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This course serves as an introduction to analysis (real analysis), an important branch of mathematics which provides a foundation for numerical analysis, functional analysis, harmonic analysis, differential equations, differential geometry, complex analysis and many other areas of specialization within mathematics. Students will advance their ability from their mostly computational knowledge to prove anything themselves mathematically with proper reasoning and justification in Real System. This course develops the theory of calculus carefully and rigorously from basic principles and gives the students a chance to learn how to construct their own proofs.
Prerequisites:
Any one who are interested to Learn Real Analysis I, Prerequisite for Graduate or PhD Programs.
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range's tag archives
For a complete lesson on domain and range, go to - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that the form (x, y) that is used to represent a point is called an ordered pair, and a [...]
In math, the domain and range are algebraic values on the coordinate plane. Discover the definition of domains and ranges inmath with tips from a mathematics tutor in this free video on math lessons. Expert: Ken Au Bio: Ken Au is a math teacher [...]
This is one thing that every net organization man or woman is looking for and you have found it with the click on of a mouse.Every company wants a web site to remain aggressive in today's market. [...]
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Too many students end their study of mathematics before ever taking an algebra course. Others attempt to study algebra, but are unprepared and cannot keep up. "Key to Algebra" was developed with the belief that anyone can learn basic algebra if the subject is presented in a friendly, non-threatening manner and someone is available to help when needed. Some teachers find that their students benefit by working through these books before enrolling in a regular algebra course--thus greatly enhancing their chances of success. Others use "Key to Algebra" as the basic text for an individualized algebra course, while still others use it as a supplement to their regular hardbound text. Allow students to work at their own pace. The "Key to Algebra" books are informal and self-directing. The authors suggest that you allow the student to proceed at his or her own pace. In Books 5-7 of "Key to Algebra" operations on fractions are taught as students study rational algebraic expressions. This Answer Key provides brief notes to the teacher and gives the answers to all the problems in the workbooks KTA Answers Notes, Books #5-7
Review 1 for KTA Answers Notes, Books #5-7
Overall Rating:
5out of5
Date:September 30, 2008
Jessica Fry
Must have for the Algebra student books. Easy to use. I just wish they would combine all the answer keys into one book.
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Mathematics
To be an informed individual requires the ability to reason, to solve problems, and to have the tools necessary to be productive in our technological society. To become mathematically literate an individual must develop the ability to analyze, explore, conjecture, reason, use quantitative and spatial information and use mathematical tools to solve problems and make decisions. They must also develop self-confidence in their abilities and to understand and appreciate the role of math in everyday life.
DEPARTMENT GOALS:
To meet the BC Mathematics Curriculum and the New Western Consortium Mathematics Curriculum
To provide students with opportunity to take a mathematics course that reflects their abilities and meets their needs.
To provide students with mathematical skills and tools to help them achieve their academic and/or career choice
To help students to confidently use numeracy and problem solving/reasoning skills and tools in everyday life.
REMINDERS/DATES:
Pascal, Cayley and Fermat Contests for grade 8 to 11 students will take place in February. Date: TBA.
Students are asked to speak to their math teachers about registering for these contests and receiving practice materials.
Euclid Contest for grade 12 students will take place in April. Date: TBA
Students who have signed up to participate or are wishing to register are asked to see Ms. Martins.
COURSES AVAILABLE:
STA Math Department offers the following courses:
Math 8 / Math 9 / Math 10 courses are undergoing changes and will be updated shortly Principles of Math 11 Principles of Math 11 Honours Essentials of Math 11 Principles of Math 12 Changes are being made to Math 11 and 12 courses for the school year 2011-12
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Download "Travel to Geneva" by Stig Albeck for FREE. Read/write reviews, email this book to a friend and more...
Travel to GenevaComments for "Travel to Geneva"i...
Algebra is one of the main branches in mathematics. The book series of elementary algebra exercises includes useful problems in most topics in basic algebra. The problems have a wide variation in difficulty, which is indicated by the number of stars.
This is an HTML version of the ebook and may not be properly formatted. Please view the PDF version for the original work.
An excerpt is a selected passage of a larger piece, hence this is not the complete book.
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Welcome to Basic Math For Adults. Basic Math For Adults is a 17 chapter program to help review and polish basic math skills. The student who successfully completes the entire program, should be ready for pre–algebra or algebra. The program lends itself either to individualized work or to group instruction. Beginning chapters include very basic reviews in working with whole numbers and basic operations, and moves through chapters on integers, basic geometry, consumer math, and statistics and proportions.
