI-84 Plus and the Casio fx-9860G
calculators.
Foreword
This book has been written to cover the 'IGCSE Cambridge International
Mathematics (0607) Extended' course over a two-year period.
The new course was developed by University of Cambridge International
Examinations (CIE) in consultation with teachers in international schools
around the world. It has been designed for schools that want their
mathematics teaching to focus more on investigations and modelling,
and to utilise the powerful technology of graphics calculators.
The course springs from the principles that students should develop a good
foundation of mathematical skills and that they should learn to develop
strategies for solving open-ended problems. It aims to promote a positive
attitude towards Mathematics and a confidence that leads to further
enquiry. Some of the schools consulted by CIE were IB schools and as a
result, Cambridge International Mathematics integrates exceptionally well
with the approach to the teaching of Mathematics in IB schools.
This book is an attempt to cover, in one volume, the content outlined in the
Cambridge International Mathematics (0607) syllabus. References to the
syllabus are made throughout but the book can be used as a full course in
its own right, as a preparation for GCE Advanced Level Mathematics or IB
Diploma Mathematics, for example. The book has been endorsed by CIE but
it has been developed independently of the Independent Baccalaureate
Organization and is not connected with, or endorsed by, the IBO.
To reflect the principles on which the new course is based, we have
attempted to produce a book and CD package that embraces technology,
problem solving, investigating and modelling, in order to give students
different learning experiences. There are non-calculator sections
as well as traditional areas of mathematics, especially algebra. An
introductory section 'Graphics calculator instructions'
appears on p. 11. It is intended as a basic reference to help
students who may be unfamiliar with graphics calculators. Two chapters
of 'assumed knowledge' are accessible from the CD:
'Number' and 'Geometry and graphs' (see
pp. 29 and 30). They can be printed for those who want to ensure
that they have the prerequisite levels of understanding for the course.
To reflect one of the main aims of the new course, the last two chapters in
the book are devoted to multi-topic questions, and investigations and
modelling. Review exercises appear at the end of each chapter with some
'Challenge' questions for the more able student. Answers are
given at the end of the book, followed by an index.
The interactive CD contains
software (see p. 5), geometry and graphics software, demonstrations
and simulations, and the two printable chapters on assumed knowledge.
The CD also contains the text of the book so that students can load
it on a home computer and keep the textbook at school.
The Cambridge International Mathematics examinations are in the form of
three papers: one a non-calculator paper, another requiring the use of a
graphics calculator, and a third paper containing an investigation and a
modelling question. All of these aspects of examining are addressed in the
book.
The book can be used as a scheme of work but it is expected that
the teacher will choose the order of topics. There are a few occasions
where a question in an exercise may require something done later in the
book but this has been kept to a minimum. Exercises in the book range
from routine practice and consolidation of basic skills, to problem
solving exercises that are quite demanding.
In this changing world of mathematics education, we believe that the
contextual approach shown in this book, with the associated use of
technology, will enhance the students' understanding, knowledge
and appreciation of mathematics, and its universal application.
|
The following is a summary of main duties for some occupations in this unit group:
Mathematicians conduct research to extend mathematical knowledge in traditional areas of mathematics such as algebra, geometry, probability and logic and apply mathematical techniques to the solution of problems in scientific fields such as physical science, engineering, computer science or other fields such as operations research, business or management.
Statisticians conduct research into the mathematical basis of the science of statistics, develop statistical methodology and advise on the practical application of statistical methodology. They also apply statistical theory and methods to provide information in scientific and other fields such as biological and agricultural science, business and economics, physical sciences and engineering, and the social sciences.
Actuaries apply mathematical models to forecast and calculate the probable future costs of insurance and pension benefits. They design life, health, and property insurance policies, and calculate premiums, contributions and benefits for insurance policies, and pension and superannuation plans. They may assist investment fund managers in portfolio asset allocation decisions and risk management. They also use these techniques to provide legal evidence on the value of future earnings
|
Exploratorium's Skateboard Science - The Exploratorium
Watch a webcast (RealPlayer) of professional skateboarders performing as an Exploratorium staff physicist explains the physics behind this extreme sport; also, an interview with a skateboard designer, and a Flatland Freestyle demo. "Trickscience" looks
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ExploreLearning.com - ExploreLearning
A library of virtual manipulatives called "Gizmos", primarily for grades 3-12, in math and science. Math topics include the major strands of instruction according to national standards, as well as developmental math, college algebra and college-level
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Exploring Chaos and Fractals - RMIT Publishing
An electronic textbook on CD-ROM which covers the subject of chaos theory and fractal geometry and includes text, worksheets, sound, video, and animation. Course material is presented with multiple entry points and themes, and can be used within a single
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Exploring Data - Rex Boggs, Education Queensland
A website with activities, worksheets, overhead transparency masters, datasets, and assessment to support data exploration. It also contains an extensive collection of articles designed to enhance the statistics knowledge of the teacher. A resources page
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Exploring Precalculus - William Mueller
A lively and intuitive introduction to precalculus. Materials center on three themes: functions, rates of change, and accumulation. Showing the subject from many angles, illustrations include algebraic, graph-based, and real-world examples, and feature
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Expository Papers from the Geometry Center
Documents written at the Geometry Center that take advantage of hypertext to present information about mathematics or the Geometry Center in a style accessible to a wide audience. Engineering Education at the Geometry Center (Keynes, Wicklin); Outside
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EZ Learning Solutions
EZ Learning Solutions Study Guides are part of a family of study aids designed with a "back-to-basics" approach in mind. They are intended for use by students, parents, or teachers, and should be especially useful for the new math curriculum in Ontario.
...more>>
Factasia: Mathematics - Roger Bishop Jones
Math essays organized into three categories: general (threads in the web of mathematics and re-use and abstraction); real numbers (a logical development, some history, and computing with reals); and history (a short history of rigour in mathematics, classical
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A Fair Deal For Housemates - Ivars Peterson (MathTrek)
Four friends move into a house and find they must choose among four rooms of different size and quality. Instead of sharing the rent equally, they decide to divide the total so that each person ends up satisfied with his or her combination of room and
...more>>
The Fair Division Calculator - Francis Su
An interactive Java applet designed to help you determine how to divide among n people: a desirable object (such as a cake); an undesirable object (such as a set of chores); or a set of indivisible objects (rooms, desirable) with payments (rent, undesirable).
...more>>
Fair Play and Dreidel - Ivars Peterson (MathLand)
For centuries, Jews have played the game of dreidel as part of the festivities associated with Hanukkah. Surprisingly, it turns out that this ancient game is also an unfair game. In 1976, Robert Feinerman of Herbert H. Lehman College (CUNY) in Bronx,
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Family Finance - Utah State University Family Finance
PowerPoint presentations for self-guided study: financial attitudes, values & goals; budgeting; creating your financial information binder; and how to budget your money. Other resources from the Utah State University Cooperative Extension agency include
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Famous Curves Index - MacTutor Math History Archive
Links to pages illustrating more than 60 mathematical curves, with information on their history and associated curves. Anyone with the Mathematical MacTutor system or a Java-enabled browser can investigate these curves and their associated curves interactively.
...more>>
Fantasy Stock Market Game - Young Money Magazine
Students invest $10,000 in "fantasy" cash and compete against other students to build an investing portfolio. Game is free with free web site sign-up, contests run for 30 days and for each period an investor starter kit is awarded to the top player, plus
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|
These notes closely follow the presentation of the material given in David C. Lays textbook Linear Algebra and its Applications (3rd edition). These notes are intended primarily for in-class presentation and should not be regarded as a substitute for
Math 3013 Homework Set 6
CHAPTER 5 Mathematics has been called the science of patterns. The identification of patterns and common features in seemingly diverse situations provides us with opportunities to unify information. This approach can lead to the development of cla
SUBSPACES AND SPANS
JOSE MALAGON-LOPEZ
In a vector space we have two basic operations: addition and scalar multiplication. Linear algebra is about the study of the objects that are completely described in terms of such operations. Specically, we will pay
Chapter 4, General Vector Spaces Section 4.1, Real Vector Spaces In this chapter we will call objects that satisfy a set of axioms as vectors. This can be thought as generalizing the idea of vectors to a class of objects. Vector space axioms: Denition: Le
VECTOR SPACES Many concepts concerning vectors in Rn can be extended to other mathematical systems. We can think of a vector space in general, as a collection of objects that behave as vectors do in Rn. The objects of such a set are called vectors. 1
|
Essentials of Basic Mathematics
About This Book
Essentials of Basic Mathematics is a book for those instructors that want a thorough coverage of basic mathematics without the introduction to algebra. Deleting the chapters on algebra allows us to offer the book at a lower price.
Features
Getting Ready for the Next Section
These problems appear at the end of every problem set. They are the exact problems that students will see when they read through the next section of the text. Students who consistently work these problems will be much better prepared for class than students who don't work these problems.
Getting Ready for Class
Just before each problem set is a list of four questions under the heading Getting Ready for Class. These problems require written responses from students and are to be done before students come to class. The answers can be found by reading the preceeding section. These questions reinforce the importance of reading the section before coming to class.
Real-Data Application Problems
This book includes many new problems that use real-world applications for the mathematical subject, making the concepts easier to understand. Many times the charts and graphics in the text look like the types of charts and graphics students see in the media.
Descriptive Statistics
Beginning in Chapter 1 and then continuing through the rest of the book, students are introduced to descriptive statistics. In Chapter 1 we cover tables and bar charts, as well as mean, median, and mode. These topics are carried through the rest of the book. Along the way we add to the list of descriptive statistics by including scatter diagrams and line graphs.
Using Technology
Scattered throughout the book are exercises that demonstrate how graphing calculators, spreadsheets and computer graphing programs can be used to enhance the topics being covered.
Facts from Geometry
This feature gives students a chance to see how topics from geometry are related to the math they are using.
Additional Resources Available Online
Videos
Every example in the book is done in videos available online at MathTV.com. Students can choose from a variety of instructors — including the book's author — and see and hear the examples done in both English and Spanish.
Online Homework
XYZHomework.com is provided free of charge to teachers and students using XYZ Textbook-published books. The system provides teachers with an online gradebook and students with numerous dynamically generated problems.
Online Textbooks
If students have Internet access, they have access to their textbook. An online version of the textbook is available to students as part of their purchase.
Additional Problems
In addition to an identical reproduction of their printed textbook, students also have access to additional resources such as Matched Problem sets, Multiple-choice questions and exercises where they must Find the Mistake.
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Book Description: This brief book presents an accessible treatment of multivariable calculus with an early emphasis on linear algebra as a tool. Its organization draws strong analogies with the basic ideas of elementary calculus (derivative, integral, and fundamental theorem). Traditional in approach, it is written with an assumption that the student reader may have computing facilities for two- and three-dimensional graphics, and for doing symbolic algebra. Chapter topics include coordinate and vector geometry, differentiation, applications of differentiation, integration, and fundamental theorems. For those with knowledge of introductory calculus in a wide range of disciplines including—but not limited to—mathematics, engineering, physics, chemistry, and economics.
