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Taking Algebra? Take Some Time to Brush up on Pre-Algebra
Algebra is a great subject, however, initially many students struggle with the concept. Perhaps because, it's their first attempt at abstract math. A great grounding in Algebra means having confidence in pre-algebra. Here are a few resources to support you:
Understand integers and using the properties of adding, subtracting, multiplying and dividing them with this cheat sheet.
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My 14 year old son has been engaging in the high school math curriculum, Math 911, for the last month.
Math 911 Courses Include:
Introductory Algebra – FREE version available
Intermediate Algebra
College Algebra
Trigonometry
Pre Calculus
Math 911 uses a mastery approach which means your student will never be graded for any wrong answers, they will continue to work on the same problem until they master the problem with the correct answer. Each topic is organized by chapter, section, and levels. Each level teaches the student different types of problems within that concept.
Another plus Math911 does not require a textbook!
How it Worked for My Son
My son has been doing very well in the intermediate algebra course. He usually completes a section per day except when a section is rather long.
He works out the problems on a piece of scrap paper and plugs in his answer into the answer box.
On several occasions his answer was marked wrong when indeed it was correct. There appears to be some glitch in the software program. The program would state his answer was wrong, but showed the correct answer being the same as my sons. This was very frustrating to my son. However, it only happened a few times. The software program itself is very primitive in nature. I believe by upgraded to a more sophisticated software program and website would be more pleasing to the eye and perhaps would be a more popular high school math curriculum among the homeschool community.
By working on the problem step by step until his solution was correct was a huge benefit to my son. He really appreciated the mastery approach to the Math 911 software.
Buy It
Order Math911 now at the special low student special price of $49.95. Save $150, off the regular price of $199.95, but hurry and order before: September 13th!
I received this product free for the sole purpose of reviewing it in exchange for my honest opinion. I received no other compensation. Your experience may vary. Please read my full disclosure policy for more details.
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Introduction Math Mammoth Algebra 1-A Worksheets Collection was originally created for and in collaboration with SpiderSmart, Inc. tutoring company.
HCPS Algebra 1 Curriculum Guide Introduction Mathematics content develops sequentially in concert with a set of processes that are common to different bodies of mathematics ...
Acknowledgements We would like to thank the following Roanoke County educators for their work in developing the curriculum guide. Jennifer Dunford, William Byrd High ... I/CurriculumGuide.pdf
Description and Objective Create an advertisement for one of the methods for solvingsystems of linear equations. These methods are described in detail at www. mathwarehouse ...
1) Students will be able to use readily available technology to solve systems of linear equations. 2) Understand the meaning of u0022system of linear equationsu0022 and be ...
APPLICATIONS OF MATH 11 HOMEWORK OUTLINE Record the date when each section is assigned Record a check mark ( ) when the homework is complete you must SHOW YOUR ... documents/11 apps Hmwk Outline.pdf
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General AAS
Maths for Chemists Volume II: Power Series, Complex Numbers and Linear Algebra builds on the foundations laid in Volume I, and goes on to develop more advanced material. The
Pat McKeague's passion and dedication to teaching mathematics and his ongoing participation in mathematical organizations provides the most current and reliable textbook for both instructors and students. Pat McKeague's main goal is to write a textbook that is user-friendly. Students are able to develop a thorough understanding of the concepts essential to their success in mathematics because of his attention to detail, exceptional writing style, and organization of mathematical concepts. The Fifth Edition of Intermediate Algebra: Concepts and Graphs is another extraordinary textbook with exceptional clarity and accessibility.
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Browse By Age
The Art of Problem Solving: Exceptional Distance Education in Math
Over the years, the phrase 'gifted' has acquired legitimacy and adoption as an adjective to refer to legions of children who, simply stated, are considerably above average on various dimensions and metrics associated with the credible measure of intelligence. One popular dimension for measuring such 'giftedness' has come to be the academic ability, performance, and appetite of talented and motivated students.
Mainstream schools around the world have historically been woefully inadequate in catering to the needs of students with high academic ability; and given extra resources almost always opt to support the needs of the "below-average" students. As a result, private and non-profit enterprise has created an industry around the needs of gifted students – to help such students realize their potential without being forced to crawl at the pace of the others in the classroom at the middle or left of the bell curve. For the most part, such products and services have assumed the flavor of supplemental and accelerated instruction in various academic disciplines. Two programs that enjoy robust parental and student following are Stanford's EPGY and John Hopkins University's CTY. This editorial feature provides specific detail on a third program of considerable merit.
The Art of Problem Solving (AoPS) was founded in 2003 by a young mathematician, bond trader and Princeton graduate, Richard Rusczyk, who after tiring of the repetitive din of the trading floor at D.E. Shaw decided to return to his passion of teaching and coaching young minds in math and its wonders. Over the years, Richard achieved 3 things in tandem that are difficult enough to achieve in isolation. First, he convinced some exceptional mathematicians to dedicate their professional lives to sparking a keen interest for math in kids . Second, he and his team conceived of and created an exceptional stack of online courses in middle school and high school mathematics that reflected the virtues of holistic math instruction. Third, he and his team created an enduring stack of textbooks to go with their course stack. The books are written with a clarity and lucidity that makes them almost easy to view as self-sufficient courses in mathematics. It would require almost savage incompetence on the part of a teacher or the school system to adulterate the purity and impact of these books.
Over the years, Richard and his team have made it uber cool and entertaining for tens of thousands of young minds to plunge into math and pursue it with a degree of abandon. There are 2 enabling factors that have made this a reality. Firstly, AoPS has an agenda and operation that is completely devoid of the distractions that plague most educational institutions. Their single-point agenda is math instruction of the highest quality with complete focus on the student's needs. Theirs is a world untrammeled by the vagaries, vicissitudes, instructional deficiencies and pontification of a traditional school system. The second factor is the almost unreal pedigree and consequent effectiveness of the AoPS faculty, each and every one of whom spends a substantive amount of time teaching. The AoPS faculty, drawn from the alumni ranks of MIT, Princeton, Carnegie Mellon and other intellectual strongholds is good enough for them to make unnecessary any measure of obfuscation or opacity on the all important question for a prospective student- 'how good are the people I am going to learn from?'. Rarely is such transparency forthcoming from administrators of other organizations. Every faculty member is a past winner of various math competitive events, and contributes actively to the authoring of AoPS' next generation of textbooks. AoPS supplements its star faculty with teaching assistants who are drawn from similar gene pools at MIT/Princeton/Harvard/Stanford and other meccas of learning.
There are 4 knockout punches that make this the Rolls Royce of math programs.
1. The courses and books follow a relentlessly inquiry and discovery based approach to problem solving. This almost makes it incidental that the subject on tap is Math. The essential skill being taught by this remarkable team is problem solving.
2. They have learned to use, with clinical precision, online instruction without the trappings of a classroom, even without the audio component of a traditional virtual classroom. This has literally and figuratively simply cut out the noise from their classes. It also gives AoPS the latitude to hire the best from around the world; the physical location of a faculty member is irrelevant.
3. There is a rare intellectual generosity that accompanies AoPS' offerings. AoPS provides highly affordable access to its repository of problem sets and related content through its books and classes. Their adaptive learning system Alcumus, currently freely available to any registered user, is a large repository of selected problems graded by complexity.
4. Lastly, their classes and books are both priced to be effectively less than half that of the competition. In particular, their excellent catalog of books cost less than half of the weighty and colorful math tomes that feature on Amazon and other catalogs, and are recommended by other math programs.
In addition to a stack of courses that correspond to traditional Math areas, AoPS provides focused training for Math competitive events. As such, competitive events of any kind are not for every child, but for those children seeking to match their wits and stamina with a peer group, AoPS is unmatched as a coach for such events. AoPS has a dedicated deck of courses to aid preparation for such events.
AoPS follows through on a simple but frequently ignored ingredient of business building; they have a product that is significantly better in quality and lower in price than that of the competition. Simply put, they give your child an unfair advantage in Math.
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Comments
[...] June 27, 2009by SmartBean no comments e-mail print (0)Rate it!16 views As an adjunct to a SmartBean feature on Art of Problem Solving (AopS), here is a comparative review of AoPS, EPGY and CTY on a set of dimensions ranging from cost to [...]
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Integrated Algebra Regents Buddy 1.0
Integrated Algebra Regents Buddy is the ultimate tool for learning Integrated Algebra. This app was designed by a teacher who has used all possible multimedia resources in the classroom for teaching regents curriculum. Integrated Algebra Buddy is not only an app for learning Integrated Algebra but also a app for teachers. The features of this app makes studying extremely convenient. The features of this app include everything you need to prepare for the integrated algebra regents exam.This app provides 1. Integrated
Algebra lessons about all topics below. 2.Includes interactive regents fun quizzes about each topic 3. Daily news feeds about physics and the universe 4. Regents exams and keys.5. Flash cards by topicTopics1. Number Theory 2. Operations3. Variables and Expressions4. Equations and Inequalities 5. Patterns, Functions, and Relations6. Trigonometric Functions7. Coordinate Geometry8. Shapes 9. Measurement10. Working with Data11. ProbabilityThis app would be ideal for classrooms with iPads because it has the resources to prepare for a regents or to present a lesson. All the regents buddy apps are available on the app store and have been helping teachers and students since their release.
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1.1 Make conjectures by observing patterns and identifying properties, and justify the reasoning.
1.2 Explain why inductive reasoning may lead to a false conjecture.
1.3 Compare, using examples, inductive and deductive reasoning.
1.4 Provide and explain a counterexample to disprove a given conjecture.
1.5Prove algebraic and number relationships such as divisibility rules, number properties, mental mathematics strategies or algebraic number tricks.
1.6 Prove a conjecture, using deductive reasoning (not limited to two column proofs). 1.7 Determine if a given argument is valid, and justify the reasoning.
1.8 dentify errors in a given proof; e.g., a proof that ends with 2 = 1.
1.9 Solve a contextual problem that involves inductive or deductive reasoning.
(It is intended that this outcome be integrated throughout the course
by using sliding, rotation, construction, deconstruction and similar puzzles
and games.)
2.1 Determine, explain and verify a strategy to solve a puzzle or to win a game; e.g.,
guess and check
look for a pattern
make a systematic list
draw or model
eliminate possibilities
simplify the original problem
work backward
develop alternative approaches.
2.2 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game.
2.3 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.
3.1 Compare and order radical expressions with numerical radicands.
3.2 Express an entire radical with a numerical radicand as a mixed radical.
3.3 Express a mixed radical with a numerical radicand as an entire radical.
3.4 Perform one or more operations to simplify radical expressions with numerical or variable radicands.
3.5 Rationalize the monomial denominator of a radical expression.
3.6 Identify values of the variable for which the radical expression is defined.
4.1 Determine any restrictions on values for the variable in a radical equation.
4.2 Determine, algebraically, the roots of a radical equation, and explain the process used to solve the equation.
4.3 Verify, by substitution, that the values determined in solving a radical equation are roots of the equation.
4.4 Explain why some roots determined in solving a radical equation are extraneous. 4.5 Solve problems by modelling a situation with a radical equation and solving the equation.
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Today's Developmental Math students enter college needing more than just the math, and this has directly impacted the instructor's role in the classroom. Instructors have to teach to different learning styles, within multiple teaching environments, and to a student population that is mostly unfamiliar with how to be a successful college student. Authors Andrea Hendricks and Pauline Chow have noticed this growing trend in their combined 30+ years of teaching at their respective community colleges, both in their face-to-face and online courses. As a result, they set out to create course materials that help today's students not only learn the mathematical concepts but also build life skills for future success. Understanding the time constraints for instructors, these authors have worked to integrate success strategies into both the print and digital materials, so that there is no sacrifice of time spent on the math. Furthermore, Andrea and Pauline have taken the time to write purposeful examples and exercises that are student-centered, relevant to today's students, and guide students to practice critical thinking skills. Beginning Algebra and its supplemental materials, coupled with ALEKS or Connect Math Hosted by ALEKS, allow for both full-time and part-time instructors to teach more than just the math in any teaching environment without an overwhelming amount of preparation time or even classroom time.
Chapter S: Strategies to Succeed in Math
S.1 Time Management and Goal Setting
S.2 Learning Styles
S.3 Study Skills
S.4 Test Taking
S.5 Blended and Online Classes
Chapter 1: Real Numbers and Algebraic Expressions
1.1: The Set of Real Numbers
1.2: Fractions Review
1.3: The Order of Operations, Algebraic Expressions, and Equations
1.4: Addition of Real Numbers
Piece it Together 1.1-1.4
1.5: Subtraction of Real Numbers
1.6: Multiplication and Division of Real Numbers
1.7: Properties of Real Numbers
1.8: Algebraic Expressions
Chapter 1 Group Activity
Chapter 1 Summary
Chapter 1 Review Exercises
Chapter 1 Test
Chapter 1 Cumulative Review
Chapter 2: Linear Equations and Inequalities in One Variable
2.1: Equations and Their Solutions
2.2: The Addition Property of Equality
2.3: The Multiplication Property of Equality
2.4: More on Solving Linear Equations
Piece it Together 2.1-2.4
2.5: Formulas and Applications from Geometry
2.6: Percent, Rate, and Mixture Problems
2.7: Linear Inequalities in One Variable
Chapter 2 Group Activity
Chapter 2 Summary
Chapter 2 Review Exercises
Chapter 2 Test
Chapter 1-2 Cumulative Review
Chapter 3: Linear Equations in Two Variables
3.1: Equations and the Rectangular Coordinate System
3.2: Graphing Linear Equations
3.3: The Slope of a Line
Piece it Together 3.1-3.3
3.4: More about Slope
3.5: Writing Equations of Lines
3.6: Functions
Chapter 3 Group Activity
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Test
Chapter 1-3 Cumulative Review
Chapter 4: Systems of Linear Equations and Inequalities in Two Variables
4.1: Solving Systems of Linear Equations Graphically
4.2: Solving Systems of Linear Equations by Substitution
4.3: Solving Systems of Linear Equations by Elimination
Piece it Together 4.1-4.3
4.4: Applications of Systems of Linear Equations
4.5: Linear Inequalities in Two Variables
4.6: Systems of Linear Inequalities in Two Variables
Chapter 4 Group Activity
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Test
Chapter 1-4 Cumulative Review
Chapter 5: Laws of Exponents and Polynomial Operations
5.1: The Product and Power Rule for Exponents
5.2: The Quotient Rule and Zero and Negative Exponents
5.3: Scientific Notation
5.4: Addition and Subtraction of Polynomials
Piece it Together 5.1-5.4
5.5: Multiplication of Polynomials
5.6: Special Products
5.7: Division of Polynomials
Chapter 5 Group Activity
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Test
Chapter 1-5 Cumulative Review
Chapter 6: Factoring Polynomials and Polynomial Equations
6.1: Greatest Common Factor and Grouping
6.2: Factoring Trinomials
6.3: More on Factoring Trinomials
Piece it Together 6.1-6.3
6.4: Factoring Binomials
6.5: Solving Quadratic Equations and Other Polynomial Equations by Factoring
6.6: Applications of Quadratic Equations
Chapter 6 Group Activity
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Test
Chapter 1-6 Cumulative Review
Chapter 7: Rational Expressions and Equations
7.1: Rational Expressions
7.2: Multiplication and Division of Rational Expressions
7.3: Addition and Subtraction of Rational Expressions with Like Denominators and the Least Common Denominator
7.4: Addition and Subtraction of Rational Expressions with Unlike Denominators
Chapter 1-9 Cumulative Review
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Damon Prealgebra hel...A branch of mathematics that substitutes letters for numbers. An algebraic equation represents a scale, what is done on one side of the scale with a number is also done to the other side of the scale. The numbers are the constants.
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Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. It includes a CD-ROM which contains executable Windows XP programs for the PC and which demonstrates how these programs can be used to... more...
An accessible and practical introduction to wavelets With applications in image processing, audio restoration, seismology, and elsewhere, wavelets have been the subject of growing excitement and interest over the past several years. Unfortunately, most books on wavelets are accessible primarily to research mathematicians. Discovering Wavelets presents... more...
X and the City , a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow through... more...
The principal aim of this book is to introduce university level
mathematics both algebra and calculus. The text is suitable for
first and second year students. It treats the material in depth, and
thus can also be of interest to beginning graduate students. more...... more...
A clear exposition of the flourishing field of fixed point theory. Most of the main results and techniques are developed, together with applications in analysis. Researchers and graduate students in applicable analysis will find this to be a useful survey of the fundamental principles of the subject. more...
Provides an accessible introduction to measure theory and stochastic calculus, and develops into an excellent users' guide to filtering. A complete resource for engineers, or anyone with an interest in implementation of filtering techniques. Three chapters concentrate on applications from finance, genetics and population modelling. Also includes exercises. more...
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Selectsoft Publishing Speedstudy: Geometry
THIS ITEM IS DISCONTINUED
Limited Stock May Be Available, Call Us For Availability (800) 527-7638
Please Note: Pricing and availability are subject to change without notice.
Improve grades and test scores! Multimedia learning system makes even the toughest math concepts come alive. Build geometry skills fast! Speedstudy: Geometry provides a solid educational foundation that will raise grades and test scores and improve math skills in the classroom and beyond. Boost grades and test scores! Using step-by-step animations, real-time quizzes and a fun 3-D interface, Speedstudy Geometry gives students the tools they need to master key geometry concepts. Take the stress out of high school math! The curriculum-based lessons are designed by educators to help students understand and practice critical thinking and problem-solving skills in an engaging, interactive learning environment.
Topics include: Equality and Similarity, Circles, Polygons, Points, Area Angles, Vectors, Circumference, Coordinate and Space Geometry, Non-Euclidean Geometry, Planes Reasoning.
Features: Includes search, bookmark, and print functions. Features animation, sound and narration. Review quizzes and tests provided for each chapter.
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About the Math Center
The Math Center, located in LIB 101, is the place to go for help with math homework and to meet with a tutor. The Math Center is staffed by students with math expertise in a number of subjects, ranging from basic math thru calculus. The Math Center Operates Homework Help Sessions every week as well as scheduled workshops on select math topics.
Homework Help Sessions
These sessions are scheduled to provide walk in assistance for students while they are completing thier homework assignments. Each week several hours are dedicated to Homework Help. If you need ongoing or more intensive help, you should schedule an appointment with a tutor. Homework Help is for students enrolled in MATH 030, MATH 060, MATH 101S, MATH 102, MATH 109, MATH 110, and MATH 123.Homework Helpis conducted in the Math Center (LIB 101).
Monday – Thursday
3 – 7 pm
Monday Math Help
Every Monday, Math Specialists and tutors hold problem solving sessions to help students in MATH 101S. This time is dedicated to helping students learn to (algebra) problem solve. Participants are assigned to work out challening problems so that they may discover the proper steps as well as how to work through problems successfully. These sessions, open to students enrolled in MATH 101S, meet in LIB SEM (library 2nd floor).
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Dover's impressive mathematics and science list grows all the time. You won't want to miss any of our latest additions — make sure you visit this page on a regular basis.
To visit our main Math and Science Shop, please click here. And be sure to join our Math and Science Club for a 20% everyday discount, free newsletter, and other exclusive benefits.
Recommendations...
Modern Calculus and Analytic Geometry by Richard A. Silverman Highly readable, self-contained text provides clear explanations for students at all levels of mathematical proficiency. Over 1,600 problems, many with detailed answers. Corrected 1969 edition. Includes 394 figures. Index.
Fourier Series by G. H. Hardy, W. W. Rogosinski Classic graduate-level text discusses the Fourier series in Hilbert space, examines further properties of trigonometrical Fourier series, and concludes with a detailed look at the applications of previously outlined theorems. 1956 edition.
The Green Book of Mathematical Problems by Kenneth Hardy, Kenneth S. Williams Popular selection of 100 practice problems — with hints and solutions — for students preparing for undergraduate-level math competitions. Includes questions drawn from geometry, group theory, linear algebra, and other fields.
Mathematical Methods in the Theory of Queuing by A. Y. Khinchin, D. M. Andrews, M. H. Quenouille Written by a prominent Russian mathematician, this concise monograph examines aspects of queuing theory as an application of probability. Prerequisites include a familiarity with the theory of probability and mathematical analysis. 1960 edition.
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Millbrae StatisticsTherefore, I have experience with many of the areas of discrete math typically encountered in introductory college coursework: set theory, combinatorics, probability theory, matrices and operations research. Actuarial Science is the field of study that utilizes mathematics and statistics in ass...
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As atudents progress in thier educational pathway, more knowledge and skills will be required. This course will foster a development and understanding of mathematics in the real world. Students will acquire skills in adding, subtracting, multiplyuing and diving signed numbers which will include integers. Students will solve multi-step equations involving the real number system and algebraic thinking. Problems solving in this course includes applications of ratios, proportion, fractions, and percents. It continues to develop other important mathematics topics including patterns, functions, gemoetry, measurement, probability, and statistics. It provides hands-on, visuals for students who are below grade level as well as renrichment for advanced students.
Algebra I is intended to build a foundation for all higher math classes. It is the brige from the concrete to the abstract study of mathematics. This course will review algebraic expressions, integers, and mathematical proporties that will lead into working with variables and linear equations. There will be an in-depth study of graphing, polynomials, quadratic equations, data analysis, and systems of equations through direct class instruction, group work, homework, and Fuse (I-pads).
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Book Description: Now you can combine a highly effective, practical approach to mathematics with the latest procedures, technologies, and practices in today's welding industry with PRACTICAL PROBLEMS IN MATHEMATICS FOR WELDERS, 6E. Readers clearly see how welders rely on mathematical skills to solve both everyday and more challenging problems, from measuring materials for cutting and assembling to effectively and economically ordering materials. Highly readable explanations, numerous real-world examples, and practice problems emphasize math skills most important in welding today, from basic procedures to more advanced math formulas and technologies. Readers leave equipped with the strong math tools they need for success in today's welding careers.
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Discover Mathematics Through Investigation In Symmetry, Shape, and Space, geometry is the framework for an introduction to mathematics. The visual nature of geometry allows students to use their intuition and imagination while developing the ability to think critically. The beauty of the material lies in students discovering mathematics as mathematicians do through investigation. Many of the exercises require students to express their ideas clearly in writing, while others require drawings or physical models, making the mathematics a more hands-on experience. The book is written so that each chapter is essentially independent of the others to allow for flexibility. The text activities and exercises can serve as enrichment projects at elementary and secondary levels. Mathematics professionals and educators will enjoy its informal approach and will find the explorations of nontraditional geometric topics such as billiards, theoretical origami, tilings, mazes, and soap bubbles intriguing. A companion Sketchpad Student Lab Manual can be packaged with The Geometer Sketchpad or KaleidoMania at a special price.