Grade is based on:
Homework 40%
Quizzes 30%
Final Exam 30%
Grading Scale
A
93-100%
C
73-76%
A-
90-92%
C-
70-72%
B+
87-89%
D+
67-69%
B
83-86%
D
63-66%
B-
80-82%
D-
60-62%
C+
77-79%
F
< 59%
Basic Math For Adults includes a number of features.For nearly every lesson, there is a five question Daily Quiz. Each chapter also includes a pre-assessment test, a final chapter test, and a "Maintaining Your Skills" section. Also included in the program are a set of basic facts drill sheets.
Pre-assessment Tests – – For each of the 17 units, there is a prepared pre-assessment test. The design of this pre-assessment is to let you, as the teacher, know the needs of each individual student. If a student has strength in an area, he/she just as well move past certain lessons, or even an entire unit. The tests are designed so that the instructor can make a quick diagnosis of strengths and weakness for the upcoming unit. There are four questions from each lesson. (Unit 14 – Geometry, is the one exception to this.) If the student answers all four of the questions pertaining to a particular lesson correctly, that would normally indicate the student has a good understanding of that concept, and need not spend much additional time with the lesson. If the student does not demonstrate proficiency on the pre-assessment, it would make sense to do the lessons where the student is weak. Calculators should not be used on a pre-assessment test. (Calculators may be used on Unit 14 – Geometry, Unit 16 – Consumer Math, and/or Unit 17 – Proportions, Statistics, and Square Roots. This is left up to the discretion of the instructor.)
Basic Facts – One of the biggest frustrations students have in basic math is their inability to do the basic facts of addition, subtraction, multiplication, and division. Failure to have a good grasp on basic facts slows a student down, decreases accuracy, and makes the math experience drudgery. Basic facts constitute the very foundation of everything a student does as he advances in math.
Basic Math For Adults includes- Drill sheets for the four basic operations (the sheets for multiplication and addition are interchangeable). There are 100 facts on each sheet (90 on the division sheets). It is suggested that the student work each day on the drill sheets in the beginning stages of the program. A realistic goal for the student is to complete the facts sheets in two minutes with 100% accuracy.
Drilling basic facts can be pretty dull. It is important for the student to know that he is progressing. Goal setting and charting progress are two valuable tools in keeping students motivated.
Daily Quizzes – There is a quiz to follow nearly every lesson in the program. There are five questions on each quiz. The first four questions deal with the lesson that has just been completed. The fifth question is normally a review question from an earlier lesson or unit. It is suggested that these quizzes be done independently after the lesson has been corrected and any problems answered for the student. This is an excellent means for the instructor to evaluate progress. If the student does not do well on the quiz, it will be obvious that more time needs to be spent working on that particular concept. Answer Keys for each quiz are included on the final page of each unit's set of quizzes.
Answer Keys – The answers for each lesson are included in a special section called Answer Keys. These include the keys for the tests and the Maintaining Your Skills sections.
Post tests – There is a post test for each unit to be given at the conclusion of the unit. This should be completed independently and is intended as a means to allow the instructor to evaluate the students' mastery of the concepts presented in the unit. Similar problems are generally grouped together, so it is easy to determine weak areas that the student may need to review.
Maintaining Your Skills – The last lesson in each unit (with the exception of Unit 1) is a Maintaining Your Skills lesson. These should be completed after the unit test has been taken. There are a variety of formats used in these review exercises; occasionally they may be in a multiple choice format or they may all be word problems. The final lesson in Unit 17, for example, is patterned after a GED test. It is often easy to skip over the review lessons. It is suggested that these review lessons be treated with the same importance as any other lesson.
Using Calculators – Each instructor may have different feelings about the use of calculators. My suggestion is that calculators not be used, especially in the units on basic operations, decimals, fractions, and percents. It may be appropriate to use calculators on the chapters on geometry, consumer math, and statistics. Again, this is left up to the individual teacher.
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Seventh Grade Math: Pre-Algebra begins by reviewing the basic arithmetic operations and their relationships. This course shows how to graph algebraic relations and how to solve simple linear equations. It provides a fundamental set of algebra skills that can be used to study various problems that have real-world applications.
Eighth Grade Math:Algebra 1 course includes the study of rational number properties, variables, polynomials, and factoring. Students learn to write, solve, and graph linear and quadratic equations and to solve systems of equations. They also learn to model real-world applications, including statistics and probability investigations.
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Hi Friends. Ever since I have encountered square root exercises for 7th grade at college I never seem to be able to cope with it well. I am well versed at all the other sections, but this particular section seems to be my weak point. Can some one aid me in learning it properly?