Buyback (Sell directly to one of these merchants and get cash immediately)
Currently there are no buyers interested in purchasing this book. While the book has no cash or trade value, you may consider donating it
|
Getting Started Using the Technology at Your Disposal: One Problem, Three Different Approaches
Mary Sue Wyss
Abstract
Pascal's Pyramid is constructed out of toothpicks and gum drops. Observations of either the number of gum drops, toothpicks, tetrahedrons, or octahedrons in each level can produce data reflective of "change". Both second and third degree polynomials are generated. The three different approaches to analyzing the data include finite differences, use of the TI-81 and/or TI-82, and Excel.
Since each approach uses the same data set, the focus is directed on the best analytic method or "tool" of investigation for the data given. In addition, through this introductory exercise, students will become acquainted with their graphing calculator (matrix key) and spreadsheet software that utilizes graphs. Exploration and analysis is geared toward junior high Algebra students but could prove to be an enjoyable introductory exercise for upper level students and technically timid teachers.
Activity A: Finite Differences
For "nice" data sets, this is usually the most direct method of deducing the function. Finite differences reinforce pattern recognition and prepare students for sequences and series.
Step 1: Make a table of x-values and y-values to represent the levels of Pascal's Pyramid and the number of gum drops per level.
x
y
1
1
2
3
3
6
4
10
n
Table 1.A
Step 2: Make another table that shows the differences and ratios of y to x. Since the second difference taken is constant, we know we are dealing with a quadratic function. What is it?
x
y=f(x)
difference in f(x)
change in f(x)
1
1
2
3
2
1
3
6
3
1
4
10
4
1
n
1
Table 2.A
Step 3: By taking the differences, we were offered some valuable information about the characteristic nature of our function. Naturally, our function is more involved than just x2. Therefore, we may want to look at an alternative table such as ratios or multiples of y to arrive at the precise function. Let's make another table.
x
y
2.y
2.y rewritten
1
1
2
1 x 2
2
3
6
2 x 3
3
6
12
3 x 4
4
10
20
4 x 5
5
15
30
5 x 6
n
n (n+1)
Table 3.A
As a result of table 3.A, we see that 2y can be generalized in terms of n. We are very close to our answer. If we divide this generalization;
2y = n ( n + 1 )
then y = n (n + 1)
2
and we are done.
Activity B: Using the TI-81/82 Graphing Calculator
While finite differences may be the most direct route to finding our function, matrices will also work. Since the function is so "nice", this may be a good way to introduce students to the use of the matrix function key on the graphing calculator.
Step 1: We need to look at our data from table 1.A of Activity A. Given the matrix multiplication of [A] x = [B] where the scalar x = [A] -1[B], we find that [A]-1[B] produces the coefficients of our quadratic: y = ax2+bx+c. (We'll be using the first three points in our data set.)
To enter this into our calculator, begin by pressing . "Right arrow" over to EDIT and press . Our matrix is a 3 x 3. Press "3" and "3". Now we are ready to input our matrix given the following equations:
y = ax2+ bx + c
1 = 1a + 1b + c
3 = 4a + 2b + c
6 = 9a + 3b + c
Step 2: We want to exit from our new [A] matrix and create a 3 x 1 matrix [B]. To exit matrix [A], press . Again, arrow over to edit and "arrow down" to 2:[B] and . You want to make a 3 x 1 matrix. Put the "y-values" into [B].
Step 3: Press , to get back to the home screen. Press if home screen is not clear. Recall that from the scalar x=[A] -1[B]we get our coefficients for y = ax2+ bx + c. To let the calculator multiply the matrices, press then "down arrow" to 1:[A]:. Press . Since we want the inverse, press . The display to screen should be [A]-1. Now we want to go back to and "down arrow" to 2:[B]: and press . Your home screen should display the matrix [A]-1[B]
Step 4: Press to display the scalar x.
This tells us that a = 1/2, b = 1/2, and c=0 for all practical purposes.
Activity C: Using "Excel" Spreadsheets and Graphs
Excel offers us a quick way to see the behavior of the function. Through this method, students will learn how to incorporate a little guesswork by varying the parameters. The function we are using in this exercise is nice and known; however, most other sets we will be using later are not. With this exercise, students should be able to concentrate on how to set up a template and acquire a feel for parameterizing a function.
Step 1: We'll need to set up the same tables of data as in Activity A. Each column represents the table headings as follows.
A
B
C
D
E
1
Level (x)
Gum Drops (y)
ROC of f(x)
Change of f(x)
2
3
1
1
1
1
4
2
3
2
1
5
3
6
3
1
6
4
10
4
1
7
5
15
5
1
8
6
21
6
1
Table 1.C
Column D's heading ROC of f(x) refers to the rate of change of gum drops.
Step 2: Once you have the data in, you can select the graph icon in the top right corner. Continue by selecting the scatter plot and then press next. Select an area to place your graph and open a box for it. You should see the following display:
Graph 1.C
You can enhance the appearance of your graph by clicking twice on the graph and then accessing the axis title options. Whatever the case, it is apparent that the function is quadratic in nature for the data given. Students may put formulas into the cells B3 and C3 to create more data points and then re-graph to verify the quadratic nature of the function. The formulas appear below for cells B3 and C3.
B
C
1
Level (x)
Gum Drops (y)
2
1
1
3
=B3+1
=C3+B4
Table 2.C
Step 3: We will be using the same intuition as in Activity A to find the function that best fits the data. We know the function is of the form y = ax2+ bx + c. Let's begin by making a column heading entitled ax2 in column G. We can input the respective values for ax2 in by way of a formula later.
Step 4: To vary the parameter "a", we'll need to set up a cell with the "a" value in it. We'll set that up in the "A" column as shown below.
A
1
a=
2
1
Table 3.C
Step 5: We are now ready to input a formula into our column G that will generate the rest of the column without making the calculations ourselves. This column will be dependent on the number we have placed in cell A2. To start with we will take a=1. To put the equations into G4, use the cell display below.
G
1
ax^2+bx
2
3
1
4
=$A$3*B4^2
Table 4.C
After highlighting down the column (however far), and entering, we have a column of new values. We would like to graph these new values against x to see how well they compare to our function. (The $ symbol between A3 and after indicates that we want that value used as a constant.)
Step 6: To get a clear visual idea of how close our guess is to the real function, we'll graph by highlighting the x column and then press and keys which will allow you to go over to the G column and highlight that.
Step 7: After both columns are highlighted, select the graph icon again from the top right corner of the screen. Select another scattergram that has two graphs showing and open a window on your spreadsheet to display the graph.
Graph 2.C
Step 8: As we can see, the graphs don't match. We can change the values of our "a" parameter to vary the graph. Try some different values of "a" to see what seems best.
Step 9: As hard as we try, the estimated data does not fit well to the actual data. We may need to consider another parameter "b" from the equation y = ax2+ bx + c. This is easy to do by setting up another cell like we did for our "a" parameter. This can be done in cell A4 and A5 as follows.
A
4
b=
5
0.2
Table 5.C
Step 10: We want to change the equation in the G1 column to read ax2+ bx. After doing that, we want to go to G4 to add the "bx" to the equation. The equation should look as follows.
G
1
ax^2+bx
2
3
1
4
=$A$3*B4^2+$A$5*B4
Table 6.C
Toy with both parameters to investigate the affect on the graph. Hold one constant and vary the other. Try some extreme points to emphasize the change before arriving at the correct solution of a = .5, and b = .5.
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An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles. [via]
George Thomas' clear, precise calculus text with superior applications defined the modern-day, three-semester or four-quarter calculus course. The ninth edition of this proven text has been carefully revised to give students the solid base of material they will need to succeed in math, science, and engineering programs. This edition includes recent innovations in teaching and learning that involve technology, projects, and group work. [via]
George Thomas' clear precise calculus text with superior applications defined the modern-day calculus course. This proven text gives students the solid base of material they will need to succeed in math, science, and engineering programs. [via]
This well-accepted introduction to computational geometry is a textbook for high-level undergraduate and low-level graduate courses. The focus is on algorithms and hence the book is well suited for students in computer science and engineering. Motivation is provided from the application areas: all solutions and techniques from computational geometry are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. For students this motivation will be especially welcome. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. All the basic techniques and topics from computational geometry, as well as several more advanced topics, are covered. The book is largely self-contained and can be used for self-study by anyone with a basic background in algorithms. In the second edition, besides revisions to the first edition, a number of new exercises have been added. [via]
More editions of Computational Geometry : Algorithms and Applications:Engaging introduction to that curious feature of mathematics which provides framework for so many structures in biology, chemistry, and the arts. Discussion ranges from theories of biological growth to intervals and tones in music, Pythagorean numerology, conic sections, Pascal's triangle, the Fibonnacci series, and much moreGreen Lion Press has prepared a new one-volume edition of T.L. Heath's translation of the thirteen books of Euclid's "Elements" In keeping with Green Lion's design commitment, diagrams have been placed on every spread for convenient reference while working through the proofs; running heads on every page indicate both Euclid's book number and proposition numbers for that page; and adequate space for notes is allowed between propositions and around diagrams. The all-new index has built into it a glossary of Euclid's Green terms The book is also quite a funny satire on society and class distinctions of Victorian England exploreIn 1884, an amiably eccentric clergyman and literary scholar named Edwin Abbott Abbott published an odd philosophical novel called Flatland, in which he explored such things as four-dimensional mathematics and gently satirized some of the orthodoxies of his time. The book went on to be a bestseller in Victorian England, and it has remained in print ever since.
With Flatterland, Ian Stewart, an amiable professor of mathematics at the University of Warwick, updates the science of Flatland, adding literally countless dimensions to Abbott's scheme of things ("Your world has not just four dimensions," one of his characters proclaims, "but five, fifty, a million, or even an infinity of them! And none of them need be time. Space of a hundred and one dimensions is just as real as a space of three dimensions"). Along his fictional path, Stewart touches on Feynman diagrams, superstring theory, time travel, quantum mechanics, and black holes, among many other topics. And, in Abbott's spirit, Stewart pokes fun at our own assumptions, including our quest for a Theory of Everything.
You can't help but be charmed by a book with characters named Superpaws, the Hawk King, the Projective Lion, and the Space Hopper and dotted with doggerel such as "You ain't nothin' but a hadron / nucleifyin' all the time" and "I can't get no / more momentum." And, best of all, you can learn a thing or two about modern mathematics while being roundly entertained. That's no small accomplishment, and one for which Stewart deserves applause. --Gregory McNamee[via]
Imagine an equilateral triangle. Now, imagine smaller equilateral triangles perched in the center of each side of the original triangle--you have a Star of David. Now, place still smaller equilateral triangles in the center of each of the star's 12 sides. Repeat this process infinitely and you have a Koch snowflake, a mind-bending geometric figure with an infinitely large perimeter, yet with a finite area. This is an example of the kind of mathematical puzzles that this book addresses.