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Representation Standard
for Grades 9–12
Instructional
programs from prekindergarten through grade 12 should enable all students
to—
create and use representations to organize, record, and communicate
mathematical ideas;
select, apply, and translate among mathematical representations
to solve problems;
use representations to model and interpret physical, social,
and mathematical phenomena.
If mathematics is the "science of patterns" (Steen 1988), representations are
the means by which those patterns are recorded and analyzed. As students
become mathematically sophisticated, they develop an increasingly large
repertoire of mathematical representations and the knowledge of how to
use them productively. This knowledge includes choosing specific representations
in order to gain particular insights or achieve particular ends.
The importance of representations can be seen in every section of this chapter.
If large or small numbers are expressed in scientific notation, their
magnitudes are easier to compare and they can more readily be used in
computations. Representation is pervasive in algebra. Graphs convey particular
kinds of information visually, whereas symbolic expressions may be easier
to manipulate, analyze, and transform. Mathematical modeling requires
representations, as illustrated in the "drug dosage" problem and in the
"pipe offset" problem. The use of matrices to represent transformations
in the plane illustrates how geometric operations can be represented visually
yet also be amenable to symbolic representation and manipulation in a
way that helps students understand them. The various methods for representing
data sets further demonstrate the centrality of this topic.
p.
360
A wide variety of representations can be seen in the examples in this chapter.
By using various representations for the "counting rectangles" problem
in the "Problem Solving" section, students could find different solutions
and compare them. The use of algebraic symbolism to explain a striking
graphical phenomenon is central to the "string traversing tiles" task
in the "Communication" section. Representations facilitate reasoning and
are the tools of proof: they are used to examine statistical relationships
and to establish the validity of a builder's shortcut. They are at the
core of communication and support the development of understanding in
Marta's and Nancy's work on the "string traversing tiles" problem. Although
at one level the story of Mr. Robinson's class is about connections, at
another level it is about representation: one group of students places
coordinates that "make things eeeasy," the class gains insights from dynamic
representations of geometric objects, and the students produce proofs
in coordinate and Euclidean geometry. A major lesson of that story is
that different representations support different ways of thinking about
and manipulating mathematical objects. An object can be better understood
when viewed through multiple lenses. »
What should representation
look like in grades 9 through 12?
In grades 9–12, students' knowledge and use of representations should
expand in scope and complexity. As they study new content, for example,
students will encounter many new representations for mathematical concepts.
They will need to be able to convert flexibly among these representations.
Much of the power of mathematics comes from being able to view and operate
on objects from different perspectives.
In elementary school, students most often use representations to reason about
objects and actions they can perceive directly. In the middle grades,
students increasingly create and use mathematical representations for
objects that are not perceived directly, such as rational numbers or rates.
By high school, students are working with such increasingly abstract entities
as functions, matrices, and equations. Using various representations of
these objects, students should be able to recognize common mathematical
structures across different contexts. For example, the sum of the first
n odd natural numbers, the areas of square gardens, and the
distance traveled by a vehicle that starts at rest and accelerates at
a constant rate can be represented by functions of the form f(x) = ax2.
The fact that these situations can be represented by the same class of
functions implies that they are alike in some fundamental mathematical
way. Students are ready in high school to see similarity in the underlying
structure of mathematical objects that appear contextually different but
whose representations look quite similar.
p.
361
High school students should be able to create and interpret models of more-complex
phenomena, drawn from a wider range of contexts, by identifying essential
features of a situation and by finding representations that capture mathematical
relationships among those features. They should recognize, for example,
that phenomena with periodic features often are best modeled by trigonometric
functions and that population growth tends to be exponential, or logistic.
They will learn » to describe some real-world
phenomena with iterative and recursive representations.
Consider the graph of the concentration of CO2
in the atmosphere as a function of time and latitude during the period
from 1986 through 1991 (see fig. 7.39) (Sarmiento 1993). Teachers might
use an example such as this to help students understand and interpret
several aspects of representation. Students could discuss the trends in
the change in concentration of CO2 as
a function of time as well as latitude. Doing so would draw on their knowledge
about classes of functions and their ability to interpret three-dimensional
graphs. They should be able to see a roughly linear increase across time,
coupled with a sinusoidal fluctuation with the seasons. Focusing on the
change in the character of the graph as a function of latitude, students
should note that the amplitude of the sinusoidal function lessens from
north to south. Students can test whether the trends they observe in the
graph correspond to recent theoretical work on CO2
concentration in the atmosphere. For example, the author of the article
attributes the sinusoidal fluctuation to seasonal variations in the amount
of photosynthesis taking place in the terrestrial biosphere. Students
could discuss the differences in amplitude across seasons in the Northern
and Southern Hemispheres.
Fig. 7.39. A three-dimensional graph
of the concentration of C02
in the atmosphere as a function of time and latitude (Adapted
from Sarmiento [1993])
Electronic technologies
provide access to problems and methods that until recently were difficult
to explore meaningfully in high school. In order to use the technologies
effectively, students will need to become familiar with the representations
commonly used in technological settings. For example, solving equations
or multiplying matrices using a computer algebra system calls for learning
how to input and interpret information in formats used by the system.
Many software tools that students might use include special icons and
symbols that carry particular meaning or are needed to operate the tool;
students will need to learn about these representations and distinguish
them from the mathematical objects they are manipulating.
What should be the teacher's role in developing representation in grades
9 through 12?
p.
362
An important part of learning mathematics is learning to use the language, conventions,
and representations of mathematics. Teachers should introduce students
to conventional mathematical representations »
and help them use those representations effectively by building
on the students' personal and idiosyncratic representations when necessary.
It is important for teachers to highlight ways in which different representations
of the same objects can convey different information and to emphasize
the importance of selecting representations suited to the particular mathematical
tasks at hand (Yerushalmy and Schwartz 1993; Moschkovich, Schoenfeld,
and Arcavi 1993). For example, tables of values are often useful for quick
reference, but they provide little information about the nature of the
function represented. Consider the table in the "Algebra" section in this
chapter that gives the number of minutes of daylight in Chicago every
other day for the year 2000. The values in the table suggest that the
function is initially increasing and then becomes decreasing. Knowledge
of the context of a graph of those values suggests that the behavior is
actually periodic. Similarly, algebraic and graphical representations
of functions may provide different information. Some global properties
of functions, such as asymptotic behavior or the rate of growth of a function,
are often most readily apparent from graphs. But information about specific
aspects of a function—the exact value of f() or exact values of
x where f(x)has a maximum or a minimum—may best
be determined using an algebraic representation of the function. Suppose
g(x) is given by the equation g(x) = f(x)
+ 1, for all x. The analytic definitions of f(x) and
g(x) may offer the most-effective ways of computing specific
values of f(x) and g(x), but graphing the function
reveals that the "shape" of g(x) is precisely the same as that
of f(x)—that the graph of g(x) is obtained by
translating the graph of f(x) one unit upward.
As in all instruction, what matters is what the student sees, hears, and understands.
Often, students interpret what teachers may consider wonderfully lucid
presentations in ways that are very different from those their teachers
intended (Confrey 1990; Smith, diSessa, and Roschelle 1993). Or they may
invent representations of content that are idiosyncratic and have personal
meaning but do not look at all like conventional mathematical representations
(Confrey, 1991; Hall et al. 1989). Part of the teacher's role
is to help students connect their personal images to more-conventional
representations. One very useful window into students' thinking is student-generated
representations. To illustrate this point, consider the following problem
(adapted from Hughes-Hallett et al. [1994, p. 6]) that might be presented
to a tenth-grade class:
A flight from SeaTac Airport near Seattle, Washington, to LAX Airport
in Los Angeles has to circle LAX several times before being allowed
to land. Plot a graph of the distance of the plane from Seattle against
time from the moment of takeoff until landing.
p.
363
Students could work individually or in pairs to produce distance-versus-time
graphs for this problem, and teachers could ask them to present and defend
those graphs to their classmates. Graphs produced by this class, or perhaps
by students in other classes, could be handed out for careful critique
and comment. When they perform critiques, students get a considerable
amount of practice in communicating mathematics as well as in constructing
and improving on representations, and the teacher gets information that
can be helpful in assessment. One representation of the flight that a
student might produce is shown in figure 7.40. »
Fig. 7.40. A representation that
a student might produce of an airplane's distance from
its take-off point against the time from takeoff to landing
This representation indicates a number of interesting and not uncommon misunderstandings,
in which literal features of the story (the plane flying at constant height
or circling around the airport) are converted inappropriately into features
of the graph (Dugdale 1993; Leinhardt, Zaslavsky, and Stein 1990).
Representations of this type can provoke interesting classroom conversations,
revealing what the students really understand about graphing. This revelation
puts the teacher in a better position to move the class toward a more nearly
accurate representation, as sketched in figure 7.41.
Fig. 7.41. A more nearly accurate
representation of the airplane's distance from its take-off
point against the time from takeoff to landing
Mathematics is one of humankind's greatest cultural achievements. It is
the "language of science," providing a means by which the world around us
can be represented and understood. The mathematical representations that
high school students learn afford them the opportunity to understand the
power and beauty of mathematics and equip them to use representations in
their personal lives, in the workplace, and in further study.
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Teaching Conic Sections
Teaching Conic Sections
So I currently teach a precalc class and new this year we are required to teach conic section.
We cover parabolas, circles, ellipses, and hyperbolas. Since I haven't taught this before, I was wondering if anyone has suggestions on how to teach it? The book we use has a bunch of formulas, but I'm looking for a way to teach it to my students without using all the formulas so they don't have to memorize a bunch of formulas before their exam. What has worked for others?
You should be able to design good lessons directly based on the book sections. As long as you use a Pre-Calculus book you will have rich enough information available.
Be sure to demonstrate the conic sections using a realistic three-dimensional model. Also use the definitions of each conic section and the distance formula to derive the equation for each conic section, and include the analytical cartesian graph for each.
You are right on-target about not just giving a bunch of formulas. The demonstration and the derivations are important for learning and understanding.
Teaching Conic Sections
As a student who struggled through conic sections, I found that by exploring how they were really just variations of the of the same things cemented my understanding of the topic. So if I were in your shoes I would try to show the similarities and differences of the different sections. Specifically between the hyperbola and parabola and the circle and ellipse.
As someone who not long ago learnt Conic Sections, I found the derivations of the formula much easier than remembering them. It was good to see the formulas at first but I much preferred the derivations.
As above said, use a 3D model as well. The 2D drawing didn't really do it justice for me.
I was definitely going to derive the formulas using the distance formula and talk about applications. I wouldn't scratch formulas altogether, but our book has like 8 different formulas, which isn't fair to give all of them to my students if I don't give them on an exam.
Something one of my physics professors said to our class is recalled to me by this thread. He said students of today are so used to tv games, comics, etc. rather than playing with things with their hands, that they can't visualize 3d objects anymore. He was of course exaggerating. I think it quite odd if a student can't visualize what's going on with conic sections, so yes a model would be quite good. Maybe you could get someone to cut it at all the right angles.
Also, the old books on geometry, particularly solid geometry, should be good with conic sections, so maybe go down to the library and have a look at them.
Ah yes, I have a fun experiment using that! You should certainly teach that!
Here it goes: Dandelin was a Belgian, and some people decided to celebrate him. So what they did was the following. They made an ice-cream cone, they put a small biscuit in there (they made it like an ellipse so it would fit inside the cone). And they they put a ball of ice-cream in the cone. Then they would sell it to people.I always tought that it was very clever, and it was quite the financial succes too!did they then discover another, smaller, ice-cream (just like discovering another layer of chocolates when you finish the first layer!), which touched the other focus on the other side of the biscuit?
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Linear Algebra For Dummies
Synopsis
Your hands-on guide to real-world applications of linear algebra
Line up the basics — discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices
Found In
eBook Information
ISBN: 9780470538166
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Course Description
MTH105
Intro - Contemporary Mathematics
- F/W/Sp This course surveys the broad applicability of mathematics as a
problem-solving tool and the breadth of phenomena that mathematics can
model. A wide range of real world problems are examined using the tools of
mathematics. The course focuses on development of mathematical maturity, and
problem-solving. Course topics are selected from probability, statistics,
personal finance, population growth, symmetry, linear programming, fair
division and voting theory. A computer laboratory is required.
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Trigonometry (Quickstudy Reference Guides - Academic)
Book Description: The basic principles of trigonometry are covered in this colorful 4-page guide. Excellent for the beginning student or enthusiast. Topics covered include: trigonometry with triangles trigonometry with an unit circle analytic trigonometry
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300.00
Materials Cost:
None
Total Cost:
$300
Special Notes
State Course Code
02071ometry provides a curriculum focused on the mastery of critical skills and the understanding of key geometric concepts. Through a "Discovery-Confirmation-Practice" based exploration of geometric concepts, students are challenged to work toward a mastery of computational skills, to deepen their conceptual understanding of key ideas and solution strategies, and to extend their knowledge in a variety of problem-solving applications. Course topics include reasoning, proof, and the creation of a sound mathematical argument; points, lines, and angles; triangles; quadrilaterals and other polygons; circles; coordinate geometry; and three-dimensional solids. The course concludes with a look at special topics in geometry, such as constructions, symmetry, tessellations, fractals, and non-Euclidean geometry.
Within each Geometry Geometry assessments include a computer-scored test and a scaffolded, teacher-scored test.
To assist students for whom language presents a barrier to learning or who are not reading at grade level, Geometry includes audio resources in both Spanish and English.
The content is based on the National Council of Teachers of Mathematics (NCTM) standards and is aligned to state standards.
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What I Learned by Teaching Real Analysis
By Fernando Q. Gouvêa
My main mathematical interests are in number theory and the history of
mathematics. So what was I doing teaching Real Analysis? We do that
sometimes, my colleague Ben Mathes and me: I teach Analysis, and he gets to
teach Algebra. We have fun and vary our course assignments a little bit,
and the students get the subliminal message that mathematics is still
enough of a unified whole that people can teach courses in areas other than
their own.
I had taught Colby's Real Analysis course once before. The first time I
teach a new course, I tend to just dive in and see what happens (it went
all right). The second time, however, is when one starts to want to think
about the course. This article is one of the results of that process. It
may be that everything I have to say is well known to anyone who
specializes in analysis; if so, I'm sure they'll write in to tell me
that. Still, maybe I can share a few insights.
Analysis courses can vary a lot, so let me first lay out the bare facts
about our version. Real Analysis at Colby is taken mostly by juniors and
seniors, with a sprinkling of brave sophomores. It is a required course for
our mathematics major, and it has the reputation of being difficult. (This
course and Abstract Algebra contend for the "most difficult" spot.)
The content might best be summarized as "foundations of analysis":
epsilonics, the topology of point sets, the basic theory of convergence,
etc. As the title of a textbook has it, the goal of the course is to cover
"the theory of calculus."
The first thing to do was to choose a textbook. The most common choice at
Colby has been Walter Rudin's classic, Principles of Mathematical
Analysis. It is a hard book for students to read, but reading such
books is a good skill for a mathematics major to acquire, and Rudin's
book repays the effort that students need to put into reading it. There is
a lot of beautiful mathematics in it, and students eventually come to
respect, perhaps even enjoy, the book.
But two serious problems have developed, neither of which is really
Prof. Rudin's fault. The first is the price. Principles is now so
expensive that I feel guilty making students buy a copy. The second is the
internet. Many instructors around the world have used this book, and in the
goodness of their hearts have posted solutions to some of the problems for
their students. They have neglected to set up their sites so that only
their students have access to them, however. As a result, almost any
problem from Rudin's book has a solution online somewhere, and Google
will find it for whoever wants it. Since I want my students to think about
hard problems rather than learn to find their answers online, I decided I
should look for another text.
To my rescue came the MAA Online book review column. Steve Kennedy had
written a glowing review of Understanding Analysis, by Stephen
D. Abbott (you can see it at The
first paragraph of that review went like this:
This is a dangerous book Understanding Analysis is so
well-written and the development of the theory so well-motivated that
exposing students to it could well lead them to expect such excellence in
all their textbooks. It might not be a good idea to create such
expectations. You might not want to adopt this text unless you're
comfortable teaching from a book in which the exposition will nearly always
be clearer than your lectures. Understanding Analysis is perfectly
titled; if your students read it, that's what's going to happen.
And the price is very reasonable. So I decided this would be my textbook. I
also decided to encourage students to buy a supplementary book, and made
two suggestions: A Course of Modern Analysis, by Whittaker and
Watson, and A Primer of Real Functions, by Boas. As I explained to
them, one can't imagine two more different books, and both of them are
also very different from Abbott. Plus, one can buy all three for about the
cost of buying Rudin's Principles.
Now, I make no pretense of having carefully examined the available
textbooks, which is why this isn't a "what's the best textbook"
article. I went with what I knew, and with Steve Kennedy's
recommendation. It worked out pretty well, though next time I'll
probably want to choose different books for the supplement slot.
OK, so we launch into the course itself. Before we start, it is useful to
ask what we want to achieve. The first answer comes easily: we want to
introduce students to epsilon-delta proofs, and to use this technique to
prove all those theorems they took for granted in their calculus
course. But the answer generates questions of its own. Why do this? What do
students gain from such knowledge?
That's easy to answer if your students are likely to be going to
graduate school. But most of my students are not, at least not immediately
or not in mathematics. (A vast majority of Colby students do end up getting
an advanced degree, but that's different from going on to get a Ph.D. in
mathematics.) So the question becomes a little sharper. I decided to take
it for granted that my students wanted to learn mathematics, irrespective
of their future career plans. The sharper question is, then, are
epsilon-delta proofs a crucial thing for them to learn, and, if so,
why?
Now, it's easy to mount an argument that learning this stuff is in fact
not that important. After all, lots of people learn and use sophisticated
mathematics without ever having felt the need to delve into the foundations
of the calculus. Convergence questions can usually be settled by "this
gets small, and that's even smaller" arguments. Turning those into
formal epsilon-delta arguments is a nice party trick, and one that
professional mathematicians have to know how to do, but no one should get
too excited about it.
As a counter to that, let's note that some of my students were planning
to go to graduate school, and they would need to know the trick. And the
course is there in the curriculum, and listed as required. So it must be
important after all. This makes it clear that in order to justify the
formalism of real analysis, one needs to find situations and problems in
which the epsilon-delta approach is essential.
There is, of course, a very famous moment (by no means the only such
moment, but probably the best known) in the history of mathematics that
serves as an example: Cauchy's "proof" that the sum of a series of
continuous functions is continuous. As presented by Cauchy, this is a
classic "this is small, and so is this" argument. And, of course, it
doesn't work, because hidden in the argument is a uniformity
assumption. I decided to use this example (or a simplified version of it)
fairly early on.
Abbott's book turned out to be a good fit, because the author was
clearly worried about similar issues. Each of his chapters begins with an
example where things "go wrong" in ways that can only be understood
by using the formal tools of analysis. Some of these are more convincing
than others, but I was delighted to be using a textbook that noticed that
such examples are crucial to the course.
One of the main threads in the course, then, was the idea of
uniformity. The very definitions of uniform continuity and uniform
convergence require the epsilon-delta formalism, and the notions simply
cannot be understood without it. Over and over, I showed students examples
of things that went wrong because something failed to be uniform, and
showed them how to fix it by adding the uniformity assumption.
To this, I added two other threads, both stolen from articles written by
wiser mathematicians than me. The first was the problem of partitioning the
real numbers into two disjoint sets A and B, and then finding two functions
f and g where f is continuous on A and discontinuous
on B, and g does the reverse. The easiest case is when A is a
singleton set (well, A empty is even easier, I guess), and students are
usually able to push that a little. The case A = Q is the clincher:
in this case the function g exists, but not the function f
(i.e., no function can be continuous at all rational points and
discontinuous at all the irrationals). This follows from a beautiful (and
fairly easy) theorem of Volterra that William Dunham wrote up in an article
for Mathematics Magazine some years ago. (The precise reference is
given below.)
This thread doesn't really connect to the issue of uniformity, but it
fits in well with the point set topology. I also like it because it shows
that not every kind of monster exists. What I mean is this: when students
first start learning point set topology, they get a feeling that things can
get arbitrarily pathological, that anything can be done. Cantor sets and
similar objects tend to reinforce that feeling. Volterra's theorem,
however, shows that in fact not everything can be done, and it does it
without having to introduce something like Baire category theory.
The second added thread is the problem of constructing a "nice"
function that interpolates the factorials. In other words, I posed to
students the question of how one should define x! when x is not an
integer. David Fowler wrote a series of articles for the Mathematical
Gazette on this topic, and I stole his ideas without remorse. For
example, it's easy to construct a continuous function that does the
trick: define x! to be 1 if x is between 0 and 1, and then extend it by
using the functional equation x! = x(x-1)!. Unfortunately, the resulting
function fails to be differentiable. Finding the simplest way to define x!
on [0,1] so that the extended function is differentiable is a nice
exercise. Eventually, of course, we ended up with the Gamma function (on
the reals). To do that, we had to deal with improper integrals depending on
a parameter. (Unfortunately, Abbott doesn't cover improper integrals and
integrals depending on a parameter, so I had to fish this part out from
other texts.) The nice thing is that for most properties of the Gamma
function (continuity, differentiability, etc.) we had to deal with issues
of uniformity again, neatly closing the circle. In fact, "as long as the
convergence is uniform" came up so often in the last few classes that it
became clear to me that this was the core concept I was teaching.
What did my students learn? By the end of the semester they certainly had a
good enough understanding of uniform convergence and of the techniques used
to understand and prove things related to it. I don't know that that
understanding will last very long unless it is reinforced in other
courses. But they did understand, I think, that the difficult formalism of
analysis is there for a reason, and that it is needed if we are to do
interesting things with functions. I don't think they'll forget
that. And that's good enough for me.
|
Mathematics and Computer Science Undergraduate Courses
Mathematics Courses
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This course is designed to promote mathematical literacy among liberal arts students and to prepare students for GSR 104. The approach in this course helps students increase their knowledge of mathematics, sharpen their problem-solving skills, and raise their overall confidence in their ability to learn and communicate mathematics. Technology is integrated throughout to help students interpret real-life data algebraically, numerically, symbolically, and graphically. Topics include calculator skills, number sense, basic algebraic manipulation, solving linear equations, graphing of linear equations, and their applications. Access to mathematics instructional software is provided to support and enhance student learning. A graphing calculator is required.