Hi, I believe that I can to help you out. Have you ever tried out a program to help you with your algebra assignments? a while ago I was also stuck on a similar problems like you, and then I found Algebrator. It helped me a great deal with square root exercises for 7th grade and other algebra problems, so since then I always rely on its help! My algebra grades got better since I found Algebrator.
Welcome aboard friend. This subject is very appealing, but you need to know your basics and techniques first. Algebrator has helped me a lot in my course. Do give it a try and it will work for you as well.
A great piece of math software is Algebrator. Even I faced similar difficulties while solving adding exponents, evaluating formulas and angle-angle similarity. Just by typing in the problem from homeworkand clicking on Solve – and step by step solution to my algebra homework would be ready. I have used it through several algebra classes - College Algebra, College Algebra and Algebra 1. I highly recommend the program.
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Physics major preoccupied with pure math
Physics major preoccupied with pure math
I lack talent in pure mathematics. (Although applying mathematical methods has been natural for me.) Im a physics freshman. I can prove and I can self study mathematics given enough time.
I guess it's still too early to decide, but, I suppose, I'll be doing theoretical/mathematical physics in grad school because I really like mathematics and physics - and I find experiments to be tedious. I am preoccupied with mathematics. I feel that if I don't learn enough pure math I won't be as good in its applications to physics.
The math only courses I'll be taking are Calc I, Calc II, and ODE. The rest are in math methods classes. The curriculum is fixed so I can't do anything about it, besides self studying the gaps.
For instance, in Multivariable Calculus Theory and Application by K. Kuttler linear algebra is required for vector calc. But my other book, cookbook calculus, goes up to stoke's theorem without linear algebra.
The problem is that self-studying is really hard for someone with no formal schooling nor talent for pure mathematics. I also don't have the time. I'm at a loss on which manner should I proceed with my mathematics education.
How should I study math? I.e. do I really need to learn the math or just the methods?
In my experience, studying pure math doesn't help at all with physics. I've taken a fair amount of pure math courses, even some grad classes, and I still don't see a good connection between the two. A physics course will teach you the math along with the physics anyway. Knowing how to use the math will help immensely more than the proofs of it. Physicists are incredible at approximating and mathematicians are great at generalizing. Choose your poison. It's two different mindsets for each and I haven't seen many make the connection, I know I certainly haven't.
On another note, this is my last semester of classes to finish my PhD and I've found that if you thoroughly know Calc 1-3, linear algebra, and differential equations you'll be able to handle anything in your physics courses.
Physics major preoccupied with pure math
Depends on what kind of physics you are going to do.
Studying certain things in pure math gives great insight into physics. I'm more of a mathematician. Knowing some pretty deep bits of math are the key to my understanding of certain physics concepts. This is coming from the perspective of someone who requires a very deep, intuitive understanding of what they study.
There are lots of examples.
For example, Hamilton's equations in classical mechanics have a beautiful geometrical meaning and are motivated by the analogy between optics and mechanics. As far as I can tell, the best way to get at this meaning is to use a decent amount of pure math stuff. Namely, some differential forms, symplectic geometry, and maybe contact geometry.
There is some nice hyperbolic geometry to be found in the space-time of special relativity. Also, in close relation to this, the Mobius transformations of complex analysis show up.
General relativity makes heavy use of differential geometry. If you use more sophisticated math, you'll understand it better. In fact, Penrose introduced techniques of differential topology that are now standard in the field because he came from more of a math background. This allowed him to prove a theorem to the effect that black holes always have singularities in them.
Gauge theories in particle physics seem to be best understood using the theory of principal bundles and connections.
And the list could go on.
The way to understand many things in physics on a deep level seems to me to, at least sometimes, involve some pretty deep math. The separation of math and physics seems to me to be pretty detrimental to both fields. Math misses out on a lot of inspiration and physics misses a lot of deep conceptual insights. On the other hand, it is possible for physicists to over-do it with the math.
Seems like the physicists are too eager to calculate without wanting to know the deeper meaning and the mathematicians are too steeped in abstraction. That's at least the impression I am under.
For a good overview of a lot of the things that I have mentioned, you can take a look at Penrose's book, The Road to Reality.
^ problem is, I find it really hard to study pure mathematics. Sometimes I study at the rate of 1hr a page. It's painful actually. But I really like pure math. It's wonderful. I just find it hard right now, being a complete beginner and all. Are there some fairly easy math books that are rigorous and intuitive at the same time?
problem is, I find it really hard to study pure mathematics. Sometimes I study at the rate of 1hr a page. It's painful actually.