The Fractal Geometry of Nature is a mathematics text. But buried in the deltas and lambdas and integrals, even a layperson can pick out and appreciate Mandelbrot's point: that somewhere in mathematics, there is an explanation for nature. It is not a coincidence that fractal math is so good at generating images of cliffs and shorelines and capillary beds. [via]
This textbook demonstrates the excitement and beauty of geometry. The approach is that of Klein in his Erlangen program: a geometry is a space together with a set of transformations of that space. The authors explore various geometries: affine, projective, inversive, non-Euclidean and spherical. In each case they carefully explain key results and discuss the relationship among geometries. This richly illustrated and clearly written text includes full solutions to over 200 problems and is suitable both for undergraduate courses on geometry and as a resource for self studyThis book is intended to provide a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism, thermodynamics, the deformation tensors of elasticity, soap films, special and general relativity, the Dirac operator and spinors, and gauge fields, including Yang-Mills, the Aharonov-Bohm effect, Berry phase, and instanton winding numbers. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space; consequently, the book should also be of interest to mathematics students. This book will be useful to graduate and advanced undergraduate students of physics, engineering and mathematics. It can be used as a course text or for self study. [via]
Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited [via]
Exposition of 4th dimension, concepts of relativity as Flatland characters continue adventures. Popular, easily followed yet accurate, profound. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Accessible to lay readers but also of interest to specialists. Includes 141 illustrations [via]
More editions of The Golden Ratio: The Story of Phi, the World's Most Astonishing Number:
This classic work is now available in an unabridged paperback edition. The Second Edition retains all the characterisitcs that made the first edition so popular: brilliant exposition, the flexibility permitted by relatively self-contained chapters, and broad coverage ranging from topics in the Euclidean plane, to affine geometry, projective geometry, differential geometry, and topology. The Second Edition incorporates improvements in the text and in some proofs, takes note of the solution of the 4-color map problem, and provides answers to most of the exercises. [via]
"There is perhaps no better way to prepare for the scientific breakthroughs of tomorrow than to learn the language of geometry." --Brian Greene, author of The Elegant Universe
The word "geometry" brings to mind an array of mathematical images: circles, triangles, the Pythagorean Theorem. Yet geometry is so much more than shapes and numbers; indeed, it governs much of our lives--from architecture and microchips to car design, animated movies, the molecules of food, even our own body chemistry. And as Siobhan Roberts elegantly conveys in The King of Infinite Space, there can be no better guide to the majesty of geometry than Donald Coxeter, perhaps the greatest geometer of the twentieth century.
Many of the greatest names in intellectual history--Pythagoras, Plato, Archimedes, Euclid-- were geometers, and their creativity and achievements illuminate those of Coxeter, revealing geometry to be a living, ever-evolving endeavor, an intellectual adventure that has always been a building block of civilization. Coxeter's special contributions--his famed Coxeter groups and Coxeter diagrams--have been called by other mathematicians "tools as essential as numbers themselves," but his greatest achievement was to almost single-handedly preserve the tradition of classical geometry when it was under attack in a mathematical era that valued all things austere and rational.
Coxeter also inspired many outside the field of mathematics. Artist M. C. Escher credited Coxeter with triggering his legendary Circle Limit patterns, while futurist/inventor Buckminster Fuller acknowledged that his famed geodesic dome owed much to Coxeter's vision. The King of Infinite Space is an elegant portal into the fascinating, arcane world of geometry.
This comprehensive, best-selling text focuses on the study of many different geometries -- rather than a single geometry -- and is thoroughly modern in its approach. Each chapter is essentially a short course on one aspect of modern geometry, including finite geometries, the geometry of transformations, convexity, advanced Euclidian geometry, inversion, projective geometry, geometric aspects of topology, and non-Euclidean geometries. This edition reflects the recommendations of the COMAP proceedings on Geometry's Future, the NCTM standards, and the Professional Standards for Teaching Mathematics. References to a new companion text, Active Geometry by David A. Thomas encourage students to explore the geometry of motion through the use of computer software. Using Active Geometry at the beginning of various sections allows professors to give students a somewhat more intuitive introduction using current technology before moving on to more abstract concepts and theorems.An introduction to the geometry which, as modern science now confirms, underlies the structure of the universe.
The thinkers of ancient Egypt, Greece and India recognized that numbers governed much of what they saw in their world and hence provided an approach to its divine creator. Robert Lawlor sets out the system that determines the dimension and the other ubiquitous ratios and proportions.
Art and Imagination: These large-format, gloriously-illustrated paperbacks cover Eastern and Western religion and philosophy, including myth and magic, alchemy and astrology. The distinguished authors bring a wealth of knowledge, visionary thinking and accessible writing to each intriguing subject. 202 illustrations and diagrams, 56 in two colors [via]
Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Topics include applications to urban geography and planning plus comparisons to Euclidean geometry. Every principle is illustrated and clarified with numerous research problems, exercises, and graphs. Selected answers to problems.
This book is intended as a textbook for a first-year graduate course onalgebraic topology, with as strong flavoring in smooth manifold theory.Starting with general topology, it discusses differentiable manifolds,cohomology, products and duality, the fundamental group, homology theory,and homotopy theory. It covers most of the topics all topologists willwant students to see, including surfaces, Lie groups and fibre bundle theory.With a thoroughly modern point of view, it is the first truly new textbookin topology since Spanier, almost 25 years ago. Although the book is comprehensive,there is no attempt made to present the material in excessive generality,except where generality improves the efficiency and clarity of the presentation. [via]
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Purchasing Options
Features
Helps students acquire a new appreciation for the process of mathematical insight
Covers both simple and challenging problems in combinatorics, algebra, trigonometry, and number theory at a level suitable for elementary/primary school students
Demonstrates how problems in one area, such as algebra, can be transformed to a different area, such as geometry, making the problems easier to solve
Develops students' understanding of the creative problem-solving process by building on an increasingly complex collection of problems
Figure slides available upon qualifying course adoption
Summary
Wearing Gauss's Jersey focuses on "Gauss problems," problems that can be very tedious and time consuming when tackled in a traditional, straightforward way but if approached in a more insightful fashion, can yield the solution much more easily and elegantly. The book shows how mathematical problem solving can be fun and how students can improve their mathematical insight, regardless of their initial level of knowledge. Illustrating the underlying unity in mathematics, it also explores how problems seemingly unrelated on the surface are actually extremely connected to each other.
Each chapter starts with easy problems that demonstrate the simple insight/mathematical tools necessary to solve problems more efficiently. The text then uses these simple tools to solve more difficult problems, such as Olympiad-level problems, and develop more complex mathematical tools. The longest chapters investigate combinatorics as well as sequences and series, which are some of the most well-known Gauss problems. These topics would be very tedious to handle in a straightforward way but the book shows that there are easier ways of tackling them.
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Students will be required to use MATLAB occasionally and should know how to set up vectors, perform mathematical operations on vectors, write simple programmes and plot functions. Demos will be given in examples classes throughout the term and examples given on handouts. Useful MATLAB resources and tutorials can be found on the web, including, HERE. An extensive range of MATLAB manuals are also available at the library.
Example Sheets
On average, there is one example sheet per week. Some sheets have more questions than you will be able to do in one week but can be used for revision later. Example classes start in week 2, so you should aim to have done most of sheet 1 for week 2. You will get the most out of the example classes if you try the questions beforehand. You can then ask questions about the problems you are unable to do. You should attend ONE example class per week (not both).
Solutions will be posted here a short while after the corresponding examples classes have taken place.
Please do not email to ask for solutions!
For the lectures on finite difference methods (in weeks 9 and 10) students will need the following MATLAB codes. Download the files and save to your P-drive. Open them in the MATLAB editor and read the instructions. Students should try and reproduce the examples from the handouts on this topic using these codes and attempt all of the questions on examples sheets 7 and 8.
Coursework
Exam resources
Past papers are avaliable from main School of Math website. Note that this course began in 2006. Solutions to these exam papers are not provided. Solutions to examples sheets will help you revise for the exam.
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Presentations on Day Two
Capturing Patterns and Functions: Variables and Joint Variation (G. Lappan)
Functions and Relations: A Unifying Theme for School Algebra in Gracles 9-12 (C. Hirsch)
Micic3le School Algebra from a Modeling Perspective (G. Kleiman)
Why Mocleling Matters by. GoclboIcl)
Modeling: Changing the Mathematics Experience in Postseconciary Classrooms (R. Dance)
Algebraic Structure in the Mathematics of Elementary-Schoo} Children (C. Tierney)
Structure in School Algebra (Micic3le School) (M. van Recuwijk)
The Role of Algebraic Structure in the Mathematics Curriculum of Gracles ~1-14 (G. Foley)
Language and Representation in Algebra: A View from the Micic3le (R. BilIstein)
Teaching Algebra: Lessons Learned by a Curriculum Developer (D. Resek)
The Nature and Role of Algebra: Language and Representation (D. Hughes Hallett)
ss
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Cap Aiding Patterns and Functions:
Va~ialoles and Joint Variation
Glenda Lappan
Michigan State University
East Lansing, Michigan
In ordinary English context helps distinguish among possible meanings of common words. As a representation
of ideas, a word stated free of some meaningful context does not communicate very well. For example, the
definition of a word in the dictionary usually includes several possible meanings. The word used in context helps
the listener or reader to differentiate among the various meanings and understand what the speaker or writer intends.
In mathematics, we face the same dilemmas. Many mathematical words have different or at least different shades
of meaning. In learning to understand both how to communicate in and how to decipher the language of
mathematics, students have to determine meaning from contexts of use. Two of the key concepts in developing a
deep understanding of functions are variables and joint variation. Variable is one of those mathematical words that
has many meanings that must be determined from context of use.
In the new curricula that have been developed as a response to the NCTM's Curriculum and Evaluation
Standards for School Mathematics and Professional Teaching Standards for School Mathematics, students learn
mathematics through engagement with problems embedded in interesting contexts. This means that students have
to learn to interpret different kinds of contexts. Students have to negotiate the "story" of the context whether the
"story" is from the real world, the world of whimsy, or the world of mathematics to find ways to mathematicize
the situation, presented in the story to manipulate the representations to find solutions, to interpret the solution in the
original context, and to look for ways to generalize the solution to a whole class of problems. In addition, students
have to interpret the context of the mathematization of the situation. Is the meaning of variable that of a place holder
for an unknown? Or is the meaning of variable that of a domain of possible values for one of the changing
phenomena in the context? Or is variable used in yet another way in the mathematization?
Joint variation of variables is the heart of understanding patterns and functions. As students grow in their
ability to derive meaning for variables in contexts, they encounter variables that are changing in relation to each
other. This pattern of change, or joint variation, becomes the object of study as certain kinds of change produce
recognizable tables, graphs, and symbolic expressions. At the middle-school level, these important families of
predictable joint variation are linear, quadratic, and exponential functions. In order to see how students can grow in
their understanding of variable and joint variation, let us turn to a series of examples of significant stages of
development in one of the reform middle-school curricula, the Connected Mathematics Project.