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This course covers basic operations with algebraic expressions, solving equations in one variable, linear equations and their graphs, linear inequalities, exponents, multiplying and dividing polynomials, and factoring polynomials. Applications are included throughout. Access to mathematics instructional software is provided to support and enhance student learning. A graphing calculator is required.
MAT 55 Intermediate Algebra
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This course covers rational expressions, systems of linear equations in two variables, radicals, and complex numbers, quadratic equations, graphs of quadratic functions, exponential and logarithmic functions. Applications are included throughout. Access to mathematics instructional software is provided to support and enhance student learning. A graphing calculator is required.
Prerequisite:
MAT 045 or equivalent, or a satisfactory score on appropriate placement exam.
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Linear, quadratic, exponential, and logarithmic functions. Ratios, percentages, matrices, and linear programming emphasizing applications to various branches of the sciences, social studies, and management. Credit will not be allowed if student has passed Math 130. This course will not be counted toward a major in the department.
Prerequisite:
MAT 055 or equivalent.
MAT 102 Introductory Probability and Statistics
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Basic concepts of probability and statistics, and applications to the sciences, social sciences, and management. Probability, conditional probability, Bayes Formula, Bernoulli trials, expected value, frequency distributions, and measures of central tendency. Credit will not be allowed for MAT 102 if student has previously passed MAT 130; 102 will not be counted toward a major in the department.
Prerequisite:
MAT 055 or equivalent, or permission of the department chair.
MAT 125 College Algebra
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This course provides a survey of the algebra topics necessary for Calculus. Topics covered include the analysis of graphs of basic functions, transformations of graphs, composition of functions, inverse functions, quadratic functions and their graphs, polynomial and rational inequalities, absolute value inequalities, radicals and fractional exponents, exponential and logarithmic functions and equations, exponential growth and decay problems, and the analysis of circles, parabolas, ellipses, and hyperbolas. MAT 125 consists of the first half of MAT 130. Passing both MAT 125 and 126 is equivalent to passing MAT 130.
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MAT 145 Calculus for Business and Social Sciences
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This course emphasizes the applications of the following topics in Business and Social Sciences: Functions and their graphs, exponential and logarithmic functions, limits and continuity, and differentiation's and integrations in one and several variables. Credit will not be allowed if student has passed MAT 150. This course will not be counted toward a major in the department.
Prerequisite:
MAT 130 or the equivalent.
MAT 150 Calculus I
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Limit processes, including the concepts of limits, continuity, differentiation, and integration of functions. Applications to physical problems will be discussed.
Prerequisite:
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This course is the first part of a two-semester course sequence with MAT 172. This course is designed for prospective early childhood and elementary school teachers. The contents of this course include concepts and theories underlying early childhood and elementary school mathematics. The students will explore the "why" behind the mathematical concepts, ideas, and procedures. Topics include problem solving, whole numbers and numeration, whole numbers operations and properties, number theory, fractions, decimals, ratio and proportion, and integers.
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Prerequisite:
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MAT 195 Special Topics
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Prerequisite:
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This course is the second part of a two-semester course sequence with MAT 313, with a focus on applied statistics. It covers basic statistical concepts, graphical displays of data, sampling distribution models, hypothesis testing, and confidence intervals. A statistical software package is used.
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MAT 313.
MAT 320 History of Mathematics
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A survey of the history of mathematics from antiquity through modern times.
MAT 451 Internship
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This is a one-semester internship in which the student works for at least 60 hours in an applied mathematical or statistical setting under the supervision and guidance of the course instructor and on-site professionals in the field.
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Mathematics major and permission of the instructor.
MAT 455 Advanced Calculus I
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This course is the first part of a two-semester course sequence with MAT 456. This course covers a theoretical approach to calculus of functions of one and several variables. Limits, continuity, differentiability, Reimann integrability, sequences, series, and contour integration.
Prerequisite:
MAT 206, 210, 307.
MAT 456 Advanced Calculus II
(3)
This course is the second part of a two-semester course sequence with MAT 455. This course covers a theoretical approach to calculus of functions of one and several variables. Limits, continuity, differentiability, Reimann integrability, sequences, series, and contour integration.
Prerequisite:
MAT 455.
MATMAT 499 Independent Study
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Intensive supervised study and research on topics of the student's selection.
CSC 150 Computer Programming II
(3)
This course will continue the development of discipline in program design, in style and expression, and in debugging and testing, especially for larger programs. It will also introduce algorithms analysis and basic aspects of string processing, recursion, internal search/sort methods, and simple data structures.
Prerequisite:
A grade of C or better in CSC 130.
CSC 195 Special Topics
(1-5)
Special topics in the discipline, designed primarily for freshmen. Students may enroll in 195 Special Topics multiple times, as long as the topics differ.
Prerequisite:
Permission of the instructor.
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This course gives the organization and structuring of the major hardware components of computers. It provides the fundamentals of logic design and the mechanics of information transfer and control within a digital computer system.
CSCCSC 305 Introduction to File Processing
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CSC 315 Data Structure and Algorithm Analysis
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This course will apply analysis and design techniques to nonnumeric algorithms that act on data structures. It will also use algorithmic analysis and design criteria in the selection of methods for data manipulation in the environment of a database management system.
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CSC 326 Operating Systems and Computer Architecture
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The course will introduce the major concept areas of operating systems principles, develop an understanding of both the organization and architecture of computer systems at the register-transfer and programming levels of system description, and study interrelationships between the operating system and the architecture of computer systems.
Prerequisite:
CSC 150, CSC 315; MAT 140; CSC 202 recommended.
CSC 336 Organization of Programming Languages
(3)
This course will develop an understanding of the organization of programming languages, especially the run time behavior of programs. It will also introduce the formal study of programming language specification and analysis and will continue the development of problem solution and programming skills introduced in the elementary level material.
CSC 341 Software Engineering
(3)
This course will present a formal approach to state-of-the-art techniques in software design and development. It will expose students to the entire software life cycle, which includes feasibility studies, the problem specification, the software requirements, the program design, the coding phase, debugging, testing and verification, benchmarking, documentation, and maintenance. An integral part of the course will be involvement of students working in teams in the development of a large scale software project.
CSC 403 Computer Networking
(3)
The fundamental principles of computer communications. The Open Systems Interconnection Model is used to provide a framework for organizing computer communications. Local area and wide area networks are discussed. The principles of Internetworking are introduced. Communications software is used to illustrate the principles of the course.
Prerequisite:
CSC 150.
CSC 406 Object Oriented Programming
(3)
This course will cover all of the major features of a selected Object Oriented programming language as well as Object Oriented design principles such as: reusability of code, data abstraction, encapsulation, and inheritance.
CSCCSC 499 Independent Study
(1-3)
Intensive supervised study and research on topics of the student's selection.
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Description
In more and more schools, students are now being assessed not only on traditional (algorithmic and computational) math skills, but also on how-and how well-they handle reasoning and problem solving. However, until now, these additional skills have been difficult to assess in an objective, accurate... Expand and efficient way. But not any more. "Comprehensive assessment" includes the traditional paper-and-pencil tests plus relatively new ways (e.g., portfolios, journals, observations, interviews, projects, performance tasks, rubrics) to assess what students know about math, and how they reason, solve problems and communicate about it, This unique new handbook provides everything you need-background information, problems for various grade levels, detailed answers, forms, teaching suggestions-to assess students throughout the semester or at any time...easily, accurately and effectively!
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Measure and Integration. A Concise Introduction to Real Analysis
John Wiley and Sons Ltd, July 2009, Pages: 238
A uniquely accessible book for general measure and integration, emphasizing the real line, Euclidean space, and the underlying role of translation in real analysis
Measure and Integration: A Concise Introduction to Real Analysis presents the basic concepts and methods that are important for successfully reading and understanding proofs. Blending coverage of both fundamental and specialized topics, this book serves as a practical and thorough introduction to measure and integration, while also facilitating a basic understanding of real analysis.
The author develops the theory of measure and integration on abstract measure spaces with an emphasis of the real line and Euclidean space. Additional topical coverage includes:
Measure spaces, outer measures, and extension theorems
- Lebesgue measure on the line and in Euclidean space
- Measurable functions, Egoroff's theorem, and Lusin's theorem
- Convergence theorems for integrals
- Product measures and Fubini's theorem
- Differentiation theorems for functions of real variables
- Decomposition theorems for signed measures
- Absolute continuity and the Radon-Nikodym theorem
- Lp spaces, continuous-function spaces, and duality theorems
- Translation-invariant subspaces of L2 and applications
The book's presentation lays the foundation for further study of functional analysis, harmonic analysis, and probability, and its treatment of real analysis highlights the fundamental role of translations. Each theorem is accompanied by opportunities to employ the concept, as numerous exercises explore applications including convolutions, Fourier transforms, and differentiation across the integral sign.
Providing an efficient and readable treatment of this classical subject, Measure and Integration: A Concise Introduction to Real Analysis is a useful book for courses in real analysis at the graduate level. It is also a valuable reference for practitioners in the mathematical sciences.
Preface.
Acknowledgments.
Introduction.
1 History of the Subject.
1.1 History of the Idea.
1.2 Deficiencies of the Riemann Integral.
1.3 Motivation for the Lebesgue Integral.
2 Fields, Borel Fields and Measures.
2.1 Fields, Monotone Classes, and Borel Fields.
2.2 Additive Measures.
2.3 Carathéodory Outer Measure.
2.4 E. Hopf's Extension Theorem.
3 Lebesgue Measure.
3.1 The Finite Interval [-N,N).
3.2 Measurable Sets, Borel Sets, and the Real Line.
3.3 Measure Spaces and Completions.
3.4 Semimetric Space of Measurable Sets.
3.5 Lebesgue Measure in Rn.
3.6 Jordan Measure in Rn.
4 Measurable Functions.
4.1 Measurable Functions.
4.2 Limits of Measurable Functions.
4.3 Simple Functions and Egoroff's Theorem.
4.4 Lusin's Theorem.
5 The Integral.
5.1 Special Simple Functions.
5.2 Extending the Domain of the Integral.
5.3 Lebesgue Dominated Convergence Theorem.
5.4 Monotone Convergence and Fatou's Theorem.
5.5 Completeness of L1 and the Pointwise Convergence Lemma.
5.6 Complex Valued Functions.
6 Product Measures and Fubini's Theorem.
6.1 Product Measures.
6.2 Fubini's Theorem.
6.3 Comparison of Lebesgue and Riemann Integrals.
7 Functions of a Real Variable.
7.1 Functions of Bounded Variation.
7.2 A Fundamental Theorem for the Lebesgue Integral.
7.3 Lebesgue's Theorem and Vitali's Covering Theorem.
7.4 Absolutely Continuous and Singular Functions.
8 General Countably Additive Set Functions.
8.1 Hahn Decomposition Theorem.
8.2 Radon-Nikodym Theorem.
8.3 Lebesgue Decomposition Theorem.
9. Examples of Dual Spaces from Measure Theory.
9.1 The Banach Space Lp.
9.2 The Dual of a Banach Space.
9.3 The Dual Space of Lp.
9.4 Hilbert Space, Its Dual, and L2.
9.5 Riesz-Markov-Saks-Kakutani Theorem.
10 Translation Invariance in Real Analysis.
10.1 An Orthonormal Basis for L2(T).
10.2 Closed Invariant Subspaces of L2(T).
10.3 Schwartz Functions: Fourier Transform and Inversion.
10.4 Closed, Invariant Subspaces of L2(R).
10.5 Irreducibility of L2(R) Under Translations and Rotations.
Appendix A: The Banach-Tarski Theorem.
A.1 The Limits to Countable Additivity.
References.
Index.
"The book is well thought out, organized and written. It has all the results in measure theory that are necessary for both pure and applied mathematics research." (Mathematical Reviews, 2011)
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"…useful both in the academia and industry…suited for students taking specialist courses…[and] a valuable reference for practicing engineers." (IEEE Circuits & Devices Magazine, November/December 2006)
"This book is warmly recommended to anyone having to design or understand how computer arithmetic operates at almost every conceivable level of detail." (Computing Reviews.com, June 8, 2006)
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Absolutely wonderful book Get this for your 6th grade student. It reviews math they have had and teaches how to figure out word problems. It has great explanations and examples. It has practice problems and then quizzes at the end of a unit. Answers are either right after the problems or at the back of the book. Parents can use this to help kids, and math teachers can certainly use it for probably 5th through 8th or ...
Worked really well for me I bought this book (and a bunch of others) because I wanted to prepare myself for a college math assessment test and score high enough that I could jump straight into statistics (I know, pretty ambitious!).
My current situation?
1) I haven't studied algebra (or any math at all for that matter!) in about 20 years
2) I didn't learn math in English
So, after opening the first algebra ...
very good start to teach yourself the bases of the probability theory.. I find this book one of the simplest books that help to explain the elementary of the probablity theory. The auther used very easy examples along with solved problems to explain the basics of probability. Applications of probability theory like Simulation, Game theory, and actuarial science have been addressed in a very simple way. If you are searching for the simplest book to understand ...Math I had a probability and statistics class and this book was somewhat helpful. I actually found that the teacher's instruction was more understandable than the book. But it wasn't completely unuseful. Itis good to have for class.
I used this book for an online stats with ease. I did not have the luxary of an instructor guide me through problems and have my questions clarified in class. I took the class online and I had no problem inderstanding how to wrok out the problems. It goes into detail on how to work out problems and gives examples step by step. There are also a lot of practice problems in the text with odd numbers answered for review. The CD in also a great ...
Student Solutions Manual Elementary Statistics: A Step By Step Approach Purchased this solution manual to assist with obtaining correct answers to the textbook problems. However, this book was not worth the $60 plus dollars it cost, including shipping to obtain it. This manual is extremely thin in size and contain; and should have been added as an appendix inclusion inside the textbook, vice making it a separate purchase. I recommend spending more time with course ...
not good experience Contacted seller twice before receiving the book and seller did not respond to either inquiry. When I received the book, it was in WAY worse condition then stated. The binder was in awful shape and the pages were filled with writing....in ink. This was not stated in description. I contacted seller after receiving the book to discuss this, again, no response. I would not buy again from this ...
Lucky 13 The book goes into details about the real world of using math. Recommend this book for any math class. It consist of all math problems from simple math to trig. and geo. algebra, etc...great to have for future classes
Ths is the best book! Three cheers for Bluman! I owned the 5th edition for school and accidentally returned it. Wow that was a big mistake. I got the 6th edition and it just was a relief that I had found it. Probably more expensive than I really wanted to spend, but it was worth it. So, now I'm doing a self-study and I'm enjoying the book tremendously!
Decent Introdution To Business/Consumer math Before reading this book, I already understood many of the concepts presented, but I had never learned them "formally", so I gave it a shot. I liked the format, the concepts were presented in small portions with quizzes after each portion (then a final quiz for the whole chapter). If I had to do it over again, I would definitely choose this book.
Hope this helps...
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Snellville PhysicsAlgebraic math is a major stepping stone to multiple sciences and must be mastered to facilitate future academic progress in the sciences. As algebra skills consolidate, we move toward calculus (differential and integration calculus) which employs extremely powerful math skills. Pre-calculus is the bed rock of algebraic math upon which calculus stands s...
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resource book which looks at the design of mechanisms, for example gears and linkages, through the eyes of a mathematician. There are a wide variety of examples including car steering, anglepoise lamps, bicycles, cine cameras, folding push chairs and the design of robots. Readers are encouraged to make models throughout and to look for further examples in everyday life. Suitable for GCSE, A level, and mathematics/technology/engineering courses in Further Education.
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About AppShopper
Graduate Sequence and Set Practice
iOS iPhone
Graduate Sequence and Set Practice provides students with a variety of challenging word problems that will help them develop a solid foundation of math skills. Graduate Sequence and Set Practice will help students prepare for the math portion of standardized tests, such as the SAT (Scholastic Aptitude Test), and will help improve performance on test day.
A few sample questions are shown in the screenshots. Additional sample questions are listed at the end of this description.
For each application, use the Configure button in the help window to turn the sound and timer on or off. The Solution button in the help window offers three options: 1.Select Rules to see the rules for working with each application. 2.Select Show Solution to see the correct answer. 3.Select Analyze to see a detailed explanation of the answer.
The screenshots show some sample questions. A few more are listed here:
1. Set: In a neighborhood, families have dogs or cats. 14 families have dogs, 7 have cats, and 2 have both. How many families are there in the neighborhood?
2. Arithmetic sequence: The first 3 terms of an arithmetic sequence are 37, 34, and 31. Which term is the first negative term?
3. Geometric sequence: If you add a value to each of these numbers (24, 6, -6), the result is a geometric sequence. What is this value?
4. Specific sequence: The first 2 terms of a sequence are 4 and 8. From the second term, the next term equals the current term divided by the previous term. For instance, the third term is 2, which is 8 / 4. What is the fiftieth term?
Disclaimer: SAT is a registered trademark of the College Entrance Examination Board, which does not sponsor or endorse this product.
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Course Overview
Most students who enter this course are used to calculation-based mathematics, such as algebra, trigonometry, and calculus. The purpose of this course is to help you make the transition to the later math courses in which proofs, logic, language, and notation play an integral role. The prerequisites are a logical mind, enjoyment of patterns, and a willingness to work. Usually completion of Calculus II and your interest are enough.
Content Goals:
facility in interpreting and using mathematical language and notation;
a firm background in elementary logic and practice in reasoning;
experience dealing with sets, functions, relations;
improvement of computer skills, particularly Mathematica;
Skills:
asking good questions;
discovering and writing proofs;
evaluating the proofs of others;
knowing when you are correct, when you are on a useful path, and when you're lost;
This year the course becomes 4 credit hours. The content includes material from my own text, Essentials of Mathematics. Most of your time will be spent on digesting the definitions, axioms, and theorems in the book and proving the theorems. In addition, there will be lab problems from various areas of math. These will help you to expand your mathematical horizons, learn to explore, and develop computer skills. I also encourage you to read the recommended book by Ian Stewart, Letters to a Young Mathematician. Other interesting books are found in additional resources.
Grading
Your grade will be based on the following:
homework
15%
labs
10%
3 tests
10% 15% 15%
paper and presentation
10%
final exam
25%
Homework should consume about 8 hours per week outside of class. The first test will occur at the end of Chapter 1, approximately the week of 9/17. Subsequent tests will be announced a week ahead of time. After each test, you will receive an update on your cumulative grade. Shortly after the first test, you will begin work on the paper. Due toward the end of the semester, it will report on an article you have read. Please see the paper and talk guidelines. Thursdays are lab days, meeting in 205E. Lab due dates are announced with each lab. The final exam is Tuesday 12/11, 4-6 pm.
Policies
Becoming a mathematician involves learning new skills and adopting new habits of mind. The purpose of this course is to gently push you in the right directions. Two of the goals, asking your own questions and dealing with the frustration of not knowing answers immediately, are achieved only when the professor takes a step away. Therefore, my teaching style is to let you explore on your own until you're ready for help. I have not abandoned you, I'm simply transferring to you the responsibility of forming the question.
Class work is subject to some rules that both further our goals and assure that the class runs smoothly.
Read your email regularly, as I sometimes send class announcements that way. Upon request, I can also send confidential grade information to you at your Stetson email address or through Blackboard. You can forward your Stetson email or configure Blackboard for another address. IT can provide help (ext. 7217). If you have special needs, don't hesitate to discuss them, either with me or with the Academic Resources Center. I hope you're looking forward to the semester.
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Book Description: Certain contemporary mathematical problems are of particular interest to teachers and students because their origin lies in mathematics covered in the elementary school curriculum and their development can be traced through high school, college, and university level mathematics. This book is intended to provide a source for the mathematics (from beginning to advanced) needed to understand the emergence and evolution of five of these problems: The Four Numbers Problem, Rational Right Triangles, Lattice Point Geometry, Rational Approximation, and Dissection. Each chapter begins with the elementary geometry and number theory at the source of the problem, and proceeds (with the exception of the first problem) to a discussion of important results in current research. The introduction to each chapter summarizes the contents of its various sections, as well as the background required. The book is intended for students and teachers of mathematics from high school through graduate school. It should also be of interest to working mathematicians who are curious about mathematical results in fields other than their own. It can be used by teachers at all of the above mentioned levels for the enhancement of standard curriculum materials or extra-curricular projects.
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StarsSuite prevents "domino effect" at Southern Arizona High SchoolRead More
Effective online courses
The EdOptions Online Academy; a completely virtual learning option from a fully accredited online high school.Read More
Math 7
(1 credit) Builds on material learned in earlier grades, including fractions, decimals, and percentages and introduces students to concepts students will continue to use throughout their study of mathematics. Among these are surface area, volume, and probability. Real-world applications facilitate understanding, and students are provided multiple opportunities to master these skills through practice problems within lessons, homework drills, and graded assignments within the STARS system. (36 lessons and submissions, 4 exams)
What People are Saying
"With EdOptions you just have a lot of possibilities" - Jacqui Clay, Educator (AZ)
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Algebra 102
Developed by Cliff Koperski and optimized for all phone and tablet sizes.
In this lesson you will learn how Algebra is used in everyday life and how to solve basic problems using multiplication and division along with addition and subtraction from Algebra 101. This application includes a detailed description of basic algebra functions, an unlimited number of practice problems and a step by step solution to each problem.
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Easy, simple and intuitive, just write the mathematical expression on the screen then let MyScript® technology perform its magic converting symbols and numbers to digital text and delivering the result in real time.
The same experience as writing on paper with the advantages of a digital device (Scratch-outs, results in real time, …).
Solve mathematical equations by hand without actually having to crunch the numbers yourself BENEFITS AND FEATURES
MyScript Calculator can solve complicated handwritten math equations. Forget using a regular calculator app, now you can write out your mathematic equations more naturally. The app works well to quickly solve equations and always did a good job of recognizing our handwriting. Why wasn't this app around when we were in school?
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Wednesday, February 22, 2012
In an previously content, "How to Response Concerns in a Official Examination-A Past or present student's Guide", I described how to respond inquiries to obtain the best possible outcomes in an evaluation. This content carries on that concept but now in regards to responding to questions in a proper Arithmetic evaluation. The techniques described in the past content should be used to the Arithmetic evaluation as well as the ones described below.
It is essential to determine what I mean by a issue in Arithmetic before you begin to research the techniques to fix them.