Partly, this is due to the silly way that many math books are written. Very inefficient way of learning. One option is to try to come up with parts of the proofs for yourself, rather than reverse-engineer proofs from a book. It's good to have some practice reading formal proofs, though.
But I really like pure math. It's wonderful. I just find it hard right now, being a complete beginner and all. Are there some fairly easy math books that are rigorous and intuitive at the same time?
The best book is Visual Complex Analysis, but it's not that rigorous. But I think that is okay. If you want intuitive and rigorous, your best bet is to try to use more than one book in a lot of cases. But then, sometimes, it can be hard to translate fully from one approach to the other. All of Vladimir Arnold's books are good, but not always easy.
Are there some fairly easy math books that are rigorous and intuitive at the same time?
There are indeed. Axler's Linear Algebra done right reads like a novel - its fantastic. Spivak's calculus is also easy to read, and provides some nice examples. Both of these books can easily be studied without any backround, even without previous knowledge of proofs. Vector Calculus by Colley is a good multivariable/vector calc book as well.
I've found that if you thoroughly know Calc 1-3, linear algebra, and differential equations you'll be able to handle anything in your physics courses.Quote by Headacheguy
Are there some fairly easy math books that are rigorous and intuitive at the same time?It's completely irrational to think that starting from pure math then applying it to physics is advantageous.
Not true. As I said, that depends on what you want to do. Some people don't really want to be physicists; they want to be mathematicians who work on physics-related problems. And they are not useless people. They have a role to play. Everyone has a role.
It's also not just a matter of "wanting to do physics". It's hard to explain what I mean by that, but for example, I had a math prof who said math was always just easier. It seemed like he "wanted" to do physics. But he was better at math, so he did math.
In my own case, I was the same way. I wanted to be a physicist. But that didn't really work out that well for me. Neither did math, actually, in some ways, but it seemed more congenial to my way of thinking than the way physics was taught in my undergrad, so I went with math, hoping to eventually get back to physics. It wasn't a question of thinking that that was the best way to do physics. It was more like what I had to do because of my way of doing things. To some extent, it worked. I found a lot of what was missing in my classical mechanics class that was instrumental in turning me away from physics by studying math.
It looks like I might not make it in either physics or math because I refused to be a cog in the machine. It had to be my way or the highway. But it's very difficult when you have to swim against the stream. Math and physics are difficult enough even without having to swim against the streamI have to agree with lsaldana.
I dont see how you cant at least feel crutched without feeling like you know at least some of the topic lsaldana discusses. Group theory is important in solid state and QFT. Functional derivatives are used all the time. Complex analysis is just a given .
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Monday, February 4, 2013
Click on the graphs above to interact with and see the relationship between algebraic definitions of functions and their graphical representations. As we progress through this unit your algebraic, numerical, and graphical understanding of this function should be deepened and allow you to apply your understanding of the behavior to rational functions in a modeling context. This unit will focus on simple rational functions with a special emphasis on modeling rates, average cost, and geometric ratios.
The homework of this unit will continue to push and develop your ability to interpret functions in their graphical context. The homework can be accessed from this link: visualizing relationships.
TenMarks does have a series of problem sets on rational functions so please take advantage of the.practice and review available there.
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WebEq:This
is a technical site. You can download a free and very powerful equation editor
that will also create visuals for you. It is located in the U. of Minnesota
Geometry Center. From the home page, you will find the WebEq subpage. This is
well worth the time to look for.
Euclid's
Elements:This
site contains the 13 books of Euclid's Elements. The value here is that every
diagram associated with a theorem, is self-animating. One can see the diagram
move in a variety of ways, always maintaining the conditions of the theorem.
This is so fascinating that I spent far too much time here, browsing, and wishing
that I were teaching geometry again. (This is a great place to send students
to see what Euclid is all about.)
Connections
+:A
very good site to explore. Find the subheading Math and click. You'll find the
Geometry Junkyard there, also. As I went back and looked again I found more
of interest. Particularly interesting were the sites devoted to polyhedra and
polytopes. Some sites have lesson plans associated with them. This is a treasure
trove of cool stuff in geometry
NonEuclid:A
very interesting, interactive site exploring the math and the understanding
of Non-Euclidean geometry using straight edge and compass constructions from
the point of view of the Riemann model. Good way to go. Perfect for the better
student.
TRIG
MtL-Trigonometry:A
complete course in Trig, interactive via java applets. Parts are still under
construction. Very nice otherwise.This could be used effectively as a supplement
to the course being taught.
The
Integrator:This
seems to be a good, interactive integral calculator. It is perhaps not much
more than a very complete sourcebook of integrals. Needs some exploration to
see just how extensive it is.