In the first situation given on the next page, students are challenged to determine variables of interest and to find
ways to represent how these variables change in relation to each other over the day. The story line is that six college
students are in the process of planning a five-day bicycle tour from Philadelphia to Williamsburg in the summer as
a money-making business. They are exploring the route of the tour while gathering data on each day's trip. Day
five encompasses a trip from Chincoteague Island to Norfolk, Virginia. The data are presented as word notes on the
trip.
57
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THE NATURE AND ROLE OF ALGEBRA IN THE K-14 CURRICULUM
Malcolm and Sarah's notes:
We started at 8:30 A.M. and rode into a strong wind until our midmorning break.
About midmorning, the wind shifted to our backs.
· We stopped for lunch at a barbecue stand and rested for about an hour. By this time, we had traveled about halfway
to Norfolk.
· Around 2:00 P.M., we stopped for a brief swim in the ocean.
· At around 3:30 P.M., we had reached the north end of the Chesapeake Bay Bridge and Tunnel. We stopped for a few
minutes to watch the ships passing by. Since bikes are prohibited on the bridge, we put our bikes in the van and drove
across the bridge.
· We took 7 1/2 hours to complete the day' s 80-mile trip.
In this problem, the variables of time and distance traveled change in relation to each other but not in a
mathematically predictable way. The elements, terrain, creature comforts, and rules of bridge use change the rates
at which the distance is changing as time passes. The graph may be linear in parts, curved in parts, and constant in
parts.
In the second situation, below, students are challenged to solve a problem that is stated in an open-ended way.
To solve the problem, students have to find ways to represent and think about what the variables are and about two
pairs of variables that are changing at different rates relative to each other.
Bonne challenged his older brother, Amel, to a walking race. Amel and Bonne had figured their walking rates. Bonne
walks at 1 meter per second, and Amel walks at 2.5 meters per second. Amel gives his brother a 45 meter head start. Amel
knows his brother would enjoy winning the race, but he does not want to make the race so short that it is obvious his
brother will win. What would be a good distance for the race if Amel wants his brother to win but wants it to appear to
be a close race?
Here students have to decide how to represent the progress of each brother so that they can determine what a
good length would be for the race. Since the rate of change between time and distance for each brother is constant,
each brother's time versus distance relationship is linear. The variables of time and distance in this situation change
in a predictable way. One can predict the distance traveled for any number of seconds, which is a very different
pattern of joint variation from the first situation.
Students can graph both functions on the same axes and see that the two lines cross. They have to figure out the
significance of the point at which the lines cross and how this relates to determining a good distance for the race. Of
course, students may reason from tables of data for each of the brothers. But, in any case, they have to identify the
variables and make sense of which variable depends on the other and how the two pairs of variables relate to each
other. Here the expression 2.5t can represent Amel's progress over t seconds. The variable stands for a whole
domain of possible times. Students could write the functions = 2.5t or d = 2.5t to show the independent variable,
time, and the dependent variable, distance. They might also write 2.5t = 45 + It to show the equation that must be
solved to find the point of intersection. Here the variable is standing for an unknown value, the value of t that makes
the equation true.
In the third situation, below, students again have to deal with variables and the pattern of change between
related variables, but the nature of the change or variation is different from either of the first two situations.
U.S. Malls Incorporated wants to build a new shopping center. The mall developer has bought all of the land on the
proposed site except for one square lot that measures 125 meters on each side. The family that owns the land is reluctant
to sell the lot. In exchange for the lot, the developer has offered to give the family a rectangular lot of land that is 100
meters longer on one side and 100 meters shorter on another side than the square lot. Is this a fair trade?
Here students may talk about the problem at a general level or solve the particular case by comparing areas.
However, the question of whether the results are true in general for a beginning square of any size remains. Here the
problem can be restated with smaller numbers as follows:
What happens if you own a square piece of land that is n meters by n meters and you are offered a piece of land that is
2 meters shorter on one side and 2 meters longer on the other? How does the area of the new lot compare to the original?
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PRESENTATIONS ONDAY TWO
Increase:
59
Here is a table that many groups of students make to record what is happening as the original square sides
Original Square
Length
3 m
4m
5 m
n
New Rectangle
Area
9 m2
16 m2
25 m2
.
n2
Length
5 m
6 m
7 m
.
n+2
Width
1 m
2m
3 m
Change in Area
Area
5 m2
12m2
21 m2
.
(n+2)(n-2) n2- (n+2)(n-2) = 4
4m2
4m2
4m2
The students notice that the change in areas from the square to the rectangle seems to be constant, 4 m. Since
the students also develop a symbolic expression that tells what they do each time to find the change in area between
the square and the rectangle, n2- (n + 2~(n -2), the question of equivalence of expressions naturally arises. Why
does n2- (n + 2~(n - 2) = 4? Students have various ways of looking at this equivalence. They can graph the data in
different ways to observe the behavior of the graphs. There are different graphs that can be made from the data and
that show different kinds of change. The functions, A = n2, A = (n + 2~(n - 2), where A is area and n is the length of
the side of the square, show quadratic growth, and D = n2- (n + 2~(n - 2), where D is the difference between the
areas, gives a constant value and hence a horizontal graph. But the students also are motivated to examine different
ways to transform the symbolic expression. What is another way to express (n + 2~(n -2~? By looking at a rectangle
that is n + 2 on one edge and n -2 on the other, students can use the distributive property to see that this expression
is equivalent to n2 _ 4.
n 2
n-2
n2 _ 2n
2n-4
Therefore, the whole expression n2 _ (n2 _ 4) is always equal to 4.
The three problems I have presented here would be appropriate for different stages of a student' s development
of algebraic skill, but, nonetheless, all three serve to illustrate the centrality of variable and joint variation in
understanding and using function to make sense of situations.
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Functions and Relations:
A Unifying Theme for School Al,gelora in Grades 9-12
Christian Hirsch
Western Michigan University
Kalamazoo, Michigan
One of the most important transitions from middle- to high-school mathematics is the emergence of algebraic
concepts and methods for studying general numerical patterns, quantitative variables and relationships among those
variables, and important patterns of change in those relationships. The mathematical ideas that are central to that
kind of quantitative reasoning are variables, functions, and (to a somewhat lesser extent) relations and their
representations in numerical, graphic, symbolic, and verbal forms. Organizing school algebra around the study of
the major families of elementary functions (linear, exponential, quadratic and polynomial, rational, and periodic)
offers the opportunity to bring greater coherence to the study of algebra. Situating that study in explorations of
contextual settings can provide more meaning to algebra and can provide a broader population greater access to
algebraic thinking.
GOALS AND APPROACHES
From a functions and relations perspective, the continued study of algebra at the high-school level should
enable all students to develop the ability to examine data or quantitative conditions; to choose appropriate algebraic
models that fit patterns in the data or conditions; to write equations, inequalities, and other calculations to match
important questions in the given situations; and to use a variety of strategies to answer the questions. Achievement
of these goals would suggest that the study of algebra be rooted in the modeling of interesting data and phenomena
in the physical, biological, and social sciences, in economics, and in students' daily lives. Through investigations of
rich problem situations in which quantitative relations are modeled well by the type of function under study,
students can develop important ideas of recognizing underlying mathematical features of problems in data patterns
and expressing those relations in suitable algebraic forms.
Answering questions about the situations being modeled leads to questions such as the following, some of
which are at the heart of a traditional algebra program. For a given function modeling rule fix), find
· fix) for x = a;
· x so that f~x)=a;
· x so that maximum or minimum values offer) occur;
· the rate of change inf near x = a;
· the average value off over the interval (a,b).
Early work by Fey and his colleagues at the University of Maryland (cf. Fey and Good, 1985; Fey, Held, et al.,
1995) using computer utilities demonstrated the promise of such a modeling and function-based approach. The
61
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62
THE NATURE AND ROLE OF ALGEBRA IN THE K-14 CURRICULUM
emergence of hand-held graphics calculators puts such an approach in reach of all students and teachers of high-
school mathematics.
Graphics calculator technology provides powerful new visual, numenc, and even symbolic approaches to
answering questions such as those given on the previous page. The technology also facilitates exploration of more
general properties of each family of functions and of all functions collectively; these can then be formally organized
and verified at a later point in the curriculum.
A UNIFYING CONCEPT
Functions are a central and unifying concept of school algebra and, more generally, of school mathematics (c.f.
Coxford et al., 1996~. For example, symbolic expressions for function rules provide compact representations for
patterns revealed by data analysis. Fundamental concepts of statistics, such as transformations of un~vanate or
bivanate data, and of probability, such as probability distnbutions, are expressed and understood through the idea of
function. The function concept can be generalized naturally to mappings such as (x, y) ~ (3x, 3y) or the following,
x O -!
Y 1 0
'lye
which describe transformations of the plane. In discrete mathematics, early experiences with recursive descriptions
of linear change (NEXT = NOW + b) and exponential change (NEXT = NOW x b) lead naturally to more general
modeling with difference equations. Again, matrices are linked with transformations, and matrix methods are
dependent on syntax and inference rules of algebraic symbolism. Finally, the mathematics of continuous change or
calculus is fundamentally the study of the behavior of functions, including rates of change and accumulation.
SUMMARY
Organizing school algebra around functions and their use in mathematical modeling can provide a meaningful
and broadly useful path to algebra for all students. Algebra as a language and means of representation is a natural
by-product of this approach. Patterns that emerge through modeling with functions and studying families of
functions can motivate at a later stage a study of the structure of algebra through deductive methods. Finally, the
theme of functions and relations offers a way to provide a more unified approach to the high-school mathematics
curriculum.
REFERENCES
Coxford, Arthur F., James T. Fey, Christian R. Hirsch, Harold L. Schoen, Gail Burrill, Eric W. Hart, Ann E. Watkins, Mary Jo
Messenger, and Beth Ritsema. (1996.) Contemporary Mathematics in Context: A Unified Approach. Chicago: Everyday
Learning Corporation.
Fey, James T., and Richard A. Good. (1985.) "Rethinking the Sequence and Priorities of High School Mathematics Curricula."
In The Secondary School Mathematics Curriculum, 1985 Yearbook of the National Council of Teachers of Mathematics,
edited by Christian R. Hirsch and Marilyn J. Zweng, pp. 43-52. Reston, VA: NCTM.
Fey, James T., and M. Kathleen Held, with Richard A. Good, Charlene Sheets, Glendon W. Blume, and Rose Mary Zbiek.
(1995.) Concepts in algebra: A TechnologicalApproach. Dedham, MA: Janson Publications.
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Middle School Algebra from a Modeling Perspective
Glenn M. Kleiman
Education Development Center, Inc.