These issues are almost entirely 'word' issues. More often than not, the undergraduate needs to use a wide range of Statistical abilities or concepts to obtain a remedy. Often, particularly in the aging of secondary university, there will be an different perspective in which to use your Statistical information. On the other hand, there may be a sequence of sometimes complicated actions necessary to accomplish a outcome. Lastly, the response is not one which is apparent.
Below are a record of techniques, if used together, will help you obtain higher achievements in fixing actual issues in Arithmetic not just ones you have practised. However, keep in mind, if you don't know your fundamentals in Arithmetic then no set of techniques will help you fix the issues.
So technique Variety 1 is and will always be:
"Know all your studying perform and techniques as well as you can."
The staying techniques are as follows:
2. Keep in mind everything that you need to fix the issue is in the query itself. (So record what information the issue gives you as your beginning point).
3. Verifying is a necessary aspect of every issue you are to fix. Here is a checking process to use:
• It is best to examine as you do each phase in the issue as this helps you to save time often avoiding needless perform.
• Make sure you have done only what you have been requested to do. Check, actually, that you have actually responded to the query completely.
• Check you have duplicated down all the information for the query properly.
• Create sure the way to go (its dimension, etc.) suits, in a realistic feeling, into the scenario/context of the query.
4. Create sure you have been nice, clean, organized, sensible, obvious, and brief. This will help you with your checking and allow the examiner/teacher to adhere to your reasoning quickly.
5. This technique was described in the first content. It is aspect of responding to any evaluation issue, especially in Arithmetic. It is: List the actions you need to take, to be able, to obtain a remedy.
Below is an example of what I mean by this technique in Arithmetic.
The Diving Share Problem
"How lengthy does it take to complete a swimming pool area with a bucket?"
Here is how I show this strategy:
Step 1: I create the above issue on the panel.
When I do this, I ask the learners for their reaction:
It will be: "We can't do it"
You ask: "Why?"
Their reply: "There are no dimensions"
Your reply: "You don't need them. If I provided you them to you what would you do?"
Step 2: Now I have the learners create down the actions they would use.
Step 3: Then I talk about the actions the category choose and record the actions on the panel.
e. g. Look for the quantity of the pool area.
Find the quantity of the pail.
How lengthy does it take to complete the pail and add into the pool?
How many pails of normal water do I need to complete the pool?
Find complete a chance to complete the pool area.
Step 4: Now, I outcome in the factor that the above actions do not talk about the dimension the pool area. It doesn't issue what it actions you still adhere to the same process.
Step 5: Lastly, I highlight that a appropriate answer relies on the appropriate actions, i.e. technique of remedy.
As a undergraduate, you can't understand these techniques instantaneously and anticipate that they will 'come to you a quickly in a proper evaluation scenario. You must exercise using them. Compose a record of the techniques and have them with you as you try each new issue. Assess how well you use them and perform to enhance those you discover challenging to use or are quickly overlooked. Look to your instructor for help with this process. Keep in mind in an evaluation, be regimented, create out the record of techniques you will use before you begin and use them to fix the issues.
Thursday, February 9, 2012
With many alternatives available to you from The School student Financial loans Organization to personal organizations it is important that you are conscious of all the alternatives available to you and which choice will fit you best.
Applying for a School student Loan
Eligibility
The first process is to examine that you are qualified for an education mortgage, this will preserve putting things off implementing for a financial mortgage that you are not eligible to. Various different requirements are taken into consideration to identify whether you are qualified for an education mortgage, and if you are, how much you can lend. Some of the requirements consist of which School you plan to be present at, the course you plan to research, where you stay, age and whether this is your first program or if you have used formerly.
In inclusion who you stay with, whether you're mother and father or a associate may need to back up your program. Based on whether your mother and father or associate generate over a set determine or currently declare certain advantages can impact whether you are qualified for a financial mortgage. If approved they may need to deliver in evidence of their income to back up your program.
How to apply
Applying on the internet for an education mortgage by viewing studentfinance.direct.gov.uk is the fastest and simplest way to get utilizing. Many of the program can be completed on the internet, however in some conditions you may be needed to deliver in certain records, you will also need to indication and come back a mortgage announcement papers also.
When to apply
If you are a new student coming into your first season then you should implement before Thirty first of May 2012, if you are an current student coming into your second or third season you should implement before the 29th of July 2012. Do not anxiety if you have skipped these schedules as backdated programs are possible but this may take a bit more time than regular.
Grants and Bursaries
You do not need to make a individual program for prospective allows or bursaries as your qualifications will be evaluated simultaneously when you implement for an education mortgage.
What loans are available?
The student loans company offer student loans for learners learning in Britain, Scotland, Wales and North Isle. They are primarily divided into two categories:
Maintenance Loans
Maintenance loans are there to offer financial assistance for existence expenses. The resources are there for food, consume, guides, enjoyment, going out, and anything else that drops into existence. There are not limitations for learners who want to implement for this mortgage and are individual from expenses expenses. The mortgage can be paid back once your course at School has completed.
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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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Salathe is extremely helpful and fun. His examples are very clear and are meant to interest anyone, including those who do not like math. He is a great professor and always goes above and beyond to help his students.
Best mathematics professor of any kind I've run across. His explanations are simpler than most and yet clarify the material in five minutes better than some professors do in an hour. He is not easy per se, but he is fair, and his tests reflect that -- certainly compared to other professor's tests, they expect only moderate mastery of the material.
Salathe is hilarious. He keeps class fun and interesting. He teaches to the homework and test. He gives good study guides. He teaches little tricks to help, so if you don't have a strong background in algebra/trig/geometry don't worry, he will help!
Seriously the best math professor I've ever had. His tests are the absolute basic forms of the problems and if you attend class you will have no problem getting an A. Homework is in the textbook and if you fall asleep in class... he will catch you.
Lectures are basically necessary for acing the class, unless you're a genius. The class is pretty easy if you pay attention and stay awake during class. Always available for extra help, and he gives good examples for the concepts.
Great professor. Highly recommend taking him if you can. HIs lectures are interesting, although the pace is quick so be sure to stay awake... Exams are incredibly straight-forward, almost identical to the practice sheets he gives before the test. Very helpful teacher and worthwhile class overall.
Basically a straight up boss. tests are pretty easy except for the final. The review sheets are helpful. Very funny man, you will not be too bored in his long lectures. Likes to bring in baby toys when explaining things.
Great teacher, doesn't make you memorize any formulas. He teaches you how to derive them from any picture. The class moves pretty quickly, but is easy to understand. He will wake you up in lecture (funny if its not you) and will make plenty of jokes to keep the class fun. Textbook is only necessary for homework, nothing else.
Great professor. Moves quickly through lecture, so you have to pay attention (he wakes you up if you're sleeping) and take good notes, but he still manages to keep it light so it's not too boring. Go to class to make sure you understand the material. Homework can be brutal, but so worth it once you see how easy his exams are. Take him if you can.
Excellent teacher. Details all subject matter and its purposes with thorough examples, and helps understand why the math works instead of just stating facts. Slight accent becomes unnoticeable after time. Same Calc book as Calc 21. 1.5 hour sessions well spent.
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ne... read more
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Product Description:
needed to develop a feeling for the subject or when they illustrate a general method. On the other hand, an unusual amount of space is devoted to the discussion of the fundamental concepts of distance, motion, area, and perpendicularity. Topics include the projective plane, polarities and conic sections, affine geometry, projective metrics, and non-Euclidean and spatial geometry. Numerous figures appear throughout the text, which concludes with a bibliography and index
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Application for Math Lab Employment
If
interested in working in the math lab, please fill out the
form below. The math lab director will contact you shortly
thereafter for an initial interview. For a printable form,
please click here: Printable
Math Lab Application.
Contact Information
Name:
E -mail:
Local Phone:
Local Address:
Educational Information
Major:
Minor:
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Major GPA:
# Semesters Here:
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Graduation Date:
Course information for tutors:
Math Lab tutors are required to have completed Math 114 or
equivalent.
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taken at UWEC
(check all that apply)
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as a grader
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References
List at least two faculty who can serve as references. Please
include how they know you (Which class(es) did you have with
them? Did you grade for them?).
Reference 1:
Name:
Reference 2:
Name:
Please briefly answer the following
1. Why do you want to be a Math Lab tutor?
2. What skills and qualities do you posses that will enhance
your ability to tutor?
3. Have you had any experience tutoring (formally or
informally)? If yes, please describe.
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Cambridge Maths Tutorial Vodcasts cover 10 senior maths topics in
a series of 5-10 minute animated video podcasts that can be used
independently by students at home, or displayed in the classroom as a
pre-topic visual demonstration.
The vodcasts have been developed by university student and maths
tutor, Thor Taylor, who has selected the ten most commonly requested
problems that students bring up in maths tutorial sessions. Still a
teenager himself, Thor presents each topic, aided by animated graphics
and equations, to offer clear, accessible and engaging step-by-step
explanations. Click on the video window to see a demonstration.
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Have fun! :)
Algebra Help Math Sheet This algebra reference sheet contains the following algebraic operations addition, subtraction, multiplication, and division. It also contains associative, commutative, and distributive properties. There are example of arithmetic operations as well as properties of exponents, radicals, inequalities, absolute values, complex numbers, logarithms, and polynomials. This sheet also contains many common factoring examples.
The free software listed here is perfect for the most mischievous pranks and computer gags. This software is great for playing jokes on those unsuspecting users. Click on any of our computer pranks below to get more information and download them.
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Algebra II. This is the study of intermediate topics in Algebra, which incorporates a review of Algebra I, and includes equations of multiple variables, properties of polynomials and rational expressions, and their graphs and applications. The course will cover the study of functions, complex numbers, conics, exponential and logarithmic functions, trigonometry, and probability. The use of word problems will be incorporated to enhance the student's problem solving skills in order to facilitate the student's ability to handle a level of complexity beyond that of beginning Algebra.
Mrs. Rolle
Algebra 2
Please click on the link below to visit my website. Here you will find the 2012-2013 class syllabus, homework assignments, and answers to questions you may have.
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Homework #1
due date:
Noon, Thursday, September 5, 2002
Assignment 1
Homework, tests, and solutions from previous offerings of this
course are off limits, under the honor code.
Problem 1
Form a study group of 3-4 members. With your group, discuss
and synthesize the major themes of this
week of lectures. Turn in a one page summary of your
discussion. You need turn in only one summary per group,
but include the names of all group members. Please do not
write up just a "table of contents."
Problem 2
Construct a WWW page (with your
picture) and email Mike Wakin
(wakin@rice.edu) your name (as you want it to appear on the
class web page) and the URL. If you need assistance setting
up your page or taking/scanning a picture (both are easy!),
ask your classmates.
Problem 3: Learning Styles
Follow this learning
styles link (also found on the Elec 301
web page) and learn about the basics of learning
styles. Write a short summary of what you learned. Also,
complete the "Index of learning styles" self-scoring
test on the web and bring your results to class.
Problem 4
Make sure you know the material in Lathi,
Chapter B, Sections 1-4, 6.1, 6.2, 7. Specifically, be sure
to review topics such as:
Problem 5: Complex Number Applet
(a) Change the default add function to exponential (exp).
Click on the complex plane to get a blue arrow, which is
your complex number zz. Click
again anywhere on the complex plane to get a yellow arrow,
which is equal to
ezz. Now drag the tip of the blue arrow along
the unit circle on with
|z|=1z1 (smaller circle). For which values of
zz on the unit circle does
ezz
also lie on the unit circle? Why?
(b) Experiment with the functions absolute (abs), real part
(re), and imaginary part (im) and report your findings.
Problem 6: Complex Arithmetic
Reduce the following to the Cartesian form,
a+ibab.
Do not use your calculator!
(a) -1−i220-1220
(b) 1+2i3+4i1234
(c) 1+3i3−i133
(d) i
(e) ii
Problem 7: Roots of Polynomials
Find the roots of each of the following polynomials (show
your work). Use MATLAB to check your answer with the
roots command and to plot the roots in the
complex plane. Mark the root locations with an 'o'. Put
all of the roots on the same plot and identify the
corresponding polynomial (aa,
bb, etc...).
(a) z2−4zz24z
(b) z2−4z+4z24z4
(c) z2−4z+8z24z8
(d) z2+8z28
(e) z2+4z+8z24z8
(f) 2z2+4z+82z24z8
Problem 8: Nth Roots of Unity
ei2πN2N is called an
Nth Root of Unity.
(a) Why?
(b) Let
z=ei2π7z27.
Draw
zz2…z7zz2…z7
in the complex plane.
(c) Let
z=ei4π7z47.
Draw
zz2…z7zz2…z7
in the complex plane.
Problem 9: Writing Vectors in Terms of Other Vectors
A pair of vectors
u∈C2u2 and
v∈C2v2 are called linearly independent if
αu+βv=0
if and only if
α=β=0αuβv0
if and only if
αβ0
It is a fact that we can write any vector in
C22
as a weighted sum (or linear
combination) of any two linearly independent vectors,
where the weights αα and
ββ are complex-valued.
(a) Write
3+4i6+2i3462
as a linear combination of
1212
and
-53-53. That is, find
αα and
β
β such that
3+4i6+2i=α12+β-533462α12β-53
(b) More generally, write
x=(x1x2)xx1x2
as a linear combination of
1212
and
-53-53. We will denote the answer for a given
xx as
αxαx and
βxβx.
(c) Write the answer to (a) in matrix form,
i.e. find a 2×2 matrix
AA such that
A(x1x2)=αxβxAx1x2αxβx
(d) Repeat (b) and (c) for a general set of linearly
independent vectors
uu and
vv.
Problem 10: Fun with Fractals
A Julia set JJ is obtained by
characterizing points in the complex plane. Specifically,
let
fx=x2+μfxx2μ
with μμ complex, and define
g0x=xg0xxg1x=fg0x=fxg1xfg0xfxg2x=fg1x=ffxg2xfg1xffx⋮⋮gnx=fgn−1xgnxfgn−1x
Then for each xx in the complex
plane, we say
x∈JxJ if the sequence
|g0x||g1x||g2x|…g0xg1xg2x…
does not tend to infinity. Notice
that if
x∈JxJ, then each element of the sequence
g0xg1xg2x…g0xg1xg2x…
also belongs to JJ.
For most values of μμ, the
boundary of a Julia set is a fractal curve - it contains
"jagged" detail no matter how far you zoom in on it. The
well-known Mandelbrot set contains all values of
μμ for which the
corresponding Julia set is connected.
(a) Let
μ=-1μ-1. Is
x=1x1 in JJ?
(b) Let
μ=0μ0.
What conditions on xx
ensure that xx belongs to
JJ?
(c) Create an approximate picture of a Julia set in MATLAB.
The easiest way is to create a matrix of complex
numbers, decide for each number whether it belongs to
JJ, and plot the results
using the imagesc command. To
determine whether a number belongs to
JJ, it is helpful to define
a limit NN on the number of
iterations of gg. For a
given xx, if the magnitude
|gnx|gnx
remains below some threshold
MM for all
0≤n≤N0nN, we say that xx
belongs to JJ. The code
below will help you get started
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Algebra 2 and lists the items related to each objective that appear in the. Pre-Course Diagnostic Test, Post-Course Test, and End-of-Course. Practice Tests in this ... Chapter Standardized Tests A and B Two parallel versions of a standardized ...
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My philosophy is simple: Quality learning takes TIME, PATIENCE AND COMMITMENT. I will provide you time and patience each day to be successful, please make sure you are committed and you will have great success this year in math. Learning isn't a race-so relax and focus on the task at hand.
A list of materials you will need are: TI-30 calculator (solar is the best) Two notebooks or loose leaf paper, pencil and highlighters. NOTE: All notes and homework assignments for each day will be updated on a regular basis. If you are ill or miss school please download and print out this information so you stay current with the class. Refer to your specific class for more information.
Algebra I This course develops students' ability to recognize, represent, and solve problems involving relations among quantitative variables. Key functions studied are linear, exponential, power and periodic functions using graphic, numeric and symbolic representations. Students will also develop the ability to to analyze data, to recognize and measure variation and to understand the patterns that underlie probabilistic situations.
The Online Holt Algebraintalg Password: erhsintalg
Please refer to the calendar for homework assignments and class downloads for section notes (where applicable). NOTE: Use the link below to view these downloads.
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The Online Holt Geometrygeom1 Password: erhsgeom
Please refer to the calendar for homework assignments and class downloads for section notes (where applicable). NOTE: Use the link below to view these downloads.
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Extension fields. Splitting fields of polynomials; constructing finite fields; the group of units of a finite field is cyclic.
Group decompositions. Internal and external direct and semidirect products.
Group actions. Actions and the Sylow theorems, illustrations in mid-Summer term.
Elective information
A second course on abstact algebra, assuming a basic knowledge of group theory. Please check prerequisites carefully before asking to take this module as an elective. In choosing this module as an elective it will be assumed that you are familiar with much of the material taught in the modules Core Algebra and all of that in Introduction to Group Theory, or are willing to learn the material if necessary.
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Algebra
Algebra is helpful
But also very boring.
By the time the lesson's finished,
Over half the class is snoring.
Their alarm clock is the bell
That signals the next class.
They haven't learned a single thing,
Except how to sleep through math.
I know this poem's boring,
But it's also very true.
If you took the time to read this,
You can learn math, too.
It's not as easy as it seems,
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But with a little practice,
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Mathematics - Pre-Algebra
Intended Learning Outcomes
The main intent of mathematics instruction at the secondary level is for students to develop mathematical proficiency that will enable them to efficiently use mathematics to make sense of and improve the world around them.
The Intended Learning Outcomes (ILOs) describe the skills and attitudes students should acquire as a result of successful mathematics instruction. They are an essential part of the Mathematics Core Curriculum and provide teachers with a standard for student learning in mathematics.
The ILOs for mathematics at the secondary level are:
Develop positive attitudes toward mathematics, including the confidence, creativity, enjoyment, and perseverance that come from achievement.
Course Description
The goal of Prealgebra is to develop fluency with rational numbers and proportional relationships. Students will extend their elementary skills and begin to learn algebra concepts that serve as a transition into formal Algebra and Geometry. Students will learn to think flexibly about relationships among fractions, decimals, and percents. Students will learn to recognize and generate equivalent expressions and solve single-variable equations and inequalities. Students will investigate and explore mathematical ideas and develop multiple strategies for analyzing complex situations. Students will analyze situations verbally, numerically, graphically, and symbolically. Students will apply mathematical skills and make meaningful connections to life's experiences.
Order rational numbers in various forms, including scientific notation (positive and negative exponents), and place numbers on a number line.
Predict the effect of operating with fractions, decimals, percents, and integers as an increase or a decrease of the original value.
Recognize and use the identity properties of addition and multiplication, the multiplicative property of zero, the commutative and associative properties of addition and multiplication, and the distributive property of multiplication over addition.
Recognize and use the inverse operations of adding and subtracting a fixed number, multiplying and dividing by a fixed number, and computing squares of whole numbers and taking square roots of perfect squares.
Derive formulas for and calculate surface area and volume of right prisms and cylinders using appropriate units.
Explain that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related and the cube of the scale factor describes how corresponding volumes are related.
Find lengths, areas, and volumes of similar figures, using the scale factor.
Select appropriate two- and three-dimensional figures to model real-world objects, and solve a variety of problems involving surface areas and volumes of cylinders and prisms
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Independent chapters.
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In-depth coverage of core concepts.
Gives students an in-depth understanding of the important concepts that are taught in high school mathematics.
Provides the instructor with a generalized approach to treat problems. Gives students a much deeper understanding of problems they will be teaching, and gives them an approach to teach their students.
Detailed concept analyses--Including historical and conceptual development of mathematical concepts, and alternate language, notation, and characterizations of ideas.
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Helps students understand that mathematics is a unified whole and provides multiple perspectives for looking at mathematical ideas. Allows the instructor to relate the material in the course to almost any other
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Part of the market-leading Graphing Approach Series by Larson, Hostetler, and Edwards, PRECALCULUS FUNCTIONS AND GRAPHS: A GRAPHING APPROACH, 5/e, is an ideal student and instructor resource for courses that require the use of a graphing calculator. The quality and quantity of the exercises, combined with interesting applications and innovative resources, make teaching easier and help students succeed. Continuing the series' emphasis on student support, the Fifth Edition introduces Prerequisite Skills Review. For selected examples throughout the text, the Prerequisite Skills Review directs students to previous sections in the text to review concepts and skills needed to master the material at hand. In addition, prerequisite skills review exercises in Eduspace are referenced in every exercise set. The Larson team achieves accessibility through careful writing and design, including examples with detailed solutions that begin and end on the same page, which maximizes the readability of the text. Similarly, side-by-side solutions show algebraic, graphical, and numerical representations of the mathematics and support a variety of learning styles. This Enhanced Edition includes instant access to Enhanced WebAssign®, the most widely-used and reliable homework system. Enhanced WebAssign® students learn the basics of WebAssign quickly
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Introductory and Intermediate Algebra for College goal of this series is to provide readers with a strong foundation in Algebra. Each book is designed to develop readers' critical thinking and problem-solving capabilities and prepare readers for subsequent Algebra courses as well as ?service? math courses. Topics are presented in an interesting and inviting format, incorporating real world sourced data and encouraging modeling and problem-solving. The Real Number System. Linear Equations and Inequalities in One Variable. Linear Equations in Two Variables. Systems of Linear Equations. Expo... MOREnents and Polynomials. Factoring Polynomials. Rational Expressions. Functions, More on Systems of Linear Functions. Inequalities and Problem Solving. Radicals, Radical Functions, and Rational Exponents. Quadratic Equations and Functions. Exponential and Logarithmic Functions. Conic Sections and Nonlinear Systems of Equations. Sequences, Induction, and Probability. For anyone interested in introductory and intermediate algebra and for the combined introductory and intermediate algebra. For one-semester courses in introductory and intermediate algebra and for the combined introductory and intermediate algebra course. The goal of the Blitzer Algebra series is to provide students with a strong foundation in Algebra. Each text is designed to develop students' critical thinking and problem-solving capabilities and prepare students for subsequent Algebra courses as well as "service" math courses. Topics are presented in an interesting and inviting format, incorporating real world sourced data and encouraging modeling and problem-solving.
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Summary
This best-selling Calculus for non-math and engineering majors in the two-year/four-year market is out in a new revision. This edition contains more real data applications and integration of optional graphing calculator providing students and instructors a strong foundation for the course. Full website featuring Excel projects/tutorials accompanies text.