AP
Calculus:This
is an extensive site devoted to preparing for the Calculus AP Test. It lists
two AP Calculus Problems of the Week, The site includes links to previous problems
of the week, their solution, and other items of interest to AP Calculus teachers
and students. There are extensive tutorials. Very interactive.
Problem
Of The Week (POTW):Need
good math strategies, or math problems to keep you occupied? Come to this site,
where the problems are weekly updated, and you can submit your questions, and
see them on the site. (simple algebra, and other easy items.)
Swathmore
Math Subjects:Various
links to programs that help k-12 students understand their problems in math.
The site has it's own search engine for other math sites as well as online documentations.
Plus, there are public forums on math topics, to help.
Zona
Land:Online
tutor in the fundamentals of: math in general with animated charts and diagrams,
trigonometry, algebra, and other mathmatics. Perfect for online help and advice
about questionable subjects.
Teachers:
If you want a web site added to this page, e-mail the information here.
Please include your name and email address in your message. Send information regarding
dead links to the same address.
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Short Description for Introduction to Complex Analysis Complex analysis is a classic and central area of mathematics, which is studied and exploited in a range of important fields, from number theory to engineering. This book offers a detailed presentation of elementary topics, to reflect the knowledge base of students. Full description
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American Preparatory Institute.
Math Skills by
Objectives. New York: Cambridge Book Company, 1985. Math Skills by Objectives is a series of three workbooks with accompanying
answer booklets and a test booklet. The workbooks provide explanations and drills
in a number of math skills. Book One explains whole numbers, fractions,
decimals and percents. Book Two explains graphs and tables, consumer math
skills, measurement, and basic geometry. Book Three reviews basic
arithmetic, geometry, algebra, and test-taking skills. These books would be a good
choice for anyone who thinks they need to brush up specific math skills.
Ashley, Ruth. Background Math for a Computer World.
New York: John Wiley & Sons, 1980. Background Math for a Computer World introduces those with a limited
background to the math needed to work in the machine language of computer
programming. The book introduces the binary number system, computer logic, and
linear equations.
Chernow, Fred B. Business Mathematics Simplified and
Self-Taught. New York: Arco Publishing, Inc., 1984. Business Mathematics Simplified and Self-Taught provides detailed
explanations of a number of basic arithmetic functions, such as rounding off,
dividing by 10, 100, 1000, etc., before discussing fractions, decimals,
percentages, interest and other business math applications.
Deese, James, and Ellin K. Deese.
How to Study .
New York: McGraw-Hill Book Company, 1969. How to Study is an introduction to study skills for on-campus students. The
book covers time management, reading, and essay writing. It also provides tips for
studying foreign languages, math and science.
Hackworth, Robert D., and Joseph W. Howland. Programmed
Arithmetic. Clearwater, Florida: H & H Publishing Company, Inc., 1983. Programmed Arithmetic teaches arithmetic. Each idea is explained then
followed with examples and exercises. There are tests for each chapter with
answers at the back of the book. Students who have never mastered multiplying and
dividing fractions, or do not understand the meaning of ten to the seventh power,
will find this book helpful. The book's table of contents is thorough enough to
locate the most relevant topics.
Hartkopf, Roy. Math Without Tears. Boston: G.K.
Hall & Co., 1985. Math Without Tears will expand students' knowledge of mathematical
languages and show the relationships between them (e.g., the relationship of
trigonometry to calculus). The book explores and refutes the common idea that
mathematics yields one correct answer. The author shows that, depending upon the
mathematical system one uses, one plus one could equal two, three, or more.
Parson, Ted. Demystifying Math. Victoria, B.C.:
University of Victoria, 1985. Demystifying Math is a workbook to refresh math skills. The book begins
with arithmetic and proceeds to algebra, sets and Cartesian products, graphs of
linear equations and inequalities, systems of linear equations, exponents, and
quadratic equations. There are exercises and self-tests throughout. Students who
find these words familiar but cannot remember what they mean may find this book
useful.
Selby, Peter H. Quick Algebra Review.
New York:
John Wiley & Sons, Inc., 1983. Quick Algebra Review is intended as a refresher for those who studied
algebra in high school. There are brief explanations, examples, and many exercises
with answer keys. The table of contents and index will help readers identify
specific topics for review.
Thompson, J. E. Trigonometry for the Practical Worker.
New York: Van Nostrand Reinhold Company Inc., 1982. Trigonometry for the Practical Worker contains just about everything
students would want to know about plane trigonometry from the basic ideas to their
application to measurement. The book has exercises with answer keys to help
students test and deepen their understanding.
Tobias, Sheila. Overcoming Math Anxiety.