Newton, Massachusetts
To begin, we place algebra within the very general framework shown in Diagram 1 below.
( Situation ')
Extracting and
Representing
-
-
~/
~ Mathematical
<: Representations
Interpreting
and Applying
- ` Mathematical ,'
J
Diagram 1
Mathematical ~`
Findings
This framework emphasizes that mathematics is more than working with mathematical symbols and tools. It
also includes (a) extracting information from a situation and representing that information mathematically the
process of "mathematizing"; and (b) interpreting and applying mathematical findings to have meaning within
specific situations.
This same framework can be applied to any area of mathematics. Algebra is defined by the representations,
tools, techniques it provides, and the types of problem situations it enables one to address. Some specifics, focusing
on algebra grades 6-8, are given in this paper. These are expansions of each of the three corners of Diagram 1 above.
The organizing theme of this framework is modeling. The other themes are incorporated within modeling. The
language and representation theme is reflected in the processes of extracting and representing bringing the
original situation into a mathematical form and interpreting and applying translating back from a mathematical
63
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64
THE NATURE AND ROLE OF ALGEBRA IN THE K-14 CURRICULUM
form to the situation. As we will see below in Diagram 3, the Unctions and relations and the structure themes are
reflected in the mathematical analyses and mathematicalfindings components of the diagram.
First, let us expand upon possible types of situations in Diagram 2 below.
Pictorial or
_ Physical
Physical Arrangement Mathematical
Experiment . Prohl~m
1 ' ~
I Real World I Ad\ \
| Data | ~\\
\\
/~
Diagram 2
~ .. a.... 1
id I Game or |
/ ,~| Puzzle |
it_ ~~
The middle-school curriculum should include a wide variety of types of situations. An appropriate situation
has the following characteristics: it is engaging for many middle school students; it can lead to significant
mathematical explorations at an appropriate level of complexity; and it is manageable within the classroom.
Next, let' s expand upon the mathematical representations for the middle-school algebra curriculum. The link
across the representations in Diagram 3 below is a reminder that understanding the relationships among these
representations is also important.
~ \
/ My Mathematical ~~\
RepresentationsI F: J
Let
Pictures Tab
Diagrams |
~ _
;{ inequalities
1
Scatter Plot | | Linear
1 1 1 1 1 1
Line ~ ~Quadratic
Diagram 3
- ~
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PRESENTATIONS ONDAY TWO
65
Next, in Diagram 4 below are some of the types of mathematical findings we emphasize within the middle-
school algebra strand
Mathematical
Representations
Mathematical >
Analyses
-
Mathematical
Findings
Identify I Solve for I I Test If/Then
I Patterns I ~ Unknowns ~Conjectures
Diagram 4
Identify Functional
Relationships
Students should be able to use these findings to do such things as (1) use patterns to predict new cases in the
situation; (2) interpret solutions of unknowns in terms of filling in missing information about the situation; (3) make
if-then statements about the situation; and (4) use knowledge of functions to predict what will happen when one
thing changes in the situation.
To get to these four types of findings, students need a repertoire of mathematical tools and understandings.
Diagram 5 on the next page shows some categories of patterns students should understand; knowledge and
techniques students will need to solve equations and inequalities; some tools for testing conjectures; and types of
functions that students should become able to recognize and apply to understanding situations. All of these can be
introduced in the middle-school curriculum, in many cases at an informal, context-based level, that forms a
conceptual base for the more formal and abstract understandings that will develop in later grades.
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84
THE NATURE AND ROLE OF ALGEBRA IN THE K-14 CURRICULUM
The fact that t3/t2 equals t is algebra, that t3 for large t is much larger than t2 is calculus, and that 1000/100 = 10
is arithmetic.
When talking about school algebra, I mean something other than mathematical algebra. Algebra in the context
of school algebra is a coherent integration of elements from the three domains: arithmetic, algebra, and calculus.
ALGEBRA AT THE MIDDLE GRADES
Over the past five years, the Freudenthal Institute has been involved in a curriculum development project in
which a complete, new mathematics curriculum named MiC has been developed for American students between 10
and 14 years-of-age. One of the content strands in this curriculum is "algebra," and it contains a collection of topics
from different mathematical domains. In the algebraic structure session, I will use some examples to illustrate the
philosophy and approach in this curriculum towards algebra. In this paper, I have restricted myself to outlining the
philosophy and approach in general terms.
ALGEBRA IN MATHEMATICS IN CONTEXT
The algebra strand in MiC emphasizes the study of relationships between variables, the study of joint variation.
Students learn how to describe these relationships with a variety of representations and how to connect these
representations. The goal is not for students merely to learn the structure and symbols of algebra but for them to use
algebra as a tool to solve problems that arise in the real world. For students to use algebra effectively, they must be
able to make reasonable choices about what algebraic representation, if any, to use in solving a problem.
MiC APPROACH TO ALGEBRA
The MiC curriculum especially the algebra strand is characterized by progressive formalization. In other
words, students rely heavily, first, on their intuitive understanding of a concept, then they work with the concept
more abstractly. The realistic problem contexts support this progression from informal, intuitive understanding to a
more formal, abstract understanding. Students can move back and forth from informal to formal depending on the
concepts and the problem contexts. Their ability to understand and to use algebra formally develops gradually over
the four-year curriculum. By the end of the four-year curriculum, students have developed an understanding of
algebraic concepts and are able to work quite formally with algebraic symbols and expressions. Algebra in MiC
lays a solid groundwork for mathematics at the high-school level.
EXAMPLE
Even and odd numbers can be visualized by dot patterns. Dot patterns also can be used to visualize and to
investigate more complex (number) patterns. Symbols, expressions, and formulas (recursive and direct) can be
used to describe the patterns. The formulas themselves can then become an object of study that lead to re-inventing
such mathematical properties as distributivity and factorization. For example, when students investigate the
structure of rectangular and triangular numbers, they can use visual representations to support finding appropriate
algebraic expressions. In the algebraic structure session, I will illustrate this example with problems from the
curriculum materials.
NO ALGEBRAIC STRUCTURES BUT STRUCTURE IN SCHOOL ALGEBRA
Algebra at the middle-grade levels builds on students' intuitive and informal knowledge of arithmetic, of
symbols, patterns, regularities, processes, change, and so on as developed in the early grades. Algebra in the
middle grades does not need to lead to a complete and formal understanding of (the parts of) algebra. It is not the end
of students' education. High school follows, and that is the place to formalize the concepts.
Algebraic structure as described by Greg Foley, for example is "number theory." We should be careful
about making topics from number theory the focus of the mathematics curriculum, especially at the middle grades.
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PRESENTATIONS ONDAY TWO
85
Factoring, divisibility rules, prime factorization, manipulating symbols and expressions, and other such topics have
been the focus of the algebra curriculum, and students have not then had an opportunity to develop a meaningful
understanding of the underlying concepts. The focus should be a long-term learning strand in which students can
re-invent the algebra themselves, with the result being a mathematical system that is meaningful to students. The
MiC algebra strand serves as an example of how this goal can be achieved.
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The Role of Al,~ebraic St~nctnre in the
Mathematics Cliche of Grades I 1-14
Gregory D. Foley
Sam Houston State University
Huntsville, Texas
MATHEMATICAL THEORY VERSUS RELEVANCE
The so-called "new math" movement of the 1960s brought such logic-based organizing themes as set theory
and algebraic structure to the fore of school mathematics in the United States. Mathematical reasoning, axiomatic
structure, and within-mathematics connections were driving forces of a reform movement motivated by American-
Soviet competition and led by research mathematicians. The goal of preparing a cadre of highly capable engineers
and scientists caused us to focus on the most able students. By contrast, the National Council of Teachers of
Mathematics (NCTM) Standards-inspired school mathematics reform of the l990s has been driven by calls for
relevance realistic applications, modeling, genuine data, and mathematics in context and by a powerful collec-
tion of emerging instructional technologies. Mathematical communication, problem solving, and cross-disciplinary
connections drive the current reform. The need for a generally well-educated population to remain competitive in a
global economy has led us to conclude that "everybody counts" and that we need algebra for everyone. In the
1960s, we sought to motivate the mathematics; in the l990s, we seek to motivate the students.
This, of course, is an oversimplification. A careful reader of the NCTM Curriculum and Evaluation Standards
(1989) will notice an overarching theme of "Mathematics as Reasoning" and will see that the document says high-
school students should learn about matrices, abstraction and symbolism, finite graphs, sequences, recurrence
relations, algorithms, and mathematical systems and their structural characteristics, and that, in addition, college-
intending students should gain facility with formal proof, algebraic transformations, operations on functions, linear
programming, difference equations, the complex number system, elementary theorems of groups and fields, and the
nature and purpose of axiomatic systems. The American Mathematical Association of Two-Year Colleges'
(AMATYC) Crossroads in Mathematics (1995) contains similar calls for the content of introductory college
mathematics. Ideally, there should be a balance between solid mathematics and relevance to the student and
societal needs. The Standards documents for Grades 11-14 recognize this.
TECHNOLOGY AS CURRICULAR CATALYST
The influence of technology should not be downplayed. Technology is affecting the mathematics curriculum
in several ways. Compared to the past, current technology gives students access to relatively advanced mathemat
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88
THE NATURE AND ROLE OF ALGEBRA IN THE K-14 CURRICULUM
ical concepts and allows them to explore, descnbe, and display data with relative ease. Modern hand-held
computers, such as the TI-92, have powerful features that allow students
· to operate with integers, rational numbers, real numbers, or complex numbers;
· to define, algebraically manipulate, graph, and tabulate functions of one vanahle. narametnc equations
sequences, polar equations, and functions of two vanables;
· to solve equations, find zeros of functions, and factor and expand expressions;
· to define, algebraically manipulate, graph, and tabulate sequences, polar equations, and real-valued
functions of two vanables;
· to operate on lists, vectors, and matrices whose entries are integers, rational numbers, real numbers, or
complex numbers;
· to organize, display, process, and analyze data;
· to wnte, store, edit, and execute programs; and
· to construct and explore geometric objects dynamically and interactively.
, ~
,
In addition, modern technology and the related emergence of computer science make the knowledge of discrete
mathematical structures more important. Technology has indirectly increased the use of statistics throughout
society. It is no wonder, then, that the University of Chicago School Mathematics Project has a two-year sequence
of Functions, Statistics, and Trigonometry (Rubenstein et al., 1992) followed by Precalculus and Discrete
Mathematics (Peressini et al., 1992~. There is simply more appropriate content after second-year algebra in
preparation for postsecondary work in statistics, discrete mathematics, calculus, and linear algebra than in past
decades. Technology makes this both possible and desirable.
WHAT IS THE ROLE OF ALGEBRAIC STRUCTURE?