Table of Contents
Preface
ix
PART ONE A LIBRARY OF ELEMENTARY FUNCTIONS
1
(126)
Chapter 1 A Beginning Library of Elementary Functions
3
(74)
1-1 Functions
3
(20)
1-2 Elementary Functions: Graphs and Transformations
23
(13)
1-3 Linear Functions and Straight Lines
36
(16)
1-4 Quadratic Functions
52
(15)
Important Terms and Symbols
67
(1)
Review Exercise
68
(4)
Group Activity 1: Introduction to Regression Analysis
72
(2)
Group Activity 2: Mathematical Modeling in Business
74
(3)
Chapter 2 Additional Elementary Functions
77
(50)
2-1 Polynomial and Rational Functions
77
(16)
2-2 Exponential Functions
93
(14)
2-3 Logarithmic Functions
107
(13)
Important Terms and Symbols
120
(1)
Review Exercise
120
(3)
Group Activity 1: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions
123
(1)
Group Activity 2: Comparing Regression Models
124
(3)
PART TWO CALCULUS
127
Chapter 3 The Derivative
129
(92)
3-1 Rate of Change and Slope
130
(13)
3-2 Limits
143
(17)
3-3 The Derivative
160
(13)
3-4 Derivatives of Constants, Power Forms, and Sums
173
(13)
3-5 Derivatives of Products and Quotients
186
(8)
3-6 Chain Rule: Power Form
194
(8)
3-7 Marginal Analysis in Business and Economics
202
(11)
Important Terms and Symbols
213
(1)
Summary of Rules of Differentiation
214
(1)
Review Exercise
214
(5)
Group Activity 1: Minimal Average Cost
219
(1)
Group Activity 2: Numerical Differentiation on a Graphing Utility
220
(1)
Chapter 4 Graphing and Optimization
221
(90)
4-1 Continuity and Graphs
222
(16)
4-2 First Derivative and Graphs
238
(17)
4-3 Second Derivative and Graphs
255
(16)
4-4 Curve Sketching Techniques: Unified and Extended
271
(16)
4-5 Optimization: Absolute Maxima and Minima
287
(16)
Important Terms and Symbols
303
(1)
Review Exercise
304
(4)
Group Activity 1: Maximizing Profit
308
(1)
Group Activity 2: Minimizing Construction Costs
308
(3)
Chapter 5 Additional Derivative Topics
311
(50)
5-1 The Constant Epsilon and Continuous Compound Interest
311
(8)
5-2 Derivatives of Logarithmic and Exponential Functions
319
(12)
5-3 Chain Rule: General Form
331
(12)
5-4 Implicit Differentiation
343
(7)
5-5 Related Rates
350
(6)
Important Terms and Symbols
356
(1)
Additional Rules of Differentiation
356
(1)
Review Exercise
357
(2)
Group Activity 1: Elasticity of Demand
359
(1)
Group Activity 2: Point of Diminishing Returns
360
(1)
Chapter 6 Integration
361
(84)
6-1 Antiderivatives and Indefinite Integrals
361
(15)
6-2 Integration by Substitution
376
(12)
6-3 Differential Equations-Growth and Decay
388
(12)
6-4 A Geometric-Numeric Introduction to the Definite Integral
400
(16)
6-5 Definite Integral as a Limit of a Sum: Fundamental Theorem of Calculus
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Make These Designs
An edited version of this article appeared in The Mathematics Teacher, May 1996
Copyright 1996 by the National Council of Teachers of Mathematics.
All rights reserved. Reproduced with permission.
"Make These Designs" is an activity I have used in Algebra classes, over many years. It can be done with just about any electronic grapher. Its purpose is to reinforce students' understanding of the connection between the graph of a linear function, and the parameters m and b in the formula y=mx+b.
Students are given a set of designs, and they must create them on their electronic grapher. They should do this by entering functions of the form y=mx+b. The challenge is finding the right values of m and b. (Before reading on, you should try to do the activity yourself.) This activity is popular, as in many classes students see it as a break from the usual routine. As students show you partial results and ask you questions, you will have many opportunities to focus their attention on the underlying mathematics. When a question arises that is of concern to enough students, you may interrupt individual work for a whole-class discussion on the overhead.
Students need not solve the problems in any particular order. As they work on one figure, they may accidentally create another one. Allowing them to set their own path through the activity makes it more enjoyable, and gives them more ownership. It also makes it difficult to be competitive in an immature kind of way ("Which one are you on? I'm ahead of you."), allowing the students to concentrate on the mathematics.
It is important that students keep records of how each image was achieved, and that there be some small-group and/or all-class discussion of these records. Without such discussions, students may get through the activity, and not learn all they can from it, even if it appears to "go well". Some of the questions that you may ask during these discussions are:
How do you make lines steeper? less steep?
How do you make lines that go "uphill"? "downhill"?
How do you make lines horizontal? vertical?
How do you make parallel lines?
How do you make a parallel to an uphill line to the left of the original? to the right?
How do you make a parallel to a downhill line to the left of the original? to the right?
How do you make a parallel to an uphill line higher up? lower down?
How do you make a parallel to a downhill line higher up? lower down?
As they work on the problems, you should circulate among the students, prodding them to improve their designs. On the first figure, for example, you should encourage students to fill out the star figure, as they often fail to include lines that make an angle of less than 45 degrees with the x axis. (For an account of a similar activity and the questions that come up for students and teacher, see Magidson, 1992.)
Note the questions about left and right. It turns out that if lines are steep, as in the seventh and eighth figures, students often see the b parameter as moving the lines left or right, even though teachers see it as moving them up or down. Having the left-right discussion helps students see that changing the value of b has different effects on the x-intercept depending on whether the line is uphill or downhill, while it always affects the y-intercept the same way. In fact, this is a good opportunity to observe that b is the y-intercept. A discussion of how to find the x-intercept through symbol manipulation is a nice detour from this activity. This is a rather sophisticated level of discussion that you should not expect the first time students approach this activity -- however your own clarity on this can help you deal with their questions about moving lines left and right, and it does give you somewhere to go with the students who quickly master the basic ideas about slope and intercept.
Note also that students are asked to graph vertical lines. It is of course not possible to do it using the "y=" format. (Actually, it is possible, but not easy. Can you do it?)
Working at Many Levels
This activity is an example of an approach to curriculum that offers both access and depth in the same lesson. Access, because no one is frozen out of the activity: all students can understand the question, get started, and find a challenge to stretch their own understanding. Depth because there are many ways to increase the mathematical payoff and to keep even your strongest students challenged. (The slogan used in the Logo community to describe such curricula is "No threshold, no ceiling.")
Whether a given design is reproduced accurately is largely a matter of opinion. You may ask your students to capture the general look of a given figure, or you may ask for a nearly-exact replica. The former can be done by trial and error, and helps students develop a feel for the effect of m and b in a general sort of way. The latter requires a very clear understanding of the effect of the parameters, not to mention familiarity with the features of the electronic grapher. What level of competence you ask for depends on whether this activity is being used early or late in the process of learning about linear functions and their graphs. You may even expect different levels of accuracy from different students, as long as everyone is being challenged to move forward in their understanding. Certainly, for beginners, using about ten lines is sufficient to show understanding of the particular figure, even though the figure may include up to sixteen lines.
The graphs are mostly grouped in pairs, each of which tries to make a certain point, though of course your mileage may vary. The first two graphs show us lines with various slopes but the same intercept, however the intercept changes from the first to the second figure. The next two make the point about uphill versus downhill graphs, keeping the slope constant, but varying the intercepts. The next two address the special cases of horizontal and vertical lines. The next two raise the issue of moving lines to the left or right. The next two are an attempt to explore symmetry across the x and y axes. However you should avoid getting heavy-handed in demanding specific understandings right away. The central purpose of the activity is to advance students' grasp of the role of the parameters m and b. Any other learning is a bonus.
Making vs. "Noticing"
Many curriculum materials attempt to get the "slope-intercept" idea across by way of a lesson where students are asked to graph several lines, with the equations supplied by the curriculum writer. For example, they may be asked to graph y=x, y=2x, y=3x, and so on. Then they are asked "What do you notice?". The process is then repeated for y=x, y=x+1, y=x+2, and so on. I am sure that some students do figure out what is going on in this sort of lesson, but many do not. Part of the reason is that the graphing phase of the lesson does not engage the student intellectually: it's just a matter of entering the functions suggested by the worksheet. After looking at the graphs, students often do not notice what we want them to notice, and we are forced to give them sledgehammer hints. In effect students end up seeing the activity as one where they have to guess what the teacher is looking for. (For an account of what students sometimes "notice" in this context, see Goldenberg, 1988, 1991).
In contrast, "Make These Designs" forces students to think throughout the activity, because they are involved in a creative challenge. While this does not guarantee learning, it certainly helps, by providing an environment where the students (not the author of the worksheet) choose the formulas, and formulate the questions. This means that even if they are unable to readily answer these questions, at least they know what the questions are, which makes it a lot easier to hear the answers as they surface in group or class discussion, or in a teacher lecture. It is very difficult to hear the answers to questions one does not have, let alone understand them.
The essence of "Make These Designs" is the reversal of a traditional activity. Instead of asking for the graph given the equation, it asks for the equation, given the graph. This sort of reversal is a very powerful tool in the design of effective problem-solving activities. In fact, it can be said that one does not have a full understanding of most mathematical topics if one cannot comfortably reverse them. You do not fully understand addition if you do not understand subtraction -- otherwise how would you solve x + 1.234 = 5.123? You do not fully understand the distributive law, if you cannot factor anything. For a stimulating essay on the importance of reversal in the learning of algebra, see Rachlin, 1987. Understanding this can lead to a rethinking of all of one's teaching.
Assessment
I have often used the last figure as an "extra credit" problem if the activity is done as an introduction to m and b. On the other hand, I have used the last figure (or the whole sheet) late in the course to assess student understanding of slope and intercepts (both x- and y-). If you are using the activity as a wrap-up, students should write out full explanations of how some of the figures were created. It helps them cement their understanding, and it helps you assess it. To support students, you may give them a copy of the questions above, which can serve as a content checklist for a written report.
Extensions
The activity can easily be extended. For example, students can create their own designs, which can be printed or shown on the overhead for others to emulate. When they know some trigonometry, students can be asked to make the initial "starburst" design so that consecutive lines make a 15° angle with each other. In Algebra 2 or Precalculus, students can be asked to do a similar activity using quadratic, polynomial, rational, or trigonometric functions.
Conclusion
Using technology does not accomplish miracles, but it does provide an excellent context for the reversal of standard tasks, which yields powerful educational benefits. Still, the electronic grapher should not be the only way you address these concepts with your students. While the technology helps students' emerging understanding of the parameter/graph connection, this should not be mistaken for a full understanding of linear functions and rate of change. For example, while the slope of a line in a Cartesian graph is a very important way to think about the rate of change of the corresponding function, it is only one of the ways. Other representations, (tables of values, so-called real world situations, other visual representations such as function diagrams and manipulatives,) can also help students develop their understanding of these concepts. Do not put all your eggs in the technology basket!
Technical Notes
Originally, I used a graphing program I had written in the Logo language (Picciotto, 1990) for this activity. More recently, I have been using the TI-82, then TI-83, then TI-89 calculator. The given "window" makes each pixel be worth .2 both horizontally and vertically, and draws axes with ticks that are 1 unit apart. You may need to adjust these numbers for other electronic graphers, or create your own set of designs with the electronic grapher you use.
To get this many lines onto the screen may require using some of the special features of the calculator. On the TI-83/84, one can graph ten functions. To get more, students can use bracketed lists of parameters. (See the respective manuals for more information.)
Sidney L. Rachlin. "Algebra from x to why: A Process Approach for Developing the Concepts and Generalizations of Algebra." In Wendy Caughey (Ed.), From Now to the Future. Melbourne, Australia: The Mathematical Association of Victoria, 1987, 213-217.
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Although the classroom is not the heart and soul of The World of Math, it is a stalwart and
trustworthy guide through much of the principles used on examinations and competitions.
It is a repository of knowledge, and, although it is not meant as a replacement for four
years of high school math it can prove useful to consult in times of need.
The fundamental building block of all that is to come. Through the arithmetic and problem solving skills built in the following lessons, we will eventually construct feats of awesome complexity. But first we have to start small. Although these few lessons should already be familiar to the vast majority of you, their importance cannot be overstated. Careful study now we reap great rewards later on.
Hopefully, if you're reading this you have a basic understanding of the foundation of algebra. You understand the four most basic operations of arithmetic: addition, subtraction, multiplication, and division. You should know most of the basic properties of these operations. You should understand about variable substitution and how to solve for a variable in basic equalities. If all of the above made sense, prepare yourself for an overview of more advanced algebra topics. The following lessons are designed to impart a greater understanding of the principles of algebra, and to increase the depth and experience of students.
Geometry cannot truly be taught via the Internet. However well written the following lessons may be, they will not impart the understanding of geometric concepts that can only come with careful experimentation. The compass is a very important part of geometry; if you do not own one, you should consider buying or borrowing this surprisingly useful mathematical tool. Hopefully, your geometry teachers will be able to show you how to use a compass and how it relates to the theorems discussed in your classes. This review of geometry cannot be more than a review. It can aid your understanding or remind you of theorems that you have forgotten but it will not teach you geometry by itself. Its purpose is to impart the most basic levels of geometry to you and to immerse students in the proper terminology and mindset for more advanced studies.
By now, you should have an understanding of the fundamental principles that compose algebra. In this unit, we will build upon those principles to review the more complex aspects of high school math. Although it is impossible to learn advanced algebra from a web page alone, we hope that this abstract will prove a useful summary for the algebra student.
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Can low achieving mathematics students succeed in the study of linear inequalities and linear programming through real world problem based instruction? This study sought to answer this question by comparing two groups of low achieving mathematics
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The
new Mathematics 7-10 syllabus reflects
a contemporary approach to teaching
and learning - it is outcomes-based
with standards-referenced assessment.
For the first time, it describes a
continuum of learning through K-10
with student achievement expressed
in stage statements rather than year
levels. Implementing a stage-based
syllabus recognises that students
progress at different rates, and provides
flexibility for teachers to design
individual learning programs. It also
provides more continuity (and less
overlap and repetition) across year
levels, especially at the years 6-7
and 8-9 transitions.
New Century Maths has been thoroughly revised to reflect the spirit and detail of the new syllabus. The series contains work from different stages at each year level to accommodate students of different abilities, and at years 9 and 10 each text covers two pathways to fully cater for students whose achievements are not necessarily confined to a single pathway across the six mathematical strands. A text structured in this way both truly reflects an outcomes-based syllabus and promotes individual learning and teaching plans. You will find a host of new and familiar features requested by teachers in response to statewide surveys of secondary schools.
New Century Maths uses the latest approaches for developing mathematical understanding and caters to a wide variety of learning styles. It also makes extensive use of technology to encourage investigating concepts and to develop numeracy skills. To all the students and teachers using this book: we wish you every success with learning and teaching mathematics in the 21st century.
Features
Key features of the student
text
Each chapter opens with a list
of student outcomes, a Wordbank
of key words and definitions and
a Think! feature
- an open-ended question to stimulate
thought and discussion.
Start up exercises
review prerequisite skills for
the chapter. These can be used
to identify a student's skill
level or to practice assumed knowledge.
Important rules,
for students to record and
remember, are highlighted
in boxes like these.
Working mathematically
sections contain activities, ideas
and projects for exploration.
These investigations are often
suited to group work and student
discussion, and provide opportunities
for Questioning, Applying strategies,
Communicating, Reasoning and Reflecting.
Skillbanks
contain power tips for mental
computation, estimation and 'non-calculator
maths' to improve number sense
and numeracy skills. These are
accompanied by SkillTests on the
CD-ROM.
Power plus
exercises at the end of every
chapter provide extension and
enrichment for advanced students,
including more challenging questions,
problems and investigations.
Language of maths
at the end of each chapter contains
a list of words, with questions
to reinforce knowledge of terminology
used in the chapter. An accompanying
word puzzle is provided on the
CD-ROM and in the Teacher Resource
Pack.
Using technology
sections have activities that
use spreadsheets, calculators,
and dynamic geometry software
to teach and support technology
skills.
Just for the record
contains interesting facts and
cross-curricular connections relating
to the topic being covered.
Topic overviews
contain reflection questions and
a mind map, which summarises the
chapter content in pictorial form,
for students to complete.
Chapter reviews
contain exercises covering the
skills learned in that chapter,
with each question linked back
to the relevant exercise set.
An accompanying topic test for
the chapter is included on the
CD-ROM.
Mixed revision
exercises review the previous
three chapters, with each question
linked back to the relevant chapter.
A syllabus reference
grid, glossary and index
are provided for ready reference.
CD-ROM features
The CD-ROM, either packaged
with the text or available on
your school network, contains
the entire text in PDF format,
with margin icons hotlinked to
other sections of the book or
to additional resource material.
The icons have been colour-coded
depending on their particular
application in each instance.
Some icons will be more than one
colour where they fulfil more
than one use:
- Red = Explanation
- Green = Practice
- Purple = Revision
- Orange = Learning technology
- Teal = Using technology
Worksheets
are blackline masters in PDF format
that can be printed and copied
for classroom use. They include
'brainstarter' assignments, further
practice and review questions,
investigations, applications,
remedial or extension work, games,
puzzles and crosswords. Answers
can be found in the accompanying
Teacher Resource Pack.
Skillsheets
are reference sheets with worked
examples and exercises that teach
prerequisite skills from a previous
topic, especially useful for elementary
learners in catch-up lessons.
Topic tests,
in PDF format, can be printed
and copied for classroom use.
Answers can be found in the accompanying
Teacher Resource Pack.
Spreadsheets
or spreadsheet templates
accompany many activities.
Geometry investigations,
developed in Geometer's Sketchpad
and Cabri Geometry, accompany
many activities in the book. Clicking
this icon will open a drop-down
menu to select the software package
of choice. Please note:
demonstration-only versions
of Cabri and GSP have been provided
on the CD-ROM. These allow time-limited
and/or read-only access. To experience
the full functionality of these
software packages, the user must
purchase a complete version.
Skilltests
reinforce the skills and strategies
of the Skillbanks. The data for
the questions in the Skilltests
are randomly generated and corrected,
so students can keep practising
with new questions until they
master the skills.
SkillBuilder
is a tutorial program that teaches
and reinforces essential basic
skills.
Animations
demonstrate what happens in between
the lines of a worked example.
Students can watch how expressions
are manipulated in a fully animated
movie format.
Computer Algebra System
(CAS) investigations
written for TI InterActive! software
teach students how to use this
powerful tool to deepen their
understanding of number, algebra
and graphs. Please note:
a 90-day trial-only
version of the software has been
included on the CD-ROM. To access
the files beyond this time, the
user must purchase a complete
version of the software.
The questions in every exercise
are hotlinked back to the relevant
worked example.
The CD-ROM also contains a
teaching program in Word format
that can be downloaded for easy
editing.
Author Profiles
Judy
Binns is Head of Mathematics
at Mulwaree High School in Goulburn.
She has been responsible for teacher
inservices in the Queanbeyan District
to implement the new HSC, particularly
the General Mathematics syllabus.
She is an active member of MANSW and
has presented workshops at their annual
conferences.
Gaspare Carrozza
is Head of Mathematics at South Sydney
High School. He has conducted inservices
in both Mathematics and Computing
with a particular interest in the
professional development of teachers.
He is a past president of the Central
Maths Association and a member of
MANSW.
Robert Yen is a teacher
of Mathematics at Hurlstone Agricultural
High School, a selective high school.
He co-wrote the New Century
Maths General 11 and 12
texts. Robert writes for and co-edits
Reflections, the journal of MANSW,
as well as the column 'Mr Yen's world'
for the NSW Teachers Federation newspaper,
Education.
David Adams is Head
of Mathematics at Pascoe Vale Girls'
Secondary College. He is an author
and series editor of the successful
Nelson Maths for the CSF II
series. David has a particular interest
in learning technologies.
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Elementary Linear Algebra
9780030973543
ISBN:
0030973546
Edition: 5 Pub Date: 1994 Publisher: Thomson Learning
Summary: Intended for the first course in linear algebra, this widely used text balances mathematical techniques and mathematical proofs. It presents theory in small steps and provides more examples and exercises involving computations than competing textsFormer Library book. Shows definite wear, and perhaps considerable marking on inside. 100% Money Back Guarantee. Shipped to over one million happy customers. Your purchase benefits world literacy![0030973546
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An Investigation of Interactive Online Modules for the Teaching of Mathematics
PhD by Dr Kuva Jacobs, Director Redpoint Consulting.
The following modules were developed as part of my PhD for two mathematics courses at the University of South Australia. I am hosting these modules to provide students and academics with better online mathematics resources. Log onto quizzes using the ID of Guest.
Feel free to use these modules on this website for teaching purposes, however reuse on other websites or for commercial use is not permitted without explicit authorisation from the author.
Background
The two courses for which the modules were created provide a notable contrast in their difficulty, content, purpose and target audience. Differential Equations is a second year mathematics course offered to students enrolled in a mathematics degrees whereas Mathematics for Computing is a first year service course focussing on discrete mathematics with a student cohort consisting largely of computer science students, many of whom have little or no interest in mathematics.
Features
Two unique sets of online modules have been tailored specifically for the pair of different courses. They have been developed using a student-centred, interactive approach that adheres
to the fundamental constructivist guidelines in order to create an effective online learning environment. The modules aim to be autonomous, guiding students through information whilst providing flexibility in navigational sequences. This information is presented both visually and verbally, with the aim of accommodating a wider range of perceptual styles of learning. A conceptual overview is presented, with an emphasis on drawing together complex relationships using well-defined tasks. The modules have been created with an interface that is both visually appealing and intuitive.
Key features of the modules include:
Online Walkthroughs that introduce new concepts and definitions in a step-by-step format, governed by a clearly labelled navigational structure. Interactive graphs and animated simulations of real-world examples are included to encourage students to actively explore and interact.
Online Randomised Quizzes, with inbuilt randomised parameters and adjustable graphs test conceptual understanding. The quizzes work on the principle that practise makes perfect, by retesting incorrect answers with a new randomly selected set of numbers.
Online Worksheets, which also feature randomised parameters, allow students to work through lengthy problems and provide a more open style of assessment, such as testing the creation of a circuit diagram for a given Boolean logic expression.
Research
Analysis of feedback from the two student cohorts provided insight into the influence of these variations upon the effectiveness of the modules.
This lead to a conclusion of whether the value of these innovative teaching tools is provides a basis for a deeper level of understanding.