Boston: Houghton Mifflin Company, 1980. Overcoming Math Anxiety examines the cause of the difficulty, paying
special attention to the biases that make women feel incapable of learning and
using math. The author explores the problems in words and illustrates the ideas
with examples and drawings. The book also has explanations and exercises to help
readers overcome common mathematical stumbling blocks
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Yet this familiar expression is a gateway into the riotous garden of mathematics, and sends us on a journey of exploration in the company of two inspired guides, acclaimed au...5.3 MB21.29Schaum's Outline of College Algebra, Third Edition R Spiegel Moyer Test Questions a...416 pages21 MB14.79The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse Ouellette My Math meets A Tour of the Calculus Jennifer Ouellette never took math in college, mostly because she-like most people-assumed that she wouldn't need it in real life. But then the English-major-turned-award-winning-science-writer had a cha...336 pages1.6 MB12.99Pre-Calculus Know-It-ALL Gibilisco pre-calculus from the comfort of home!Want to "know it ALL" when it comes to pre-calculus? This book gives you the expert, one-on-one instruction you need, whether you're new to pre-calculus or you're looking to ramp up your skills. Provi...608 pages11.2 MB18.29Practice Makes Perfect Calculus William Clark McCune Makes Perfect has established itself as a reliable practical workbook series in the language-learning category. Now, with Practice Makes Perfect: Calculus, students will enjoy the same clear, concise approach and extensive exercises to ke...208 pages13 MB9.49Math Word Problems Demystified Bluman Professional2004-07-26Word problems are the most difficult part of any math course –- and the most important to both the SATs and other standardized tests. This book teaches proven methods for analyzing and solving any type of math word problem.308 pages2.1 MB14.79Math-A-Day: A Book of Days for Your Mathematical Year Pappas World Publishing, Tetra1999-10-17Pappas has come up with yet another way to make math part of your life. 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In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi...304 pages6.3 MB15.99Statistics for Earth and Environmental Scientists Schuenemeyer Drew comprehensive treatment of statistical applications for solving real-world environmental problemsA host of complex problems face today's earth science community, such as evaluating the supply of remaining non-renewable energy resources, assessin...4.3 MB109.99Latent Class Analysis of Survey Error P. Biemer theoretical, methodological, and practical aspects, Latent Class Analysis of Survey Error successfully guides readers through the accurate interpretation of survey results for quality evaluation and improvement. 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From the Preface:
"The goal of this course is to develop your ability to read, write,
think, and do mathematics and to give you command of the facts and
methods
of algebra and trigonometry. It emphasizes everything you need to
understand
to be prepared for calculus.
"A unique feature of this course is its emphasis on developing
fluency
in the abstract and symbolic language of algebra. That "foreign"
language
is extremely important because it is the most effective and efficient
language
in which to learn, understand, recall, and think mathematical
thoughts."
Homeschoolers might be interested in two additional chapters. Precalculus, Table of
Contents
(somewhat expanded to include subsections. The shorter
version
is above).
From the Preface: "A unique feature of this course is its emphasis
on developing fluency in the abstract and symbolic language of algebra.
That "foreign" language is extremely important because it is the most
effective
and efficient language in which to learn, understand, recall, and think
mathematical thoughts."
Chapter 1 is not typical. It emphasizes learning the
symbolic language of algebra. It discusses what algebraic
symbolism is for and how it is used to say what it says.