Teachers of mathematics in Grades 11-14 must understand algebraic groups, nngs, fields, and the associated
theory. They need, for example, to recognize the importance of the complex numbers being a field and the
significance of the fact that matrix multiplication is noncommutative and that matrices have zero divisors. They
should see a loganthm~c function as an isomorphism between groups and recognize geometric transformations as
forming a group under composition. Furthermore, in keeping with the NCTM curriculum standards for college-
intending students, high-school teachers need to be able to convey such understanding to their upper level students.
This should be reinforced, amplified, and extended in lower division postsecondary mathematics courses, especial-
ly those in discrete mathematical structures and linear algebra.
We must, however, be careful not to make algebraic structure the overriding focus of mathematics in Grades
11-13, except, possibly, for the most gifted and talented students. On the other hand, it is essential that, in Grades
14-16, students acquire a clear vision of the "big picture" provided by a structural understanding of algebra. While
we help students acquire this vision, we continually should call their attention to the numerous specific examples of
groups, nngs, and so on, as they learn the common structure and associated theory. There are abstract algebra
textbooks, such as Fraleigh's (1989), that do a good job of this.
Abstract algebraic structures can serve as important organizing tools for the mathematics curnculum, but we
should not fall into the trap of creating a new "new math."
REFERENCES
American Mathematical Association of Two-Year Colleges. (1995.) Crossroads in Mathematics: Standards for Introductory
College Mathematics Before Calculus. Memphis, TN: Author.
Fraleigh, J. B. (1989.) A First Course in Abstract Algebra, 4th Ed. Reading, MA: Addison-Wesley.
National Council of Teachers of Mathematics. ( 1989.) Curriculum and Evaluation Standards for School Mathematics. Reston,
VA: Author.
Peressini, A. L., et al. (1992.) Precalculus and Discrete Mathematics (University of Chicago School Mathematics Project).
Glenview, IL: Scott-Foresman.
Rubenstein, R. N., et al. (1992.) Functions, Statistics, and Trigonometry (University of Chicago School Mathematics Project).
Glenview, IL: Scott-Foresman.
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Language and Representation in Algebra:
A View from the Middle
Rick Billstein
Director, STEM Project
University of Montana
Missoula, Montana
Algebra can be thought of as a language, and students learn language best in their early years. We should begin
teaching informal algebraic concepts in the elementary grades and continue to develop the concepts throughout the
middle-school years. Algebra too often is taught as rules and tricks without an understanding of the concepts. Then
the jump to the formal level is often made too quickly for the concepts to be mastered. Topics should be developed
slowly and informally without symbol manipulation as the primary goal. The jump into symbol manipulation
should come only after students recognize the need for it.
Algebra has been described as a way of thinking about and representing many situations. Unfortunately, many
textbooks confine algebra to solving equations and manipulating symbols. Other representations, such as graphs,
tables, patterns, diagrams, and other visual displays, should be used as appropriate. Visual representations are
powerful because they help abstract mathematical ideas to become concrete. Since different representations may
provide new or fresh insights about a problem, each representation is important and plays a role in the learning of
algebra. There should be many opportunities for students to make transitions between the various representations.
As students mature mathematically, they learn which types of representations are most useful for which kinds of
problems. Students need to describe various representations in their own words. After a representation has been
used, it is important to discuss it in terms of the original context. Interaction between teachers and students is
important in development of language and representation skills.
At the middle-school level, students might be asked to translate between words, tables, graphs, and equations.
Given any one of these representations, they could be asked to determine any of the other three. Having students
work in groups and share representations makes them aware that different representations can be equivalent yet look
quite different. This is a powerful experience in middle school and will pay huge benefits at the high-school level.
Instead of always translating from words to representations, as in the traditional curriculum, we now ask students to
translate representations to words.
With the use of technology on the rise, new understandings of symbol manipulation are needed to model
situations that can be entered into a computer. For example, spreadsheets can be used to analyze complex numerical
data from a problem situation. Algebra becomes important because it is the language used to communicate with the
technology. Spreadsheet formulas are but one example of a form of algebra. Technology allows students to
experiment, to investigate patterns, and to make and test conjectures. Technology allows us to go where we could
not go before because the mathematics became too "messy." Students need experiences making representations
with and without technology.
Students should be involved in "doing" mathematics at the middle-school level. It is important that they
investigate problems and be involved in hands-on activities. "Doing" mathematics provides students with
opportunities to communicate about algebra. There is little communication in a typical algebra textbook. The
language that students use will develop as they become more mathematically mature. Curriculum materials not
89
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9o
THE NATURE AND ROLE OF ALGEBRA IN THE K-14 CURRICULUM
only must contain good problems, but also the problems must be structured in such a way that solving them will help
students achieve the desired learning outcomes.
New materials are now becoming available in which algebraic ideas are taught throughout the curriculum.
Teachers must be made aware of these materials and support must be provided to train teachers to use these
materials. Teachers must understand that when we say we want to include algebra in the middle school, we are not
talking about the algebra that they had when they were in school.
Hugh Burkhardt of the Shell Center for Mathematics Education in England describes algebra as "inherently
slippery" and has said that "having separate algebra courses is one of the United States' great self-inflicted wounds"
(1997~. Most National Science Foundation (NSF)-funded middle-school curriculum developers have struggled
with this and are constantly asked about the role of algebra in the materials and how their curricula fit with an
Algebra I course. The "Six Through Eight Mathematics" (STEM) project response has always been that algebra
should not be a separate course taught at a particular grade level but, rather, that it should be a strand taught within
the mathematics curriculum at every grade level. The teaching of algebra should be integrated with the teaching of
other mathematical strands, such as statistics or geometry.
The traditional Algebra I course should not be a required eighth-grade course as it is in many schools because
this means the sixth, seventh, and eighth-grade curriculum must be covered in only two years. Two years is not
enough time to develop adequately topics in probability, statistics, measurement, discrete math, number theory, and
geometry. Many of the negative feelings that develop towards mathematics as a result of an "algebra course" might
be eliminated if the algebra were integrated into the curriculum as a strand. Students would no longer remember
algebra as a course in manipulating expressions and solving symbolic equations. Student experiences in middle-
school mathematics courses might then actually prepare them for and encourage them to take additional
mathematics courses, especially if those courses were taught in the reform mode of the new NSF high-school
projects.
STEM has found that one way to teach algebra effectively is to make it useful to students. Real contexts that are
meaningful to students play a major role in algebraic learning. Real contexts do not mean that all problems have to
come from students' everyday lives but, rather, that problems must make sense to students. Algebraic abstraction is
motivated by the need to represent the patterns found in the context. Algebraic thinking is more important than
algebraic manipulating. To develop algebraic thinking, we need to include informal work with algebraic concepts
in the middle school and not move too quickly to the abstract level. For example, being able to set up graphs or
tables in various problem settings brings mathematical power and understanding to students. Experiences with
graphs should include a detailed plotting of points to determine a graph as well as experiences with the overall
shapes of graphs based on the information in the problem. If students are given a graph, they should be able to write
a story about it. Having students communicate about mathematics is a worthwhile goal in the new middle-school
curricula.
Don Chambers wrote, "Algebra for all is the right goal at the right time. We just need to find the right algebra"
, ~
(1994~. The NSF-funded middle school projects are taking us closer to finding the right algebra.
REFERENCES
Burkhardt, H. (1997.) Personal Conversation at the National Council of Teachers of Mathematics National Meeting in
Minneapolis, MN.
Chambers, D. (1994.) "The Right Algebra for All." Educational Leadership, 51, 85-86.
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Teaching Algebra:
Lessons [earned by a C?~ric?~?~m Developer
Diane Resek
San Francisco State University
San Francisco, California
In this symposium, I am approaching the issue of teaching algebra from the perspective of a curriculum
developer. I am one of the developers of the National Science Foundation's (NSF's) secondary curriculum,
"Interactive Mathematics Program" (IMP). The original design for the program was based on the experiences of the
developers in past curriculum projects and in their own teaching. In this new project, we have had experience
teaching algebra to students in elementary school, high school, and college. The original IMP curriculum has been
rewritten three times shaped by the authors' observations of the curriculum as it was taught in different
classrooms, by the comments and suggestions of teachers, and by student work.
What follows are some statements about what I now believe about the teaching of algebra.
INTUITION SHOULD COME FIRST
People often ask for evidence that the new curriculum projects "work." There is some evidence of this, but
there are mountains and mountains of evidence that the traditional methods don't "work." Now, exactly why the
traditional curriculum does not work is open to question. My personal belief is that the chief culprit is the teaching
of manipulative skills in a way that does not allow adequate intuition to come into play about what the symbols
mean and why the manipulation is valid and useful.
It is not that we do not know how to teach manipulation in meaningful ways. Many projects have shown us how
to do this for years. One way to develop intuition about manipulating equations symbolically is by tapping into both
the students' familiarity with the fact that equations are statements about functions and the students' comfort in
associating the symbolic form of functions with other representations of functions, graphical or numerical. Student
familiarity and comfort must be developed over time.
It is my hope that much of the work in elementary-school and middle-school algebra will be on developing
student comfort in moving between representations of functions. In general, we can decide what we need to teach
at various levels by looking at what is difficult to teach later on. Traditionally, we have looked at what skills we
thought were needed for success at one level and then taught those skills at the lower level. I am suggesting that we
look at what skills or understandings are difficult for students at one level and try to develop intuition at lower levels
that might serve as a basis for those skills or understandings.
UNDERSTANDING DOES NOT COME IN DISCRETE PACKAGES
One difficulty with building students' use of intuition is that this requires time often several years. Teaching
one concept over time conflicts with the traditional idea of organizing teaching around subject matter. Traditional-
ly, one studies a chapter on linear equations at one time and that subject is then checked off. However, if we want
91
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92
THE NATURE AND ROLE OF ALGEBRA IN THE K-14 CURRICULUM
students to understand linear functions in different representations, this must be worked on over several years.
Striving for long-term exposure to subject matter creates a difficult bookkeeping problem. It becomes difficult to
check off the skills that students have. As the public pushes us for accountability, they push for a neat and tidy
assessment system. Unfortunately, that kind of assessment system does not match the way students learn.
At any level first grade, high school, or college students do not study a deep topic and suddenly "get it."
Understanding comes gradually. It develops over time. Anyone who has asked students to write about a topic
knows this. Reading what they have written, we can see that there are things the student seems to understand and
other things he or she has not yet come to terms with. Rarely do we get a picture of perfect understanding. Our
curriculum must be structured so that students can work on tasks at different levels and so that everyone in a class
will grow.
I am not saying that teachers should not be accountable for students' learning or that students should not
eventually master key ideas. I am saying that we need to take into account how students learn and that this is
gradual. We must not let the difficulty of assessing understanding sway us from trying to teach effectively.
WE CAN LEAD STUDENTS TO WATER, BUT ...
Once we have decided what we want to teach and how we want to teach it, we have to wrap it in the right paper.
This is not because students are lazy or do not have good taste. It is because their minds cannot actively work with
material if they have no way to relate to it. Contexts and relationships to other subject matter can provide students
with a door to approach new mathematics.