To read more about my research & the outcomes, please refer to my PhD thesis or the below papers
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In mathematics and computer science, graph theory is the study of graphs; mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of vertices. A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another; see graph (mathematics) for more detailed definitions and for other variations in the types of graphs that are commonly considered. The graphs studied in graph theory should not be confused with "graphs of functions" and other kinds of graphs. created by video_lectures on 2008-06-24 23:59:44
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MAT 131
Geometric Reasoning
This course has a multi-dimensional focus on geometric reasoning. These dimensions address
geometry through: visualization, drawing and construction of figures; correspondence to structures
in the real, physical world; by reference to abstract mathematical concepts; and by argumentation
and discussion within a logical-mathematical system.
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Course Information.
This course can be seen as the use of Real and Complex Analysis in the study of numbers - particularly prime numbers. To do this course you must be comfortable with Mathematical Analysis and thus you should have done well in courses such as MATH10242 Sequences and Series, MATH20111 Real Analysis, MATH20101 Real and Complex Analysis and MATH20142 Complex Analysis.
The material covered by level 4 students will be the same as for the level 3 students, but to a greater depth. So the higher level students will see and be expected to understand a number of proofs not seen by the level 3 students. This is especially true when we prove the Prime Number Theorem.
Throughout the course the level 4 students will get more and harder questions on the problem sheets. This fits in with the School philosophy that level 4 students should spend at least 7 hours, outside lectures, on study for a course unit while for level 3 students it is a minimum of 4 hours.
You need to realise that taking the level 4 version of this course is not an easy way in which to get an extra 5 credits.
The Analysis in Analytic Number Theory
Here I have extracted the analysis that will be seen in Analytic Number Theory. Thus you will see little mention of Number Theory. Before you register for this course make sure that you are happy with, or can reasonably imagine that you become happy with, the material here.
You can download all the files in one LARGE FILE, or in parts below. There are problems for you to try in these files and the solutions will be given in the feedback classes for the course.
Recommended Texts
I have looked at a number of books in designing this course. These are listed below with a few sentences on each.
I would hope that my notes are self-contained, but if can not follow my approach to a subject you might look in the books below to find an alternative approach that might appeal to you more.
[A] T. Apostol, Introduction to Analytic Number Theory, 1st edition. 1976, Corrected 5th edition 2010, Springer, 1441928057
This is probably the best reference for the material on Arithmetic functions, sums of such functions and elementary prime number theory.
[D] H. Davenport, revised by H.L. Mongomery, Multiplicative Number Theory, 2nd edition, Springer, 1980, 0-387-90533-2.
This is another classic Analytic Number Theory text, though at too high a level for MATH31022. Read it to see what the follow on course would have been.
[EW] G. Everest, T. Ward, An Introduction to Number Theory, Graduate Texts in Mathematics 232, Springer, 2005, 1-85233-917-9.
Chapter 8 has a useful discussion on the Riemann Zeta function; with careful attention paid to questions of the where the function is holomorphic.
[HW] G.H. Hardy, E. M. Wright, An Introduction to the Theory of Numbers, 5th edition, Oxford Science Publications, 1983, 0-19-853171-0.
This is a classic reference for Number Theory. Chapters XVI - XVIII are an excellent source for material on Arithmetic Functions, while Chapter XXII has a lot of material on the elementary Prime Number Theory. The book also contains an elementary proof of the Prime Number Theorem which is beyond the scope of this course.
[IJ] H. Iwaniec, E. Kowalski, Analytic Number Theory, AMS Colloquium Publications, Vol. 53, AMS 2004, 0-8218-3633-1. This is a huge book of 610 pages where the first 42 cover more than is in MATH31022. You should read this to get a feel of where the subject has gone in the years after the proof of the Prime Number Theorem.
[J] G.J.O. Jameson, The Prime Number Theorem, LMS Student Texts 53, CUP 2003, 0-521-89110-8.
This is a major reference source for the final chapters of MATH31022. The book contains two approaches to the Prime Number Theorem, of which we only study one. And in fact, just at the end of the proof of the proof of the PNT we switch to the approach in [T] below.
[N] W. Narkiewicz, The Development of Prime Number Theory, Springer Monographs in Mathematics, Springer, 2000, 3-540-66289-8.
This gives an excellent historical perspective on the development of Prime Number Theory, but should be read more in the way of background reading.
[NZM] I. Niven, H.S. Zuckerman, H.I. Montgomery, An Introduction to the Theory of Numbers, 5th edition, Wiley, 1991,
9-971-51301-3.
This book is a very well judged book for undergraduate Number Theory. For us, Chapter 4.3 contains Mobius Inversion while Chapter 8 discusses Elementary Prime Number estimates. Be careful, the book discusses Dirichlet Series but only for real s.
[SS] W. Schwarz, J. Spilker, Arithmetic Functions, LMS Lecture Note Series 184, CUP, 1994, 0-521-42725-8.
As the title suggests, this book will tell you more about arithmetic functions than you may ever want to know. For us, only sections 1.1 - 1.4 are of interest.
[SG] G. Sansone, J. Gerretsen, Lectures on the Theory of Functions of a Complex Variable I. Holomorphic Functions, P. Noorhoff, Ltd Groningen, 1960.
This is simply a reference for results from Complex Analysis, there should be plenty of alternatives on the library shelves.
[T] G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory, Cambridge Studies in Advanced Mathematics, 46, CUP, 1995, 0-521-41261-7.
An excellent source for all things Analytic Number Theory, and thus the book goes far further than we can in MATH31022. The only reservation is that Dirichlet Series are done as Laplace-Stieltjies transforms, which is too advanced an approach for us. I finish the proof of the Prime Number Theorem by following p.169 of this book.
[THB] E.C. Titchmarsh, revised by D.R. Heath-Brown, The Theory of the Riemann Zeta-function, 2nd edition, Oxford Science Publications, 1986, 0-19-853369-1.
This is a classic reference for results on the Riemann Zeta function, but apart from the first few pages it has little for us. It should be read for background, and though it was written in 1951, Heath-Brown has written new appendices to each Chapter describing what has been proved in the 35 years since first publication.
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Grade 9, Principles of Mathematics, Academic (Enriched)
Course Code:
MPM1D3
Same as MPM1D but it is enriched. In addition, many interesting math topics will be explored. Graphing Calculators will used extensive in exploring mathematics properies and mathematics modelling. All students will prepare and participate in Garde 9 Pascal mathematics competition sponsored by University of Waterloo. Grade 9 Principles of Mathematics, Academic: This course covers four strands: 1) Number Sense and Algebra; 2) Relationships; 3) Analytic Geometry; 4) Measurement and Geometry. The course enables students to develop generalizations of mathematical ideas and methods through the exploration of applications, the effective use of technology, and abstract reasoning. Students will investigate relationships to develop equations of straight lines in analytic geometry, explore relationships between volume and surface area of objects in measurement, and apply extended algebraic skills in problem solving. Students will engage in abstract extensions of core learning th ore skills and deepen their understanding of key mathematical concepts.
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These
Interactive Diagrams are visual tools to help students explore the
dynamic aspects of mathematics and to help them connect physical
and dynamic representations of real-world situations to algebraic
symbolism.
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Mathematics Learning Lab Resource Manual
MATHPRO EXPLORER has been developed to
accompany
BASIC COLLEGE MATHEMATICS by K. Elayn Martin-Gay.
It corresponds to the objective exercises in the text. Each exercise
has an example and a guided step-by-step solution to help you
learn important algebraic concepts and skills .
MATHPRO EXPLORER has been developed to
accompany
Introductory Algebra by K. Elayn Martin-Gay.
It corresponds to the objective exercises in the text. Each exercise
has an example and a guided step-by-step solution to help you
learn important algebraic concepts and skills.
Assignment Sheet for the Textbook for
College Algebra
A. Write the assignment number from this sheet , the
page number and the
problem numbers from the book assignment on the TOP RIGHT
CORNER of your homework paper.
B. Papers clip these assignments together in the order
they appear on this
sheet.
C. Turn your textbook work in on the day you take your
exam. You must put your grade tally sheet on top of this assignment sheet and use these
two
sheets for the cover sheets.
D. Any assignment that you have completed must be
highlighted with a
highlighter on this assignment sheet. Do not highlight anything you have
not done. Highlighting your assignment sheet will indicate both to you and
to me what you have completed on your assignment sheet.
E. All textbook assignments should be correctly
completed and graded by
you . You have the answers to the assigned problems in the back of your
book.
G. You MUST record your score on your grade tally
sheet. You get a
completion grade for all textbook work. Give yourself 10 points for each
completed and corrected regular homework assignment. Record that
score on the homework line on your grade tally sheet.
H. Give yourself 20 points for each extra credit
assignment that is indicated
on your assignment sheet with a ** that you complete. Review Exercises
and Practice Test are extra credit assignments and are labeled with **. They should be highlighted in a different color (for example use a yellow
highlighter for completed daily textbook assignments and a pink
highlighter to indicate any ** extra credit completed assignments). Record
this on the line for extra credit assignments on your grade tally sheet.
I. You must show all work to get credit for extra
credit assignments. Review
Exercises and Practice Tests are good things to do to help you to study for
your exam. Be sure you do those because you earn lots of points for doing
them.
J. Do not include daily pop tests from the packet with
assignments from this
assignment sheet – daily pop test do not have answers on them – we go
over these in class. Please do not include you daily class notes with
homework.
K. You should read the material in the textbook that
precedes each
homework lesson. If you have trouble completing your homework, you
should use your study guide to help you, go for free tutoring in the math
tutoring room L247, go to the learning center for help, see me
during my office hours or work with someone in your group.
L. All work must be shown on your homework paper. I
will not give you
credit for completing an assignment if you just write the problem and the
answer especially if the problem is complicated and requires several steps.
My philosophy is if I cannot do the problem in my head, I assume you
cannot do it in your head. If the problem is simple and can be done in your
head in one step, then please do it that way.
M. You may call Mrs. Wagner in her office 209-7369;
however, I prefer
email. I will respond as soon as possible. I am in my office in the evenings
after 8:00 PM until 10:00 PM or later Monday through Wednesday. If I
am not there when you arrive, wait. I will be there soon.
N. It is best to try to reach me by e-mail. I will
respond ASAP.
O. Be sure to re-work and study your daily pop tests
and old exams in the
P. Library to help you to study for your exam.The material that is in
chapter "P" and "one" in your text book is material that you are supposed to
already know. We will not spend class time reviewing this material most of
this is material you should already know. Because you have so many problems
to do for review that are in the packet the textbook problems in Prerequisities
Chapter and Chapter 1 (labeled with *) are optional and will be counted as
extra credit assignments which you will be given 10 points each for
completing. The Chapter Reviews and Chapter Tests (labeled with **) will be
counted as 20 points each. To earn the most extra credit points do the Chapter
Review and the Chapter Test first. If you find that you do not have a firm
grasp of these basic concepts, then you should consider taking one of the
classes that precedes this course. The material that is in the Prerequisites
Chapter and Chapter 1 in your book is covered in detail in M0312. There are
not many days to change classes so make your decision quickly so that you do
not loose your money or your time.
Q. You will be expected to do all the assigned textbook
assignments
Beginning in Chapter 2 - 8. These assignments are graphing assignments,
which pertain to the material that is essential to this class. Each regular
assignment is worth 10 points and will count against your grade if you do
not complete the textbook work.
R. This is a "learn to graph class". The purpose of this
class is to teach you to
learn to recognize equations of different types, graph them, interpret what
they are telling you, i.e. You must learn to understand the equations we
cover and the graphs they form.
S. You MUST bring your calculator to class everyday.
T. If you have financial problems at the beginning of the
semester, I have a
textbook and a blank packet on file in the library for you to use.
This course begins with the material in Chapters 2 - 8
be sure you do all the
textbook assignments for these chapters. They are regular homework
assignments and are not considered to be extra credit assignments.
Exam # 1 covers textbook assignments # 1 - 47. Be sure
you have assignments
# 1 – 47 (there are no word problems on exam # 1) Remember, your textbook
homework is due the day you take your exam. I will grade it while you take
your exam. Be sure to follow the correct directions above as to how you
should order and highlight your homework.
Exam # 2 covers textbook assignments # 1 - 62. Be sure
to include textbook
assignments # 48 – 62 with your homework. Remember your textbook
homework is due the day you take your exam. I will grade it while you take
your exam. Be sure to follow the correct directions above as to how you should
order and highlight your homework. Be sure to turn in your Exam # 1
Corrections if you have not already done so. Be sure to complete your class
projects and take home exams before you take Exam # 2. They will help you to
study for Exam # 2. The take home exam is due when you walk in the door on
exam day.
Exam # 3 covers textbook assignments 1 - 82. Be
sure to include in your
textbook homework assignments # 63 - 82. Remember Exam # 2 Corrections
are due. Don't forget to look in the Library at the old exams. Don't forget you
need to turn in your take home exam when you walk in the door to take your
exam.
EXPONENTIAL FUNCTIONS, & LOGARITHMIC FUNCTIONS; USING A
CALCULATOR TO EVALUATE LOGS, Ln, & EXPONENTIALS;
SOLVING FOR X BY CLEARING EXPONENTS AND MAKING BASES
THE SAME; USING PROPERTIES OF LOGARITHMS TO SOLVE FOR
THE VARIABLE; SOLVING WORD PROBLEMS USING LOGARITHMS.
The Post Test and Final Exam will be combined. The
posttest/final exam
covers anything in the course. Be sure to study your post test daily review pop
tests. The post-test section of the final covers anything from textbook
assignments # 1 - 99. Be sure to bring your last section of homework
assignments # 93 - 99 to the final exam. I will grade your homework while you
take your final. Be sure to bring your completed packet with you to the
final
exam to be graded.
Remember, your Exam Corrections for the 4th Exam
are due the day you
take your final. If you have any other old exams you must turn them in on
exam day. Complete all your late work and study for your final!!!! Good Luck
and I hope you do well!!!
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MATH 295: Survey Of Modern Math
This course provides a transition to higher mathematics. Topics include elementary set theory, elementary symbolic logic, elementary number theory, equivalence relations and functions. Emphasis is on techniques of proofs. It is strongly recommended that students complete this course as a preparation for MATH 270 Abstract Algebra. Pre-requisite: MATH 191 Calculus II or equivalent
Credits:0
Overall Rating:4 Stars
N/A
Thanks, enjoy the course! Come back and let us know how you like it by writing a review.
User has not rated this course 0 of 0 people found this review helpful.
Dr. Bennett really makes this an enjoyable and easy to understand course. I originally took this course with another professor and dropped it four weeks in because the professor made the subject too confusing. Highly reccommend taking this coure with Dr. Bennett.
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Cramster is your textbook resource. Get the answers and solutions for Elementary Linear Algebra8th Edition and more.
Textbook solutions will help you succeed
Cramster helps you prepare for exams with fully worked-out solutions to the questions from your Elementary Linear Algebra8th Edition by textbook. We have fully explained answers to your textbooks, so you can understand how to solve Math problems, rather than just copying the answer from the back of your textbook. We provide help with many Math textbooks, including Elementary Linear Algebra8th Edition. Our step-by-step solutions show you how to solve your problems; helping you learn by example so you can apply your knowledge to other Math questions.
Need more help understanding your homework?
Broaden your interpretation and understanding of the topics in textbooks with unlimited access to Math resources. On Cramster, you can download lecture notes, formula sheets or watch video lectures from other teachers using the same textbook. If you want to earn karma points, you can post your class resources, share your knowledge and help others learn.
Practice makes perfect!
Want a higher score on your Math exam? Getting help has never been easier with instant access to thousands of practice problems. With over 40,000 questions at your fingertips, you can get all the practice you need, to help you ace your tests
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understanding an assignment
prepping for a quiz or exam
analyzing data
writing computer code
solving a problem
calculating and interpreting statistics
proving or applying a theorem
using quantitative software
designing an experiment
Credit for
photo: Albert Einstein Institute at the Max Planck Institute for
Gravitational Physics and Konrad-Zuse-Zentrum, Berlin. Visualization by
Werner Benger and Edward Seidel, director of Louisiana State University's
Center for Computation and Technology
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Trigonometry and Calculus Problem of the Week - Math Forum
Trigonometry and calculus problems from a variety of sources, including textbooks, math contests, NCTM books, puzzle books, and real-life situations, designed to reflect different levels of difficulty. From 1998 until 2002, the goal was to challenge students with non-routine problems and encourage them to put their solutions into words. Different types of problems were used to reach a diverse group of calculus students.
more>>
Carousel Math - Web Feats Workshop II
Carousels are as reliant on the laws of motion as roller coasters. Let's take a ride on the new Bear Mountain Carousel at Bear Mountain State Park in New York. After enjoying the ride, take the data that has been collected and use the applet to explore
...more>>
CASTLE Software
Computer Assisted Student Tutorial Learning Environment (CASTLE) software for Windows, for high school science, social studies, and mathematics - algebra, geometry (including probability), and trigonometry. Includes a tutorial program for student review,
...more>>
ClassZone - McDougal Littell, Publishers
In ClassZone, McDougal Littell has gathered together all of its activities, interactive online resources, research links, chapter quizzes, and other materials that support its popular middle and high school mathematics textbooks, such as Integrated Math
...more>>
CLK-Calculator - Lars Kobarg
Reverse Polish notation Calcualtor is a calculator program for Windows with unit conversion and matrix calculator, functions for vectors and complex numbers, and a
function plotter.
...more>>
Complex Numbers & Trig - Alan Selby
Complex Numbers and the Distributive Law for Complex Numbers, offering a short way to reach and explain trigonometry, the Pythagorean theorem, trig formulas for dot- and cross-products, the cosine law, and a converse to the Pythagorean theorem. A geometric
...more>>
The Constants and Equations Pages - Jonathan Stott
A growing reference resource providing alphabetically listed categories of some of the more important and useful aspects of maths and special sections on numbers, algebra, trigonometry, integration, differentiation, and SI units and symbols, with in addition
...more>>
CPO Online - Cambridge Physics Outlet
A company founded by teachers and scientists that creates hands-on equipment and curriculum for teaching science, math, and technology from grades 4-12 and beyond, and provides effective professional development in science and math that is both content
...more>>
Creative Geometry - Cathleen V. Sanders
Teachers and students will find creative and interesting "hands-on" projects for most topics in the geometry curriculum. Each project is designed to help students understand, remember, and find value in the concepts of geometry. The pages are organized
...more>>
DeadLine OnLine - Ionut Alex. Chitu
Freeware that graphs equations and precisely estimates their roots. It includes the option to evaluate the function and the first two derivatives, find extrema of the function and integrate numerically. For Visual Basic-enabled computers running Windows
...more>>
Emaths.Info - Vinod Sebastian
Math tools, formulas, tutorials, videos, tables, and "curios," such as the unusual properties of 153, 1729, and 2519. See in particular Emaths' interactive games, which include the N queens problem, Towers of Hanoi, and partition magic, which finds a
...more>>
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Welcome to alt.algebra.help. The complete posting guidelines and answers to
frequently asked questions can be found at:
PDF and DVI formats can be found at:
Below are some general guidelines from the main document to help you get
started immediately. These guidelines are not intended to be formal rules
that in any way govern the newsgroup. They serve only to identify what have
come to be accepted as norms. In this spirit, it will be nice if you
attempt to follow these guidelines. Doing so may result in a more enjoyable
visit. Not doing so may result in a less enjoyable visit. That's all.
************************************************************
Q1. Who should use alt.algebra.help?
Q2. What can be discussed on alt.algebra.help?
Q3. What general format should my article adhere to?
Q4. Can I post the same question to other newsgroups
in addition to alt.algebra.help?
Q5. Can I get (or provide) help with a homework assignment?
Q6. Can I include binary files?
*************************************************************
Q1. Who should use alt.algebra.help?
Anyone seeking (or providing) help with any topic related to algebra. This
may include students, parents, tutors, teachers, or anyone else having an
interest in algebra. This newsgroup is not moderated, so various others who
have no business here (e.g. spammers,) will also post articles asking for
help of a different kind. Ignore them, killfile them, report them to a
proper authority, do whatever you wish with them--but please do not respond
to them in the newsgroup. Doing so only further decreases the
signal-to-noise ratio.
Q2. What can be discussed on alt.algebra.help?
As the name implies, alt.algebra.help exists primarily for the purpose of
seeking help with algebra. Anything remotely related to algebra in some
form or fashion is usually welcome here. Specific topics suitable for
discussion include, but are not limited to, anything covered in a jr. high
school, middle school, high school, or undergraduate algebra course, or
their equivalent in countries other than the U.S. This does not necessarily
mean that only "algebra" in the high school sense of the word is discussed.
Other areas of mathematics are also discussed with varying frequency, e.g.
geometry, trigonometry, calculus, probability and statistics, linear
algebra, abstract algebra, and number theory, just to name a few. Educators
also share teaching practices and experiences. Discussions concerning
calculators and their (ab)use also occur with some regularity.
These are just some of the topics that are suitable for discussion here.
While some areas of these subjects (or other higher mathematics) may be
better suited for other newsgroups, as a general rule if there is someone
listening here who can help you with your question, chances are they will.
And, usually there is someone listening.
Q3. What general format should my article adhere to?
For best overall results and readability, try to use a simple fixed-width
font (e.g. Courier New). Also ensure your newsreader is configured to post
in plain text, not HTML.
Don't ask questions that are too broad, e.g. "Can someone help me with
algebra?" Try to narrow your question to the particular topic or process
you are concerned with, e.g. "Can someone explain to me the process for
solving a quadratic equation by factoring?"
Use a descriptive subject line. Readers will have a general idea of what
your message pertains to prior to downloading (and having to read) the
message body.
Don't do:
Subject: HELP!
Do:
Subject: Solving quadratic equations by factoring
Clearly explain the problem and include specific instructions, whether they
be to solve, simplify, etc. If possible, try to reproduce the instructions
to the problem exactly as they were given to you. Also, consider telling
the group the level of math you are at. There may be (err...will be)
different methods of approaching your problem, so if the group knows your
particular competency level (grade, course, etc.,) they can formulate a
response suitable for that level.
Place math expressions on a single line if possible. Your expression may
not "line up" the same way on all newsreaders, especially after being quoted
multiple times. These problems can be minimized by placing your expressions
on a single line.