CHAPTER 1, READING MATHEMATICS
1.1. Algebra
Interpretation of Expressions, Operations and Identities
1.2. Order Matters!
Notation for Grouping
Parentheses For the Quadratic Formula
Guide to Pronunciation
1.3. Functions and Notation
functional "f(x)" notation
placeholders (dummy variables)
1.4. Reading and Writing Mathematics
Placeholders (dummy variables) and unknowns
How to write Methods
Methods as Formulas
Methods as Identities
Methods as Relations between Equations
1.5. Graphs
Terminology of Graphs
Expressions and Graphs
Graphing with Calculators,
Selecting a Window
Limitations of Calculator Graphs
Graphing Expressions to Solve Equations,
Maximizing or Minimizing an Expression
Graphs Without Expressions
1.6. Four Ways to Solve Equations
The "Inverse-Reverse" Method
The Zero Product Rule Method
The Quadratic Formula
Guess-and-Check ("trial and error")
CHAPTER 2, FUNCTIONS AND GRAPHS
2.1. Functions and Graphs
Finding Windows
2.2. Composition and Decomposition
Composition and Inverses
Composition and Graphs
2.3. Relations and Inverses
CHAPTER 3, FUNDAMENTAL FUNCTIONS
3.1. Lines
Slope
Proportional
Parameters
Solving Linear Equations
Applications
Parallel and Perpendicular Lines
3.2. Quadratics
Symmetry
Location Changes, completing the square
The Quadratic Formula
Scale Changes
3.3. Distance, Circles, and Ellipses
Distance in the Plane
Circles
3.4. Graphical Factoring
The Factor Theorem
3.5. Word Problems
Build Your Own Formula
Evaluation and Solving
3.6. More on Word Problems
CHAPTER 4, POWERS
4.1. Powers and Polynomials
Polynomials
Graphs of Polynomials
End Behavior
The Use of Polynomials, Approximation
4.2. Polynomial Equations
Solving Monomial Equations
Solving Polynomial Equations
Calculator-Aided Factoring Techniques
4.3. Fractional Powers
Fractional Powers
Square Root
4.4. Percents, Money, and Compounding
Composition of Functions
Money, Compound Interest
Average Rate of Change
4.5. Rational Functions
Solving Rational Equations
Graphs
Asymptotes
End-Behavior
Uses of Rational Functions
4.6. Inequalities
Interval Notation
Graphical Solutions
Absolute Values
Inequalities for Calculus
Solving Linear Inequalities
Zeros and Inequalities
CHAPTER 5, EXPONENTIAL AND LOGARITHMIC FUNCTION
5.1. Exponents and Logarithms
Scientific Notation
Exponents and Logarithms
Properties of Exponential Functions
Properties of Logarithms
5.2. Base 2 and Base e
Base 2 (doubling time models)
Exponential Growth
Base 1/2 (half-life models)
Compound Interest
Base e
Polynomial Approximations
Change-of-Base
5.3. Applications
Richter Scale
Decibels
Exponential Models
Growth of Money
5.4. More Applications
Power Models, Kepler's Laws
CHAPTER 6, TRIGONOMETRY
6.1. Geometry for Trigonometry
Solving a Triangle
Pythagorean Theorem
Ambiguous Cases, Recognizing the Cases
6.2. Trigonometric Functions
Sine, Inverse Sine
Solving Right Triangles
Cosine, Inverse Cosine
Tangent, Inverse Tangent
Reference Angles, Basic Facts
6.3. Solving Triangles
Area
The Law of Sines
The Law of Cosines
6.4. Solving Figures
Solving Triangles
More Complex Figures
Navigation
CHAPTER 7, TRIGONOMETRY FOR CALCULUS
7.1. Arc Length and Radians
Arc Length
Area of a Sector
7.2. Trigonometric Identities
From Unit-Circle Pictures
Reference Angles
Solving Trigonometric Equations
Other Trigonometric Functions
Identities from Right-Triangle Pictures
Trigonometric Substitution
7.3. More Identities
The Sum and Difference Identities
Double- and Half-Angle Identities, Squared Identities
7.4. Waves
Describing Sine Waves
Adding Sine Waves
Applications
[This is the end of a one-semester four-credit course at Montana State
University.]
|
Numbers, Groups and Codes
9780521540506
ISBN:
052154050X
Edition: 2 Pub Date: 2004 Publisher: Cambridge Univ Pr
Summary: A thoroughly revised and updated version of the popular textbook on abstract algebra. The material is introduced with clarity and reference to problems and concepts that students will easily understand. With many examples and exercises, it will serve as the ideal introduction to this important and ubiquitous subject.
|
Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations, functions;. one-one, into and onto functions, composition of functions.
UNIT 2 : COMPLEX NUMBERS AND QUADRATIC EQUATIONS:
Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a
complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots.
UNIT 3 : MATRICES AND DETERMINANTS:
Matrices, algebra of matrices, types of matrices, determinants and matrices of order two and three. Properties of determinants, evaluation of determinants, area of triangles using determinants. Adjoint and evaluation of inverse of a square matrix using determinants and elementary transformations, Test of consistency and solution of simultaneous linear equations in two or three variables using determinants and matrices.
UNIT 4 : PERMUTATIONS AND COMBINATIONS:
Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications.
UNIT 5 : MATHEMATICAL INDUCTION:
Principle of Mathematical Induction and its simple applications.
UNIT 6 : BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS:
Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients and simple applications.
Evaluation of simple integrals of the type Integral as limit of a sum. Fundamental Theorem of Calculus. Properties of definite integrals. Evaluation of definite integrals, determining areas of the regions bounded by simple curves in standard form.