This is not to say we should never teach mathematics without a "real life" context. I am saying that we have to
introduce the mathematics in a "real life" situation that students can relate to or in the context of other mathematics
that they are working with. Once they have gone into the mathematical ideas, they can and will go on to work on the
"bare" mathematics.
A few students do think well symbolically and do not require much of a context. Most of us here were that kind
of student. In the past, success in algebra was reserved for us and others like us. Algebraic knowledge is too
important to reserve for so few. It also is not clear that people who think in this way have the most to contribute even
to pure mathematics. We have to open the doors to others. It is not that hard to do.
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The Nature and Role of Algebra.
I~an~na~e and Representation
Deborah Hughes Hallet
Harvard University
Cambridge, Massachusetts
Students arriving at college should be familiar with verbal, symbolic, graphical, and numerical representations.
They need to be able to manipulate each one and be able to convert one to another. Manipulating each of the
representations requires some degree of technical skill supported by conceptual understanding. This understanding
must comprise both an understanding of how the representation works in general and of each particular object being
represented.
To work with graphs, students need to understand how graphs are constructed. For example, they need to
understand that values of inputs to a function are measured horizontally, whereas values of outputs from the
function are measured vertically. This will enable students to interpret intercepts and to estimate values of limits
and asymptotes. Technology is changing how much technical skill students need to have in drawing graphs by
hand, but it has not changed the fact that students need to understand how the zeros and symmetries of a function
appear on a graph, where to expect asymptotes, and what sort of scale will show all the features of the graph.
Numerical data, usually in a table, is for many students the least familiar representation. Students need to
understand how the data were generated (from an experiment, by using a formula, for example). They should be
able to work with numerical data, such as rounding, interpolating, and extrapolating (where these make sense). The
ability to find patterns in data, such as where values are increasing or where there are constant differences, is a
useful skill.
The manipulation of symbols traditionally has formed the largest part of an algebra course. It is still central.
Students must be able to solve equations, collect terms, simplify, and factor. The degree of skill and the speed
required may be altered by changes in technology. For example, methods of factoring higher degree polynomials
are probably not as important as they used to be. However, what it means to factor a polynomial (for example, that
it is not usually useful to write x2 - 2x = xtx) - 2x) is as important as ever. Experience and observation will suggest
the most effective balance between paper-and-pencil work and technology. Currently, there is a wide range of
opinion about the best way to develop manipulative skill, ranging from not allowing technology to allowing it to be
used heavily. As we try to figure out how to teach this skill, we should be mindful of the fact that we were not very
successful at teaching symbol manipulation before technology complicated the situation. It is tempting to gild the
past, but weaknesses that we currently observe are probably not the result of technology. Our charge is to figure out
how to fix them.
Besides acquiring skill in manipulating graphs, numerical data, and symbols, students need to be able to move
easily between these representations. For example, given a straight line graph, students should be able to figure out
its (approximate) equation. Given a table of data from an exponentially growing population, students should be able
to figure out a formula for the function. Given a data set, students should be able to make a mental sketch of the data
or match data with the correct sketch.
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THE NATURE AND ROLE OF ALGEBRA IN THE K-14 CURRICULUM
Mastery of the language of algebra requires a two-pronged approach:
1. What does it mean?
2. How do wedoit?
Equal emphasis on both of these leads to students who know both what algebra means and how to use it
correctly.
The future is likely to change the balance between these two because the skills required to do algebra are likely
to change. However, we always will need to make sure students can use graphs, tables, symbols, and verbal
descriptions fluently.
|
Geometry Reasoning, Measuring, Applying
Author:
ISBN-13:
9780395937778
ISBN:
0395937779
Edition: 10 Pub Date: 2000 Publisher: Houghton Mifflin College Div
Summary: The theorems and principles of basic geometry are clearly presented in this workbook, along with examples and exercises for practice. All concepts are explained in an easy-to-understand fashion to help students grasp geometry and form a solid foundation for advanced learning in mathematics. Each page introduces a new concept, along with a puzzle or riddle which reveals a fun fact. Thought-provoking exercises encourag...e students to enjoy working the pages while gaining valuable practice in geometry
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...Precalculus is perhaps the most important math subject that you can take as it combines all the concepts you have learned in previous levels of math and starts to apply them in new ways. It is also the foundation that you need before going to the much more complex calculus. Given its importance...
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This book covers Option Topic 8: Sets, Relations and Groups from the IB Mathematics HL syllabus.
The book includes many explanations supported by examples and diagrams. It uses language specifically chosen with the IB student in mind. Within these pages, students will find a wealth of material to help them achieve an understanding of the Topic.
The extensive exercises include IB style examination questions.
Experienced IB teachers and authors, Györgyi Bruder & William Larson have collaborated to produce a book that will help both students and teachers come to grips with this absorbing topic
A set of threeThis book has been specifically written to meet the demands of the Mathematics Higher Level Option 10: Series and Differential Equations. The book presents an extensive and comprehensive coverage of the Option. Throughout the text, the subject matter is presented using graphical, numerical and algebraic means – enhancing the students' understanding.
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This book has been specifically written to meet the demands of the Mathematics Higher Level Option 8: Statistics and Probability. The book presents an extensive and comprehensive coverage of the option. Throughout the text, the subject matter is presented using graphical, numerical and algebraic means – enhancing the students' understanding. The text contains:
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* more than two hundred graded exercises, including examination style questions
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The material has been completely re-edited, with contributions made by workshop leaders, past and current examiners and experienced IB mathematics teachers. This has enhanced presentation and improved both clarity and accuracy throughout the text.
The text contains:
* a large increase in the number of worked examples and exercises
* detailed use of the graphics calculator is interwoven throughout to aid learning and understanding.
* practice examination questions, specifically written for the new course by experienced examiners.
This Manual contains solutions to most of the questions from the Mathematics Standard Level text, 3rd Ed. 2nd Imprint, published by IBID Press.
These solutions are not meant to dictate any particular approach but rather provide avenues for obtaining answers.
Most of the solutions are hand worked so that the natural flow of the solution process can be more readily observed. It was important to have a number of different authors involved in this project, each lending their own style and approach to solving problems.
Having obtained this Solutions Manual it is essential that you refer to it only after a real and honest effort has been made to solve each problem.
As the contents of Chapter 23 in the textbook can be used for internal assessment purposes, no solutions have been provided for any of the tasks in that chapter.. Purchase entitles you to make unlimited copies for use within your institution. You will receive a copy of a pdf by email within 24 hours after your payment is processed
This text now comes with a complimentary student CD that contains a pdf of the text and other bonus material.
The material has been completely re-edited, with contributions made by workshop leaders, past and current examiners and experienced IB mathematics teachers. This has enhanced presentation and improved both clarity and accuracy throughout the text.
This is the most comprehensive resource available specifically for this subject.
The text contains: . a large increase in the number of worked examples and exercises. . detailed use of the graphics calculator is interwoven throughout to aid learning and understanding. . practice examination questions, specifically written for the new course by experienced examiners. . revision exercises strategically placed throughout the text. . project suggestions with guided questions to help students develop project topics.
This solution manual contains hand worked solutions to most of the questions in the Mathematical Studies Standard Level text, 3rd Ed. 2nd Imprint, published by IBID Press. We stress that these are the solutions to the 2nd Imprint of the 3rd Ed., for in the course of producing these solutions, alterations to some questions were necessary in order to clarify them.
Each solution in this book represent only one of the many methods available. The solutions are not meant to dictate any one particular approach but rather provide an avenue for obtaining the answer.
We have decided on producing hand worked solutions as opposed to typeset solutions so that the natural flow of the solution process can be more readily observed. It was important to have number of different authors involved in this project, each lending their own style and approach to solving problems addressed and which is of relevance to both teacher and studentThis resource is a full colour PDF photocopy master and is priced as such. Purchase entitles you to make unlimited copies for use within your institution. You will receive a copy of a pdf by email within 24 hours after your payment is processed.
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A software to calculate expression, roots, extremum, derivateve, integral, etc.Features: Math Calculator is an expression calculator. You can input an expression including variable x, for example, log(x), then input a valueof x; You can also input an expression such as log(20) directly.Math Calculator is an equation solver Math Calculator can be used to solve equations with one variable, for example, sin(x)=0. Math Calculator is a function analyzer Math Calculator has the abilities of finding maximum and minimum.Math Calculator is a derivative calculator and calculus calculator. You can use this program to calculate derivative and 2 level derivate of a given function.Math Calculator is an integral calculator. Math Calculator has the ability of calculating definite integral
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Problem Solving and Word Problem Smarts!
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Are you having trouble with math word problems or problem solving? Do you wish someone could explain how to approach word problems in a clear, simple way? From the different types of word problems to effective problem solving strategies, this book takes a step-by-step approach to teaching problem solving. This book is designed for students to use alone or with a tutor or parent, provides clear lessons with easy-to-learn techniques and plenty of examples. Whether you are looking to learn this information for the first time, on your own or with a tutor, or you would like to review some math skills, this book will be a great choice.
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MATHEMATICS AT EUREKA
Mathematics, more than any other human endeavor, relies on deductive reasoning to produce new knowledge from the investigation of natural events, whether they occur in our immediate environment or in the immensity of space. It serves as a universal language which represents, interprets, and integrates all such knowledge.
The subject of mathematics is divided into algebra, geometry, analysis, and probability. Some of the concepts of each of these subdivisions are particularly useful in helping to discuss or solve problems in other fields. These concepts are frequently called Applied Mathematics.
REQUIREMENTS FOR A MAJOR IN MATHEMATICS –
38 hours of coursework, consisting of the following:
All of the following:
MAT171
Calculus with Analytic Geometry I
4
MAT271
Calculus with Analytic Geometry II
4
MAT272
Calculus with Analytic Geometry III
4
MAT275
Differential Equations
3
MAT280
Discrete Mathematics
3
MAT310
Probability and Statistics
3
MAT315
Linear Algebra
3
MAT320
Abstract Algebra
3
MAT340W
Foundations of Geometry
3
MAT415
Real Analysis
3
S&M286
Problem Solving in Science & Mathematics
2
One of the following:
CSC135
Computer Science I
3
CSC165
Computer Science II
3
TOTAL:
38
REQUIREMENTS FOR A MINOR IN MATHEMATICS –
20 hours of coursework in Mathematics numbered 171or above, including at least six hours at the 300-level or higher.
REQUIREMENTS FOR A MAJOR IN MATHEMATICS WITH TEACHER CERTIFICATION –
42 hours of coursework, consisting of the following:
1. The Mathematics major outlined above.
2. One additional course from the following: PHS110 (Introduction to Physical Science), PHS111 (Introduction to Earth Science), or any PHY course
Plus Professional Education Course Requirements. For a list of these courses, please refer to the Education section of the catalog concerning requirements for certification in Secondary Education. To qualify for Student Teaching, a student must have a cumulative 2.50 GPA and a 2.75 GPA in the Mathematics major outlined above.