Don't do:
x+3
-----
2
Do:
(x+3)/2
If you need to use multiple lines (e.g. a passage showing the individual
steps of solving an equation, listing a matrix, etc.) be sure to always
begin each line of the object or passage at the beginning of the "line" in
your editor (no preceding spaces,) and end each line with a hard return. In
general, anywhere there is a math expression on a line by itself, that line
should end with a hard return. Use "in-line" expressions sparingly (math
expressions that are side-by-side or interspersed with normal text,) and
only for very short expressions that can survive line-wrapping and quoting
with minimal distraction to the reader.
Don't do:
Here's how I proceeded in solving this equation: x2 + 5x
+ 7 = 1, x2 + 5x + 6 = 0 ...got 0 on one side, (x+2)
(x+3) = 0 ...factored, x = 2, 3. The answer key says the
correct answers are x = -2, -3. Where did I go wrong?
Do:
Here's how I proceeded in solving this equation:
x2 + 5x + 7 = 1
x2 + 5x + 6 = 0 ...got 0 on one side
(x+2)(x+3) = 0 ...factored
x = 2, 3
The answer key says the correct answers are x = -2, -3.
Where did I go wrong?
Be sure to explain the specific step(s) you are having trouble with and
include your attempt(s), even if you know they are wrong. You will receive
more useful help if you do this.
Use plenty of parentheses, brackets, etc. if an expression may otherwise be
interpreted in more than one way.
Don't do:
x+3/2
Do:
(x+3)/2 or x+(3/2)
Don't Do:
x^3c+7
Do:
x^(3c) + 7 or x^(3c+7)
For more information, see the section on importance of parentheses at
Q4. Can I post the same question to other newsgroups
in addition to alt.algebra.help?
Of course, assuming the subject matter is on-topic for the other newsgroups
(consult the FAQ or charter for the other newsgroups to see.) There is,
however, a right way and a wrong way to go about it. The wrong way is to
send separate posts to each newsgroup. The right way is to "cross-post,"
meaning to include all the newsgroups on the Newsgroups: line of a single
post. By cross-posting, replies in one newsgroup will automatically be
sent by default to all the other newsgroups the original post was addressed
to. If you don't cross-post but instead send separate posts to each
newsgroup, a reply in one newsgroup is posted just to that newsgroup and not
the others. This is considered poor netiquette, so please don't do it.
Although it may not bother the original poster, it can be a big
inconvenience for those replying to the post. It can be very frustrating
taking the time and effort to post a detailed response, only to learn later
the question has already been answered basically the same way in another
newsgroup (perhaps the person does not subscribe to all the newsgroups).
This situation can be avoided by properly cross-posting your question.
It's better for the original poster too, since he need follow only one of
the newsgroups to see the responses from all of the newsgroups. Also, you
should cross-post to only a very few newsgroups (say, two or three.)
Addressing too many newsgroups may result in the post being filtered out by
way of a personal killfile or similar mechanism (for instance, a spam filter
at the server level).
Q5. Can I get (or provide) help with a homework assignment?
If you are a student you can get excellent assistance here, but don't expect
too much if you just want someone to do your homework for you. If you post
something like "I need answers to these problems...NOW" or the like, you
will rarely get what you ask for. Several regular contributors are either
professional educators, or at the very least "concerned others" who enjoy
helping others while keeping the muscle between the ears limber. Most would
rather help you understand a process, as opposed to just cranking out an
answer to your problem.
Don't get the wrong impression from the above paragraph. If you are having
trouble with a problem on an assignment, or any other algebra problem for
that matter, don't hesitate to ask for help. This is what the group is for.
However, you are more likely to receive useful responses if you explain
specifically what you do not understand about the problem, include your
attempt at solving it, and ask for specific guidance with the process for
arriving at the answer. This indicates to potential responders that you
have a sincere interest in knowing how to do the problem, as opposed to
giving the possible impression that all you want is the answer.
Additionally, letting others know specifically where you are having trouble
will probably lead to a more useful response that is tailored to your needs.
If you follow these guidelines, who knows, you might just get the answer as
well. Ultimately, it is a decision made by the people responding to your
inquiry as to how much detail they provide. Some prefer providing just
enough detail to steer you in the right direction, for very good reason.
Others may offer more detail, which may or may not include the answer to the
problem. Even if someone does give you the answer, it is the process you
are expected to focus on. Giving an answer without also giving some
explanation of the process certainly does not "help," and is rarely seen
here. When it does occur it is usually frowned upon, so please think twice
before giving an answer without any explanation how it was arrived at.
Q6. Can I include binary files?
This is a "plain text only" newsgroup. Please do not attach binaries. If
you want to show the group a graphic, HTML document, or other type of richly
formatted content, consider placing it on your web server and providing the
URL within your article.
Don't do:
Consider the attached bitmap of the graph of f(x).
Do:
Consider the graph of f(x) at
The complete document includes specific examples of how to type various
mathematical expressions, answers to frequently asked questions, a reference
section for common facts and formulas, and more. The complete document can
be found at:
Contributions/suggestions are welcome at aah@ryan-usa.com.
--
Darrell Ryan
User Contributions:
Comment about this article, ask questions, or add new information about this topic:
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Matrix Structural Analysis
9780881338249
ISBN:
0881338249
Publisher: Waveland Pr Inc
Summary: This text is devoted to giving a solid understanding of matrix analysis methods combined with the background to write computer programs & use production-level programs to build actual structures.
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GCSE Maths
Overview
GCSE maths is examined at two levels or Tiers. A student will either enter for the Higher tier or the Foundation tier. The grades that can be awarded are A* (pronounced A star) A, B, C, D, E, F and G where A* is the highest grade. It is possible to be awarded a (U) grade which means unclassified. It is generally thought though by employers that grades A* - C are of value.
The Foundation tier offers the following grades G, F, E, D, C whilst the higher tier offers the following grades D, C, B, A and A*.
If a candidate fails to obtain a Grade G on the Foundation tier or a Grade D on the Higher tier they will fail the course and receive a U. Candidates who narrowly miss a Grade D on the Higher tier, however, are awarded a Grade E.
The course can either be linear or modular.
In linear exams there are generally two papers, but check with your examination board. One paper is non calculator whilst the other allows the use of a calculator. Each paper normally is weighted at 50% of the total mark.
In modular exams there are several papers which students take in the course of two years where each paper will concentrate on one area of the syllabus.
The syllabus is divided into several sections that test
Number and Algebra, Shape, Space and Measures and Handling Data
The main examination boards are Edexcel and AQA.
On this site you will find plenty of video tutorials and worked solutions to exam questions which hopefully will give you the confidence and support you need to tackle your maths GCSE.
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Instructor Class Description
Functions, Models, and Quantitative Reasoning
Explores the concept of a mathematical function and its applications. Explores real world examples and problems to enable students to create mathematical models that help them understand the world in which they live. Each idea will be represented symbolically, numerically, graphically, and verbally. Prerequisite: minimum grade of 2.0 in B CUSP 122, a score of 145-153 on the MPT-AS assessment test, or a score of 147-165 on the MPT-GS assessment test. Offered: AWSp.
Class description
Functions are the key to how mathematical models are built. Various mathematical models will be created through the usage of real world examples. This course is designed to prepare students for calculus I and serves as a prerequisite for B CUSP124. Upon successful completion of the course, students are expected to build solid skills in algebra, trigonometry, logarithms, exponentials, composition of functions, and graphing.
The class will be taught with a mixture of group activities and projects, as well as interactive lectures.
Recommended preparation
Appropriate score on the UWB math placement test.
To prepare for this class, please review your high school algebra and trigonometry. Everything we do will build on these skills.
Class assignments and grading
Homework will be assigned regularly. It will be completed using the Wiley Plus online system. You will need to purchase a registration code for this. Since that registration code includes a complete electronic version of the textbook, there is no need to buy hard copy of the text unless you prefer that and do not wish to print pages from the electronic version yourself. I will also distribute additional materials in class.
In addition to online homeworks, there will be week-long laboratory assignments, in-class worksheets, exams.
Grades will be based on student's performance on assigned work, projects, in-class worksheets and Bilin Z Stiber
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Overview - MOMENTUM MATH LVL G STUDENT ED 10-PK GR 7
Momentum Math is a mathematics intervention course created specifically to re-engage middle school students who have given up on math because they have fallen behind. The program is designed to reach all learners, including English language learners and students with special needs. Through a series of dynamic and visually engaging lessons, Momentum Math helps students master the concepts, procedures, and language that are the foundation for all mathematics, including algebra.
Engages the Learner
Students in a math intervention program need to be re-engaged in learning mathematics. Momentum Math uses a graphic format with character guides to accompany students through the lessons. The guides model expert thinking, solve problems, and share effective strategies with the student. Throughout the program, icons prompt students to represent mathematics (1) graphically, (2) symbolically, and (3) verbally. Ample opportunities are provided to immediately apply new concepts and practice new skills.
Supports the Teacher Momentum Math supports teachers who have different levels of experience in teaching math. Materials include:
• Thorough teaching notes for every lesson
• Comprehensive error analysis
• Questions to scaffold effective classroom discussions
• Supplements for review, practice, and assessment
• Mathematical background at the point of use
• Universal Access notes for English language learners and students with special needs
• Suggestions for reviewing and reteaching
Assessment
The Practice & Assessment Companion for each level contains:
• Pretests to gather information about students' strengths and weaknesses, and parallel post-tests to measure progress
• Entry and exit assessments tailored to the content and skills that should be mastered
• Data analysis and reporting tools
In addition, assessment is embedded within the daily lesson structure to allow teachers to monitor students' understanding.
Computer-Based Assessment
The ExamView Assessment Suite* allows teachers to easily roster and fully manage students' instructional paths with the ExamView Test manager. Students can take the Momentum Math assessments directly on the computer, or teachers can print them and scan the results to the classroom computer through the ExamView Test Player.
Flexibility in Program Delivery
The modular format of Momentum Math enables the program to be implemented during the regular school day in small-group or whole-class instruction, in after-school programs, or in summer school.
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Math Java Applets (Popularity: ): About 15 applets covering a number of math problems and principles. Manipula Math with Java (Popularity: ): Over 200 applets for middle school students, high school students, college students, and all who are interested in mathematics. Interactive programs and a lot of animation that helps with understanding ... Java Demos for Probability and Statistics (Popularity: ): College professor's applets. Chaos and Fractals Applets (Popularity: ): Several java applets for use in exploring the topics of chaos and fractals. Experimental Math Applets (Popularity: ): Some applets covering Besicovitch sets, conformal compactifaction, honeycombs, exponent calculator, the complex plane, elementary complex maps, Möbius transforms, multi-valued functions, the complex derivative, the complex integral, Taylor and Laurent expansions. Euclid's Elements, An Introduction (Popularity: ): Includes the entire 13 books on plane geometry, geometric and abstract algebra, number theory, incommensurables, and solid geometry. Uses java applets to illustrate the principles. Spirograph Applet (Popularity: ): Makes a spirograph, just like the kid toy. TenBlocks and IntegerZone (Popularity: ): TenBlocks turns the times tables into a series of puzzles. IntegerZone lets users explore aspects of arithmetic and number theory using the integers themselves as the interface. Graph Explorer (Popularity: ): A Java applet for graphing functions, with smooth zooming and panning across graphs, and variable parameters which can be used for animation. Java Applets for Visualization of Statistical Concepts (Popularity: ): These applets are designed for the purpose of computer-aided education in statistic courses. The intent of these applets is to help students learn some abstract statistics concepts easier than before. ... Online Tutor (Popularity: ): on-line math tutor and science tutor for school age children - Place values to Probability, geometry, ratios, percentages, fractions and measurements, solar system, weather and human body
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recipes_helperRecipesHelper
end
m 406 Section 0101 Exam 3 Topics and Samples 1. Multiplicative functions. Definition. (a) Define (1) = 1 and (n) = 2r where r is the number of distinct primes in the PF of n. Show that is multiplicative. 2. Euler -function. Definition, how to fin
Chapter 10SolitonsStarting in the 19th century, researchers found that certain nonlinear PDEs admit exact solutions in the form of solitary waves, known today as solitons. There's a famous story of the Scottish engineer, John Scott Russell, who in
Hypertext and E-CommerceInformatics 211 November 6, 2007The Basics of Hypertext Theconcept: interrelated information Content (the information) Structure (the links between the information) View (what part of the content and structure one s
Project: Design an Online Travel Agency This is a group project (5-6 students each group). You are assigned to design a website and its underlying software architecture for a travel agency located in southern California. The agency wants the website
The Mythical Man-Month by Fred Brooks (I) Published 1975, Republished 1995 Experience managing the development of OS/360 in 1964-65 Central Argument Large programming projects suffer management problems different in kind than small ones, due to
OPTIMIZATION AND LEARNINGWe can define learning as the process by which associations are made between a set of stimuli and a set of responses. We can visualize this process on a coordinate system, where the independent variable is the set of stimul
Review Questions, Calc I and App. E, 5.1-5.2 Here are some selected topics from Calculus I that you might want to review if its been a while since you've seen them: Topic: Definition of continuity Where is f (x) continuous? What is the domain of f (x
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...This subject covers topics like functions (including polynomials, rational, exponential, logarithmic, trigonometric) and graphing, equations, absolute values and inequalities, vectors and complex numbers, matrices, sequences and series. Appropriate for high school as well as college level studen...
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Solve equations and inequalities, both algebraically and graphically, and
Solving and model applied problems.
Math 113 - Upon successful completion of Math 113 - Finite Mathematics for Social Sciences, students will be able to engage in analyzing, solving, and computing real-world applications of finite and discrete mathematics.
Linear Algebra and Linear Programming
Students will be able to set up and solve linear systems/linear inequalities graphically/geometrically and algebraically (using matrices).
Sets and Counting
Students will be able to formulate problems in the language of sets and perform set operations, and will be able apply the Fundamental Principle of Counting, Multiplication Principle.
Probability
Students will be able to compute probabilities and conditional probabilities in appropriate ways.
Students will be able to solve word problems using combinatorial analysis.
Statistics
Students will be able to represent and statistically analyze data both graphically and numerically.
Graph theory
Students will be able to model and solve real-world problems using graphs and trees, both quantitatively and qualitatively.
Math 140 - Upon successful completion of Math 140 - Mathematical Concepts for Elementary Education I, a student will be able to:
Solve open-ended elementary school problems in areas such as patterns, algebra, ratios, and percents,
Justify the use of our numeration system by comparing it to historical alternatives and other bases, and describe the development of the system and its properties as it expands from the set of natural numbers to the set of real numbers,
Demonstrate the use of mathematical reasoning by justifying and generalizing patterns and relationships,
Display mastery of basic computational skills and recognize the appropriate use of technology to enhance those skills,
Demonstrate and justify standard and alternative algorithms for addition, subtraction, multiplication and division of whole numbers, integers, fractions, and decimals,
Identify, explain, and evaluate the use of elementary classroom manipulatives to model sets, operations, and algorithms, and
Use technological tools such as computer algebra systems or graphing calculators for visualization and calculation of multivariable calculus concepts.
Math 228 - Upon successful completion of Mathematics 228 - Calculus II for Biologists, within the context of biological questions a student will be able, using hand computation and/or technology as appropriate, to:
Analyze first-order difference equations and first-order differential equations and small systems of such equations using analytic, graphical, and numeric techniques, as appropriate,
Analyze basic population models, including both exponential and logistic growth models,
Solve integration problems using basic techniques of integration, including integration by parts and partial fractions,
Formulate and interpret statements presented in Boolean logic. Reformulate statements from common language to formal logic. Apply truth tables and the rules of propositional and predicate calculus,
Formulate short proofs using the following methods: direct proof, indirect proof, proof by contradiction, and case analysis,
Demonstrate a working knowledge of set notation and elementary set theory, recognize the connection between set operations and logic, prove elementary results involving sets, and explain Russell's paradox,
Apply the different properties of injections, surjections, bijections, compositions, and inverse functions,
Solve discrete mathematics problems that involve: computing permutations and combinations of a set, fundamental enumeration principles, and graph theory, and
Gain an historical perspective of the development of modern discrete mathematics.
Math 239 - Upon successful completion of Math 239 - Introduction to Mathematical Proof, a student will be able to:
Apply the logical structure of proofs and work symbolically with connectives and quantifiers to produce logically valid, correct and clear arguments,
Perform set operations on finite and infinite collections of sets and be familiar with properties of set operations,
Determine equivalence relations on sets and equivalence classes,
Work with functions and in particular bijections, direct and inverse images and inverse functions,
Construct direct and indirect proofs and proofs by induction and determine the appropriateness of each type in a particular setting. Analyze and critique proofs with respect to logic and correctness, and
Explain and successfully apply all aspects of parametric testing techniques including single and multi-sample tests for mean and proportion, and
Explain and successfully apply all aspects of appropriate non-parametric tests.
Math 301 - Upon successful completion of Math 301 - Mathematical Logic, a student will be able to:
State the following theorems and outline their proofs: The Soundness Theorem, The Completeness Theorem, The Compactness Theorem, Gödel's First Incompleteness Theorem, and Gödel's Second Incompleteness Theorem,
Evaluate the development of 20th century Mathematical Logic in terms of its relation to the foundations of mathematics,
Explain basic concepts from Recursion Theory, including recursive and recursively enumerable sets of natural numbers, and apply them to theoretical and appropriate applied problems in logic,
Explain basic concepts from Proof Theory, including languages, formulas, and deductions, and use them appropriately, and
Define and give examples of basic concepts from Model Theory, including models and nonstandard models of arithmetic, and use them in appropriate settings in logic.
Math 302 - Upon successful completion of Math 302 - Set Theory, a student will be able to:
Discuss the development of the axiomatic view of set theory in the early 20th century,
Identify the axioms of a system of set theory, for example the Zermelo-Fraenkel axioms, including the Axiom of Choice,
Define cardinality, discuss and prove Cantor's Theorem and discuss the status of the Continuum Hypothesis,
Explain the concept of complementary slackness and its role in solving primal/dual problem pairs,
Classify and formulate integer programming problems and solve them with cutting plane methods, or branch and bound methods, and
Formulate and solve a number of classical linear programming problems and such as the minimum spanning tree problem, the assignment problem, (deterministic) dynamic programming problem, the knapsack problem, the XOR problem, the transportation problem, the maximal flow problem, or the shortest-path problem, while taking advantage of the special structures of certain problems.
Math 333 - Upon successful completion of Math 333 - Linear Algebra II, a student will be able to:
Analyze finite and infinite dimensional vector spaces and subspaces over a field and their properties, including the basis structure of vector spaces,
Use the definition and properties of linear transformations and matrices of linear transformations and change of basis, including kernel, range and isomorphism,
Compute with the characteristic polynomial, eigenvectors, eigenvalues and eigenspaces, as well as the geometric and the algebraic multiplicities of an eigenvalue and apply the basic diagonalization result,
Compute inner products and determine orthogonality on vector spaces, including Gram-Schmidt orthogonalization, and
Identify self-adjoint transformations and apply the spectral theorem and orthogonal decomposition of inner product spaces, the Jordan canonical form to solving systems of ordinary differential equations.
Math 335 - Upon successful completion of Math 335 - Foundations of Geometry, a student will be able to:
Compare and contrast the geometries of the Euclidean and hyperbolic planes,
Analyze axioms for the Euclidean and hyperbolic planes and their consequences,
Use transformational and axiomatic techniques to prove theorems,
Analyze the different consequences and meanings of parallelism on the Euclidean and hyperbolic planes,
Demonstrate knowledge of the historical development of Euclidean and non-Euclidean geometries,
Use dynamical geometry software for constructions and testing conjectures, and
Use concrete models to demonstrate geometric concepts.
Math 338 - Upon successful completion of Math 338 - Topology, a student will be able to:
Define and illustrate the concept of topological spaces and continuous functions,
Define and illustrate the concept of product topology and quotient topology,
Math 340 - Upon successful completion of Mathematics 340/Biology 340 - Modeling Biological Systems, a student will be able to:
Describe standard modeling procedures, which involve observations of a natural system, the development of a numeric and or/analytical model, and the analysis of the model through analytical and graphical solutions and/or statistical analysis,
Distinguish between analytic and numerical models,
Distinguish between stochastic and deterministic models,
Use software to quantitatively test hypotheses with data and build and evaluate mathematical and simulation models of biological systems,
Present an oral report of a semester-long group project involving the development and the analysis of a model of a biological system, and
Assess the value of model results discussed in the news and in scientific and mathematical literature.
Math 345 - Upon successful completion of Math 345 - Numerical Analysis IMath 346 - Upon successful completion of Math 346 - Numerical Analysis IIProduce a mature oral presentation of a non-trivial mathematical topic.
Math 350 - Upon successful completion of Math 350 - Vector Analysis, a student will be compute and analyze:
Scalar and cross product of vectors in 2 and 3 dimensions represented as differential forms or tensors,
The vector-valued functions of a real variable and their curves and in turn the geometry of such curves including curvature, torsion and the Frenet-Serre frame and intrinsic geometry,
Scalar and vector valued functions of 2 and 3 variables and surfaces, and in turn the geometry of surfaces,
Gradient vector fields and constructing potentials,
Integral curves of vector fields and solving differential equations to find such curves,
The differential ideas of divergence, curl, and the Laplacian along with their physical interpretations, using differential forms or tensors to represent derivative operations,
The integral ideas of the functions defined including line, surface and volume integrals - both derivation and calculation in rectangular, cylindrical and spherical coordinate systems and understand the proofs of each instance of the fundamental theorem of calculus, and
Examples of the fundamental theorem of calculus and see their relation to the fundamental theorems of calculus in calculus 1, leading to the more generalised version of Stokes' theorem in the setting of differential forms.
Math 360 - Upon successful completion of Math 360 - Probability and Statistics I, a student will be able to:
Recognize the role of probability theory, descriptive statistics and inferential statistics in the applications of many different fields,
Define and illustrate the concepts of sample space, events and compute the probability and conditional probability of events, and use Bayes' Rule,
Define, illustrate and apply the concepts of discrete and continuous random variables, the discrete and continuous probability distributions and the joint probability distributions,
Apply Chebyshev's theorem,
Define, illustrate and apply the concept of the expectation to the mean, variance and covariance of random variables,
Define, illustrate and apply certain frequently used discrete and continuous probability distributions, and
Illustrate and apply theorems concerning the distributions of functions of random variables and the moment-generating functions.
Math 361 - Upon successful completion of Math 361 - Probability and Statistics II, a student will be able to:
Recall the basic concepts in probability and statistics and understand the concept of the transformation of variables and moment-generating functions,
Define and examine the random sampling (population and sample, parameters and statistic) data displays and graphical methods with technology,
Recognize and compute the sampling distributions, sampling distributions of means and variances (S2) and the t- and F-distributions,
Explain the contribution of a scientific paper to the field of biomathematics,
Develop and lay the foundation to the solution of a problem in biomathematics, and
In addition, seniors taking this course to fulfill the seminar requirement in the biology degree program should expect to develop and write a grant proposal to do research in the area of biomathematics.