REQUIREMENTS FOR A MAJOR IN ELEMENTARY EDUCATION WITH A MATHEMATICS SPECIALIZATION –
28 hours of coursework. Please refer to the Education section of this catalog for a listing of required courses.
Get to Know...
Mrs. Rachel Gudeman
Lecturer in Mathematics. Mrs. Gudeman received her B. S. from Illinois State University, and is currently attaining her M.S. in Mathematics from Illinois State University. She has taught all levels of highschool mathematics especially for the home-schooled population. She has taught at Eureka College since Fall 2012. Mrs. Gudeman enjoys teaching and helping students learn and understand mathematics in order to achieve their goals and earn a college degree.
Mrs. Elisha VanMeenen
Lecturer in Mathematics. Mrs. VanMeenen received her B. S. in Mathematics from Illinois Wesleyan University, M.B.A. from the University of Illinois, M.S. in Mathematics from Illinois State University, and is currently working on her Ph.D. in Mathematics Education from Illinois State University. She teaches full time at ISU, and is in her third semester teaching part-time general education mathematics for Eureka College. She is interested helping students learn and understand mathematics in order to achieve their goals and earn a college degree.
Mr. Kevin Brucker
Lecturer in Mathematics, came to Eureka College in 2004. His teaching focuses on Statistics and Mathematics for Elementary Teachers. He holds a B.S. in Mathematics from McKendree College and an M.A.S. (Master of Applied Statistics) from The Ohio State University. In addition to his teaching duties, Mr. Brucker works as the Teacher Education Assessment Coordinator and Transfer Advisor.
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Grades 6-8 Math
The goal of the Mathematics Department at the Carmel Campus The goal is that the students, not the teacher or a textbook, be the source of mathematical knowledge. As a result, each student is able to thrive at the pace that best suits them to reach their fullest potential mathematically. Therefore, our students are also then best prepared for entry into Stevenson's Pebble Beach Campus.
To accomplish these goals, we schedule math at the same time each day for K-5. We use a highly individualized approach to teaching math in grades 6-8 that has benefits well beyond antiquated tracking approaches to teaching math. We
We see the following tenets as essential to our curriculum:
that algebra is important as a modeling and problem-solving tool, with sufficient emphasis placed on technical facility to allow conceptual understanding;
that geometry in two and three dimensions be integrated across topics at all levels and include coordinate and transformational approaches;
that the study of vectors, matrices, counting, data analysis, and other topics from discrete mathematics be woven into core courses;
that computer-based and calculator-based activities be part of our courses;
that all topics be explored visually, symbolically, and verbally;
that developing problem-solving strategies depends on an accumulated body of knowledge.
The curriculum is problem-centered rather than topic-centered. The purpose of this format is to have students continually encounter mathematics set in meaningful contexts, enabling them to draw, and then verify, their own conclusions.
Our As a result, each student is able to thrive at the pace that best suits them to reach their fullest potential mathematically. The teachers provide individual assessment throughout the year for every student, thus helping to foster skills and content mastery that are unique and relative to every student.
Class Web Pages
See what's happening this year in grades PK-8 by viewing the individual class web pages.
Information Request
Request a complete information packet for the Carmel Campus. We will send you an informational viewbook, as well as an application for admission.
You many arrange a parent tour and a student school visit as part of the formal application process.
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Book Description: Math Solutions Publications, United States, 2009. Paperback. Book Condition: New. 2nd. 234 x 188 mm. Brand New Book. This best seller offers an unparalleled look at the significant role that classroom discussions can play in teaching mathematics and deepening students' mathematical understanding. Based on a four-year research project funded by the U.S. Department of Education, the second edition includes more examples of classroom talk focusing on pre-algebra and early grade levels; an expanded range of vignettes; chapter-ending discussion questions for book study groups; connections to NCTM's Principles and Standards for School Mathematics; and an index of every mathematical and Standards for School Mathematics; and an index of every mathematicalexample used, classified by grade level and mathematical emphasis. Bookseller Inventory # AAC9781935099017
Book Description: Paperback. Book Condition: New. 2nd. 188mm x 23mm x 234mm. Paperback. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 286 pages. 0.612. Bookseller Inventory # 9781935099017
Book Description: Math Solutions, 2009. Paperback. Book Condition: New. 18.42 x 22.86 cm. Our orders are sent from our warehouse locally or directly from our international distributors to allow us to offer you the best possible price and delivery time. book. Bookseller Inventory # 20394125
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Elementary statistics using Excel
Synopses & Reviews
Book News Annotation:
A text/CD-ROM introduction to basic statistics, placing strong emphasis on understanding concepts of statistics, with Excel included throughout as the key supplement. Offers detailed Excel instructions, and 125 samples of Excel displays, plus many pedagogical features. Can be used for students who have completed an elementary algebra course, majoring in fields such as social sciences, education, engineering, and communications. The CD-ROM contains an add-in that expands the capacity of Excel, the statistical package STATDISK, and data sets formatted for Excel and STATDISK. Triola teaches mathematics at Dutchess Community College. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Description:
System requirements: PC or Macintosh. Includes bibliographical references (p. 833
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COURSE OUTLINE
Course Outline
Institution: Clackamas Community College
Course Title: Algebra II
Course Prefix / #: Mth 065
Type of Program: Developmental
Credits: 4
Date: July 1, 2008
Outline Developed by: Mark Yannotta and Louis Kaskowitz
Course Description: A second course in a three-term sequence in introductory algebra, this course incorporates
the rule-of-four approach for functions as they are explored numerically, symbolically,
graphically, and verbally. Other course topics include properties of exponents, polynomials,
factoring, quadratic equations, two by two systems of linear equations, and one-variable
equations and inequalities.
Length Of Course: 42 lecture hours
Grading Criteria: Letter grade or Pass/No Pass.
Prerequisites: Pass Mth 060 with a C or better, or appropriate placement score
rd
Required Material: Elementary and Intermediate Algebra: A Unified Approach (3 ed.), Baratto, S. & Bergman, B.
(2008) accompanied with MathZone.
(ISBN-10: 0-073-30931-1) A graphing calculator (TI-83 or 84 series) is required.
Course Objectives: This course will foster an understanding of function sense, linear and quadratic functions,
systems of two linear equations, linear equations and inequalities, polynomial expressions and
functions, properties of exponents and applications of these topics.
Student Learning The student will be able to:
Outcomes:
Determine the equation that defines a function.
Write the equation to define a function.
Determine the domain and range of a function.
Identify the independent and the dependent variables of a function.
Use the slope/intercept form of an equation of a line.
Compare the slopes of lines.
Write an equation of a line in general form.
Write the slope-intercept form of a linear equation given the general form.
Solve a 2 by 2 linear system of equations.
Interpret and solve an application using a linear system of equations.
Identify polynomial expressions and functions.
Add and subtract polynomial expressions and functions.
Multiply two binomials using the FOIL method.
Multiply two polynomial functions.
Apply property of exponents to multiply powers having the same base.
Compose two functions symbolically and numerically
Convert scientific notation to decimal notation.
Convert decimal notation to scientific notation.
Apply the property of exponents to divide powers having the same base.
Use zero and negative real numbers as exponents.
Identify quadratic functions.
Solve equations in one variable graphically.
Solve linear inequalities graphically.
Factor expressions with a common factor.
Factor trinomials using the trial and error or the "ac" method.
Use the zero-product principle and factoring to solve equations.
Analyze a model contextually.
Major Topic Outline: Properties of exponents
Rules for working with integer exponents and scientific notation
Polynomials
Identifying, classifying, evaluating, adding, subtracting, and multiplying polynomials
Factoring
Factoring techniques such as greatest common factor, special cases, factoring trinomials
using either trial and error or the "ac" method, and factoring by grouping
Functions
Domain, range, function representations, polynomial expressions and functions, addition
and subtraction of polynomial expressions and functions, multiplication of polynomial
expressions and functions, multiplication of powers having the same base, and function
composition
Systems of Linear Equations
Algebraic methods such as substitution and elimination (addition) and graphical methods
for solving 2 by 2 systems
Linear equations and linear inequalities
Graphical methods for solving one-variable equations and inequalities
Suggested timeline: CLASS HOURS TOPIC
4 Properties of exponents
6 Polynomials
6 Factoring
8 Functions
6 Systems of Linear Equations
4 Linear equations and linear inequalities
8 Assessments / Final Exam
42
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Summary of Content: This module provides a basic course in differential and integral calculus. Initially key elements of definition, manipulation and graphical representation of functions are introduced prior to establishing calculus techniques used in the analysis of problems in engineering and physical sciences. Application to solving real life problems is developed. The module will cover:
Activities may take place every teaching week of the Semester or only in specified weeks. It is usually specified above if an activity only takes place in some weeks of a Semester
Further Activity Details: Each week a three hour session will be used flexibly between lecture activities, example and supervised tutorial sessions. Workshop activities will involve problem solving exercises and assessment activities. Use will be made of e-learning courseware, computer assisted assessment and software packages to be completed by each student through self-directed study.
Method of Assessment:
Assessment Type
Weight
Requirements
Exam 1
15
1 hour written exam, Autumn
Assignment
15
Assignments (in-class or take home)
Exam 2
60
2.5 hours written exam, Spring
Inclass Exam 1 (Written)
10
In-class test (OMR)
Convenor:
Mr F Hobbs
Education Aims: To provide students with the confidence, mathematical knowledge and fluency in mathematical techniques to help solve basic problems, in engineering or science, that requires the use of differential or integral calculus.
Learning Outcomes:
A student who completes this module successfully should be able to:
Knowledge and understanding
manipulate graphical representation of standard and more general functions;
differentiate standard functions and more complicated functions;
find and classify local stationary points;
use Maclaurin series to represent simple functions;
integrate standard functions;
use standard analytical integration techniques;
apply calculus to modelling basic physical problems;
use approximation to find roots of algebraic or trigonometric equations.
Intellectual skills
reason logically and work analytically;
perform with high levels of accuracy;
manipulate mathematical formulae, algebraic equations and standard functions;
apply fundamental mathematical concepts to problems of a routine nature in engineering or science.
Professional skills
construct and present mathematical arguments with accuracy and clarity;
apply basic solution techniques learned to mathematical problems arising in the study of engineering or science.
Transferable skills
communicate mathematical arguments using standard terminology;
express ideas and methods of solution in the analysis of mathematical problems appropriately and effectively;
use an integrated software package to enhance learning and practice problem solving skills.
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La Honda PrecalculusIt is also an essential step on the path to understanding science. In elementary mathematics, the student begins to learn how to think mathematically and correctly interpret data. To be an effective student, it is important to have a complete set of tools in your student "toolbox." These tools...
...I also helped fellow students during the course. Object Oriented Programming, OOP, has classes, inheritance (single, or multiple), encapsulation, methods, members and many other buzzwords. There are other paradigms, like procedural, and functional
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