Math 390 - Upon successful completion of MATH 390 - History of Mathematics, a student will be able to:
Trace the development and interrelation of topics in mathematics up to the undergraduate level,
Be familiar with current standards (state, national, and NCTM), both content and process, for the secondary mathematics curriculum,
Be able to do both short and long term planning of lessons and units that meet current standards for the secondary mathematics curriculum,
Have taught mathematics lessons which they have planned to small groups of fellow students and/or area 7-12 students,
Be able to assess student learning in mathematics,
Be able to find research on the teaching and learning of content in the secondary mathematics curriculum and analyze teaching ideas and textbook presentations of said content in light of the found research, and
Be familiar with technology currently used in the mathematics classroom.
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approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in the general setting of normed linear spaces and inner product spaces; best uniform polynomial approximation; orthogonal polynomials; Newton-Cotes , Gauss and Clenshaw-Curtis quadrature; the Euler-Maclaurin formula; approximation of periodic functions; the uniform convergence of Fourier series; spline approximation,with an extensive treatment of local spline interpolation,and its application in quadrature. Exercises are provided at the end of each chapter less
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Overview
Main description
Tough Test Questions? Missed Lectures? Not Enough Time?
Fortunately for you, there's Schaum's.
problems, and practice exercises to test your skills.
This Schaum's Outline gives you
1,600 fully solved problems
Complete review of all course fundamentals
Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time--and get your best test scores!
Table of contents
Schaum's Outline of College Mathematics, 4ed Elements of Algebra Functions Graphs of Functions Linear Equations Simultaneous Linear Equations Quadratic Functions and Equations Inequalities Locus of an Equation The Straight Line Families of Straight Lines The Circle Arithmetic and Geometric Progressions Infinite Geometric Series Mathematical Induction The Binomial Theorem Permutations Combinations Probability Determinants of Order Two and Three Determinants of Order Systems of Linear Equations Introduction to Transformational Geometry Angles and Arc Length Trigonometric Functions of a General Angle Trigonometric Functions of an Acute Angle Reduction to Functions of Positive Acute Angles Graphs of the Trigonometric Functions Fundamental Trigonometric Relations and Identities Trigonometric Functions of Two Angles Sum, Difference, and Product Trigonometric Formulas Oblique Triangles Inverse Trigonometric Functions Trigonometric Equations Complex Numbers The Conic Sections Transformations of Coordinate Points in Space Simultaneous Quadratic Equations Logarithms Power, Exponential, and Logarithmic Curves Polynomial Equations, Rational Roots Irrational Roots of Polynomial Equations Graphs of Polynomials Parametric Equations The Derivative Differentiation of Algebraic Expressions Applications of Derivatives Integration Infinite Sequences Infinite Series Power Series Polar Coordinates Introduction to the Graphing Calculator The Number System of Algebra Mathematical Modeling
Author comments
The late Frank Ayres, Jr., Ph.D., was formerly a professor in and head of the Department of Mathematics at Dickinson College, Carlisle, Pennsylvania. He is the author or coauthor of eight Schaum's Outlines, including Calculus, Trigonometry, Differential Equations, and Modern Abstract Algebra.
Philip A. Schmidt, Ph.D., has a B.S. from Brooklyn College (with a major in mathematics), an M.A. in mathematics, and a Ph.D. in mathematics education from Syracuse University. He is currently the program coordinator in mathematics and science education at The Teachers College at Western Governors University in Salt Lake City, Utah.
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0534407617
9780534407612
Numerical Methods: This text emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Students learn why the numerical methods work, what type of errors to expect, and when an application might lead to difficulties. The authors also provide information about the availability of high-quality software for numerical approximation routines. The techniques are essentially the same as those covered in the authors' top-selling Numerical Analysis text, but in this text, full mathematical justifications are provided only if they are concise and add to the understanding of the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the student that the method is reasonable both mathematically and computationally. «Show less
Numerical Methods: This text emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Students learn why the numerical methods work, what type of errors to expect,... Show more»
Rent Numerical Methods 3rd Edition today, or search our site for other Faires
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Thinkwell s Calculus with Edward Burger lays the foundation for success because, unlike a traditional textbook, students actually like using it. Thinkwell works with the learning styles of students who have found that traditional textbooks are not effective. Watch one Thinkwell video lecture and you ll understand why Thinkwell works better.
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Elementary and Intermediate Algebra: A Unified Approach with WindowsElementary and Intermediate Algebra w/ MacStudent's Smart CD-ROM for Windows for use with Beginning Algebra (bundle version)
Editorial review
This interactive CD-ROM is a self-paced tutorial specifically linked to the text and reinforces topics through unlimited opportunities to review concepts and practice problem solving. The CD-ROM contains chapter-and section-specific tutor
Math Fundamentals
Editorial review
The first manual in a series of three for developmental students, this booklet contains numerous exercises and review material, and complements any core text for Basic Math.
Mandatory Package College Algebra with Smart CD (Windows)
Editorial review
Smart CD is packaged with the seventh edition of the book. This CD tutorial reinforces important concepts, and provides students with extra practice problems.
Reviewed by Christina Francis, (Kansas City, MO)
r (or suppliment) before tackling this text. It will be well worth the extra [money] spent!
Reviewed by Fred Matthews, (Colorado)
College Algebra is well written. The concepts of algebra are thoroughly explained and illustrated with examples. Answers to half the problems are included in the back of the book.
Reviewed by Fred Matthews, (Colorado)
College Algebra is well written. The concepts of algebra are thoroughly explained and illustrated with examples. Answers to half the problems are included in the back of the book.
Reviewed by a reader
I am currently enrolled In a distanced learning college and was sent this book.The book Is hard to figure out and the problems give you no pretense on who to solve them go with a different book
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In the 20th century, algebraic geometry has undergone several revolutionary changes with respect to its conceptual foundations, technical framework, and intertwining with other branches of mathematics. Accordingly the way it is taught has gone through distinct phases. The theory of algebraic schemes, together with its full-blown machinery of sheaves and their cohomology, being for now the ultimate stage of this evolution process in algebraic geometry, had created -- around 1960 -- the urgent demand for new textbooks reflecting these developments and (henceforth) various facets of algebraic geometry. The famous volumes ``Éléments de géométrie algébrique'' as a series in Publ. Math., Inst. Hautes Étud. Sci. (1960-1967) by {\it A. Grothendieck} and {\it J. Dieudonné} were entirely written in the new language of schemes, without being linked up with the classical roots, and the so far existing textbooks just dealed with classical methods. It was {\it David Mumford}, who at first started the project of writing a textbook on algebraic geometry in its new setting. His mimeographed Harvard notes ``Introduction to algebraic geometry: Preliminary version of the first three chapters'' (bound in red) were distributed in the mid 1960's, and they were intended as the first stage of a forthcoming, more inclusive textbook. For some years, these mimeographed notes represented the almost only, however utmost convenient and abundant source for non-experts to get acquainted with the basic new concepts and ideas of modern algebraic geometry. Their timeless utility, in this regard, becomes apparent from the fact that two reprints of them have appeared, since 1988, as a proper book under the title ``The red book of varieties and schemes'' [cf. Lect. Notes Math. 1358 (1988; Zbl 0658.14001)]. In the process of exending his Harvard notes to a comprehensive textbook, the author's teaching experiences led him to the didactic conclusion that it would be better to split the book into two volumes, thereby starting with complex projective varieties (in volume I), and proceeding with schemes and their cohomology (in volume II). -- In 1976, the author published the first volume under the title ``Algebraic geometry. I: Complex projective varieties'' (1976; Zbl 0356.14002; corrected second edition 1980; Zbl 0456.14001), where the corrections concerned the wiping out of some misprints, inconsistent notations, and other slight inaccuracies.\par The book under review is an unchanged reprint of this corrected second edition from 1980. Although several textbooks on modern algebraic geometry have been published in the meantime, Mumford's ``Volume I'' is, together with its predecessor ``The red book of varieties and schemes'', now as before, one of the most excellent and profound primers of modern algebraic geometry. Both books are just true classics!\par As to the intended volume II of the book under review, the author planned to publish it in collaboration with {\it D. Eisenbud} and {\it J. Harris}. This would have been based on existing but unpublished notes of the author (partially revised by {\it S. Lang}), but then the author and his co-authors came to the conclusion that such a second volume was not really what was needed anymore, because {\it R. Hartshorne}'s famous book ``Algebraic geometry'' (1977; Zbl 0367.14001) already covered a good part of the material they had planned to include. Instead, D. Eisenbud and J. Harris published what they felt is needed more: a brief introduction to schemes [cf. {\it D. Eisenbud} and {\it J. Harris}, ``Schemes: The language of modern algebraic geometry'' (1992; Zbl 0745.14002)]. Their booklet may be regarded as a bridge between D. Mumford's thorough classic (under review) and the now existing several textbooks on ``scheme- theoretic'' algebraic geometry, including Hartshorne's book as well as Mumford's other classic, the ``Red book of varieties and schemes''. [W.Kleinert (Berlin)]
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Your connection to active and activity-based learning at Harvard
MATH117
Every aspect of Math 121 is highly interactive: Students spend most of classtime working in groups on problems and they then present their work and discuss as a class. Each student is responsible for some part of the in-class problems.
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Vedic Mathematics was rediscovered from ancient Sanskrit texts earlier this century by Bharati Krishna vertically and Crosswise. This may sound incredible but the Vedic system offers a very different approach to mathematics that is both powerful and fun.
"Why were we not shown this before?"
Discover Vedic Mathermatics Ref: 83206
Discover Vedic Mathermatics
This has sixteen chapters each of which focuses on one of the Vedic Sutras or sub-Sutras and shows many applications of each. Also contains Vedic Maths solutions to GCSE and 'A' level examination questions.
This is an elementary book on mental mathematics. It has a detailed introduction and each of the nine chapters covers one of the Vedic formulae. The main theme is mental multiplication but addition, subtraction and division are also covered.
This book shows applications of Pythagorean Triples (like 3,4,5). A simple, elegant system for combining these triples gives unexpected and powerful general methods for solving a wide range of mathematical problems, with far less effort than conventional methods use. The easy text fully explains this method which has applications in trigonometry (you do not need any of those complicated formulae), coordinate geometry (2 and 3 dimensions) transformations (2 and 3 dimensions), simple harmonic motion, astronomy etc., etc.
This book is an abridged version of the books which form part of the Vedic Mathematics course written for schools which covers the National Curriculum for England and Wales. Book Review Sorry, this product is out of Stock
Price: £20.00 -
Spend £40 on products in May and get a £10 Voucher to spend in June.
Vertically & Crosswise Ref: 83341
Vertically & Crosswise
Vedic Mathematics is the name given to the ancient system of Mathematics which was rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960).
According to his research all of mathematics is based on sixteen Sutras, or word-formulae. For example, 'Vertically and Crosswise` is one of these Sutras. These formulae describe the way the mind naturally works and are therefore a great help in directing the student to the appropriate method of solution.
Perhaps the most striking feature of the Vedic system is its coherence. Instead of a hotch-potch of unrelated techniques the whole system is beautifully interrelated and unified: the general multiplication method, for example, is easily reversed to allow one-line divisions and the simple squaring method can be reversed to give one-line square roots. And these are all easily understood.
This unifying quality is very satisfying; it makes mathematics easy and enjoyable and encourages innovation.
Problems Solved Immediately
In the Vedic system 'difficult' problems or huge sums can often be solved immediately by the Vedic method.
These striking and beautiful methods are just a part of a complete system of mathematics which is far more systematic than the modern 'system'. Vedic Mathematics manifests the coherent and unified structure of mathematics and the methods are complementary, direct and easy.
The simplicity of Vedic Mathematics means that calculations can be carried out mentally (though the methods can also be written down).
There are many advantages in using a flexible, mental system. Pupils can invent their own methods; they are not limited to the one 'correct' method. This leads to more creative, interested and intelligent pupils.
Interest in the Vedic system is growing in education where mathematics teachers are looking for something better and finding the Vedic system is the answer.
Research is being carried out in many areas including the effects of learning Vedic Maths on children; developing new, powerful but easy applications of the Vedic Sutras in geometry, calculus, computing etc.
But the real beauty and effectiveness of Vedic Mathematics cannot be fully appreciated without actually practising the system. One can then see that it is perhaps the most refined and efficient mathematical system possible.
Tirthaji and the rediscovery of Vedic Mathematics
The ancient system of Vedic Mathematics was rediscovered from the Sanskrit texts known as the Vedas, between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960).
At the beginning of the twentieth century, when there was a great interest in the Sanskrit texts in Europe, Bharati Krsna tells us some scholars ridiculed certain texts which were headed 'Ganita Sutras'- which means mathematics.
They could find no mathematics in the translation and dismissed the texts as rubbish.
Bharati Krsna, who was himself a scholar of Sanskrit, Mathematics, History and Philosophy, studied these texts and after lengthy and careful investigation was able to reconstruct the mathematics of the Vedas.
According to his research all of mathematics is based on sixteen Sutras, or word-formulae.
Development of Further Material
A copy of the book was brought to London a few years later and some English mathematicians (Kenneth Williams, Andrew Nicholas, Jeremy Pickles) took an interest in it.
They extended the introductory material given in Bharati Krsna's book and gave many courses and talks in London.
A book (now out of print), Introductory Lectures on Vedic Mathematics, was published in 1981.
Between 1981 and 1987 Andrew Nicholas made four trips to India initially to find out what further was known about it.
Following these journeys a renewed interest was taken by scholars and teachers in India. It seems that once they saw that some people in the West took Vedic Mathematics seriously they realised they had something special.
St James' School, then in Queensgate, London, and other schools began to teach the Vedic system, with notable success.
Today Vedic Mathematics is taught widely in schools in India and a great deal of research is being done.
Three further books appeared in 1984, the year of the centenary of the birth of Sri Bharati Krsna Tirthaji. These were published by The Vedic Mathematics Research Group.
Maharishi Schools
When Maharishi Mahesh Yogi began to explain the significance and marvelous qualities of Vedic Mathematics in 1988, Maharishi Schools around the world began to teach it.
At the school in Skelmersdale, Lancashire a full course was written and trialled for 11 to 14 year old pupils, called The Cosmic Computer. (Maharishi had said that the Sutras of Vedic Mathematics are the software for the cosmic computer- the cosmic computer runs the entire universe on every level and in every detail).
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Search Course Communities:
Course Communities
Lesson 7: Linear Systems
Course Topic(s):
Developmental Math | Systems of Equations
A calculator based introduction to systems of linear equations. Systems are solved using the graphing method: first by estimating the apparent intersection of the two lines and then later by using the intersect function on the calculator to find the exact solution. Inconsistent and consistent solutions are also discussed. There are both applications based problems and non applications based problems.
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Consumer Mathematics A, the first semester of a two semester series, focuses on basic math skills used in everyday life with the goal of developing intelligent consumers. The practical applications of math are studied using real world situations. Personal finances are emphasized through the study of personal earnings, the elements of business, credit, and life insurance. Prerequisites include Algebra I and Geometry.
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Cliffs Quick Review For Geometry - 01 edition
Summary: When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core geometry concepts -- from perimeter, area, and similarity to parallel lines, geometric solids, and coordinate geometry -- and get the best possible grade.
At CliffsNotes, we're dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented wri...show moreters who know how to cut to the chase -- and zero in on the essential information you need to succeed. ...show less
Ed Kohn, MS is an outstanding educator and author with over 33 years experience teaching mathematics. Currently, he is the testing coordinator and math department chairman at Sherman Oaks Center for Enriched Studies.
2001Shopbookaholic Wichita, KSSusies Books Garner, NC
2001 Paperback This Book is in very good
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Find a Concordville can guide, but students must do the work.Introduction to the basics of symbolic representation and manipulation of variables. Liberal use of concrete examples. May require review of arithmetic concepts, including fractions and decimals
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Algebra I (PAP/Honors)
One Credit Course
Instructor: Ms. Brisa H. Bermea
Algebra I covers the basic structure of real numbers, algebraic equations, and functions. The topics studied are linear equations, inequalities, functions and systems, quadratic equations and functions, polynomial expressions, data analysis, probability and properties of functions. The honors courses provide higher expectations for students. Students have the opportunity to work at an accelerated pace and develop their higher-order thinking skills.
Geometry (Regular)
One Credit Cours
Geometry (PAP/Honors)
One Credit Course The honors courses provide higher expectations for students. Students have the opportunity to work at an accelerated pace and develop their higher-order thinking skills.
Algebra II (Regular)
One Credit Course
Instructor: Ms. Brisa H. Bermea
Algebra II (PAP/Honors)
One Credit Course
Instructor: Mr. Samuel Ayala. The honors courses provide higher expectations for students. Students have the opportunity to work at an accelerated pace and develop their higher-order thinking skills.
Advanced Math
One Credit Course
Instructor: Mrs. Yirah Valverde
This course is designed for students who have completed Algebra 1, Geometry and Algebra II and are in need of additional support after taking Algebra 2. Students in this course will apply concepts from Algebra 1, Geometry and Algebra II to solve meaningful real-world problems. In doing so, they will reinforce their algebra and geometry skills before entering the Pre-Calculus and Calculus class
Pre-Calculus
One Credit Course
Instructor: Mr. Samuel Ayala
Precalculus covers many of the topics covered on previous classes. The topics studied are polynomial, exponential, logarithmic, rational, radical, piece-wise, and trigonometric and circular functions and their inverses. Parametric equations, vectors, and infinite sequences and series are also studied.
Pre-Calc (EA)
One College Credit Course
Instructor: Mr. Reichenbach
This course covers the basic concepts of trigonometry and analytic geometry, including trigonometric functions and their graphs, relationships, and applications. Basic analytical geometry topics include the conics, translations, rotations, and basic vector geometry. At the end of the course the students receiving a passing grade will also receive college credit for this class.
Calculus (EA)
One College Credit Course
Instructor: Dr. Liguori
The Calculus topics are those traditionally offered in the first year of calculus in college, and are designed for students who wish to obtain a semester of advanced placement in college. The topics studied include limits, continuity, derivatives and integrals of algebraic and transcendental functions and their applications, and elementary differential equations. At the end of the course the students receiving a passing grade will also receive college credit for this class.
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"He who is not courageous enough to take risks will accomplish nothing in life."
--Muhammad Ali
"Strength does not come from winning. Your struggles develop your strengths. When you go through hardships and decide not to surrender, that is strength."
--Arnold Schwarzenegger
"The ultimate measure of a man is not where he stands in moments of comfort, but where he stands at times of challenge and controversy."
--Martin Luther King, Jr.
"Education is the most powerful weapon which you can use to change the world."
--Nelson Mandela
"I can accept failure. Everyone fails at something. But I can't accept not trying"
--Michael Jordan
"Do or do not. There is no try."
--Yoda
Mathematics in nature, fractals
>
Welcome Parents, Guardians and Students updated August 22, 2008 Parents, Guardians and Students,
Welcome to my class website. This website contains information for my honors geometry, algebra 1, and algebra 1 part 1 classes. Each class has its own page...
Algebra 1
Topics we will be studying this year include; basic number operations, equations, graphing equations and functions. We will also cover polynomials, quadratics and square roots. We will also address an introduction to geometry as well as preparation for CAPT.
This course will provide a study of the properties of triangles, parallel lines and planes, quadrilaterals and other polygons, circles, angles and arcs, ratios and proportions, and transformations. A scientific calculator is required for this course.
The literal translation of geometry is "earths measure", geo meaning "earth" and metres meaning "measure". Geometry is a branch of mathematics that focuses on measurements, properties and the relationship of points, lines, planes, surfaces and shapes. Although it differs from algebra considerably, a great deal of the work done will pull from topics mastered in algebra last year.
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National STEM Centre (converted from Atom 1.0)
National STEM Centre
Mon, 20 May 2013 09:38:57 GMTThis collection of forty starting activites for A level mathematics provided by RISPs is intended to enrich the lives of mathematics students in lots of A Level classrooms. All the risps presented here tackle topics from AS/A2 Core (Pure) Mathematics syllabus.<br />
<br />
Additionally every risp here leads directly into the A Level Mathematics syllabus. It is hoped these risps will enrich lessons without being tangential to the main business of the classroom. If a risp does not practise key elements of the syllabus, it has not been included.<br />
<br />
These activities are available as a complete collection, presented in ebook, or by topics suitable for AS or A2 level students. The ebook is in two parts: part one immediately gives all the risps together with their teachers' notes, indexed by topic. Part two tells the story of how these activities came about, and offers a philosophy as to how they might best be used.<br />
<br />
Broadly speaking, a risp may be used in three ways:<br />
• to introduce a topic<br />
• to consolidate a topic<br />
• to revise a topic, or a number of topics.<br />
<br />
An introductory risp is specifically designed to give a pathway into new theory. The hope is that by starting to ask for themselves some of the questions that the theory is intended to answer, students will be prepared for the exposition that is to follow.<br />
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A consolidation risp provides good practice in the use of skills whilst attempting to answer some wider question. This type of risp will assume some relevant theory to have been previously studied. A consolidation risp will generally be a good revision risp as well. A revision risp is akin to a consolidation risp, but is likely to be more synoptic, drawing together bits of theory from a range of topic areas.<br />
<br />
The teachers' notes always begin with a suggestion about the most appropriate use for each risp.Risps: Rich Starting Points for A Level Core MathematicsRisps: Rich Starting Points for A Level Core Mathematics
05 Oct 2010 12:12:37 GMTAtom 1.0 XSLT+PHP Transform v1.1 (
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revolutionary text covers single-equation linear regression analysis in an easy-to-understand format that emphasizes real-world examples and exercises. This intuitive approach avoids matrix algebra and relegates proofs and calculus to the footnotes. Clear, accessible writing and numerous exercises provide students with a solid understanding of applied econometrics. This new approach is accessible to beginning econometrics students as well as experienced practitioners. "A. H. Studenmund's practical introduction... MORE to econometrics combines single-equation linear regression analysis with real-world examples and exercises. Using Econometrics: A Practical Guide provides a thorough introduction to econometrics that avoids complex matrix algebra and calculus, making it the ideal text for the beginning econometrics student, the regression user looking for a refresher or the experienced practitioner seeking a convenient reference."--BOOK JACKET.
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