UNIT 10: DIFFERENTIAL EQUATIONS:
Ordinary differential equations, their order and degree. Formation of differential equations. Solution of differential equations by the method of separation of variables, solution of homogeneous and linear differential equations of the type: dy+ p (x) y = q (x) dx
UNIT 11: CO-ORDINATE GEOMETRY:
Cartesian system of rectangular co-ordinates 10 in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes. Straight lines Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines. Circles, conic sections
Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent. Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency.
UNIT 12: THREE DIMENSIONAL GEOMETRY:
Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines.Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, intersection of a line and a plane, coplanar lines.
UNIT 13: VECTOR ALGEBRA:
Vectors and scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, scalar and vector triple product.
UNIT 14: STATISTICS AND PROBABILITY:
Measures of Dispersion: Calculation of mean, median, mode of grouped and ungrouped data calculation of standard deviation, variance and mean deviation for grouped and ungrouped data. Probability: Probability of an event, addition and multiplication theorems of probability, Baye's theorem, probability distribution of a random variate, Bernoulli trials and Binomial distribution.
Force and Inertia, Newton's First Law of motion; Momentum, Newton's Second Law of motion; Impulse; Newton's Third Law of motion. Law of conservation of linear momentum and its applications, Equilibrium of concurrent forces. Static and Kinetic friction, laws of friction, rolling friction. Dynamics of uniform circular motion: Centripetal force and its applications.
UNIT 4: WORK, ENERGY AND POWER
Work done by a constant force and a variable force; kinetic and potential energies, workenergy theorem, power. Potential energy of a spring, conservation of mechanical energy, conservative and nonconservative forces; Elastic and inelastic collisions in one and two dimensions.
UNIT 5: ROTATIONAL MOTION
Centre of mass of a two-particle system, Centre of mass of a rigid body; Basic concepts of rotational motion; moment of a force, torque, angular momentum, conservation of angular momentum and its applications; moment of inertia, radius of gyration. Values of moments of inertia for simple geometrical objects, parallel and perpendicular axes theorems and their applications. Rigid body rotation, equations of rotational motion.
UNIT 6: GRAVITATION
The universal law of gravitation. Acceleration due to gravity and its variation with altitude and depth. Kepler's laws of planetary motion. Gravitational potential energy; gravitational potential. Escape velocity. Orbital velocity of a
Thermal equilibrium, zeroth law of thermodynamics, concept of temperature. Heat, work and internal energy. First law of thermodynamics. Second law of thermodynamics: reversible and irreversible processes. Carnot engine and its efficiency.
UNIT 9: KINETIC THEORY OF GASES
Equation of state of a perfect gas, work doneon compressing a gas.Kinetic theory of gases - assumptions, concept of pressure. Kinetic energy and temperature: rms speed of gas molecules; Degrees of freedom, Law of
Electric charges: Conservation of charge, Coulomb's law-forces between two point charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field: Electric field due to a point charge, Electric field lines, Electric dipole, Electric field due to a dipole, Torque on a dipole in a uniform electric field. Electric flux, Gauss's law and its applications to find field due to infinitely long uniformly charged straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell. Electric potential and its calculation for a point charge, electric dipole and system of charges; Equipotential surfaces,
Electrical potential energy of a system of two point charges in an electrostatic field. Conductors and insulators, Dielectrics and electric polarization, capacitor, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, Energy stored in a capacitor.
UNIT 12: CURRRENT ELECTRICITY
Electric current, Drift velocity, Ohm's law, Electrical resistance, Resistances of different materials, V-I characteristics of Ohmic and nonohmic conductors, Electrical energy and power, Electrical resistivity, Colour code for resistors; Series and parallel combinations of resistors; Temperature dependence of resistance. Electric Cell and its Internal resistance, potential difference and emf of a cel l, combination of cells in series and in paral lel. Kirchhoff's laws and their applications. Wheatstone bridge, Metre bridge. Potentiometer - principle and its applicat ions.
UNIT 13: MAGNETIC EFFECTS OF CURRENT AND MAGNETISM
Biot - Savart law and its application to current carrying circular loop. Ampere's law and its applications to infinitely long current carrying straight wire and solenoid. Force on a moving charge in uniform magnetic and electric fields.Cyclotron. Force on a current-carrying conductor in a uniform magnetic field. Force between two parallel current-carrying conductors-definition of ampere. Torque experienced by a current loop in uniform magnetic field; Moving coil galvanometer, its current sensitivity and conversion to ammeter and voltmeter. Current loop as a magnetic dipole and its magnetic dipole moment. Bar magnet as an equivalent solenoid, magnetic field lines; Earth's magnetic field and magnetic elements. Para-, dia- and ferro- magnetic substances. Magnetic susceptibility and permeability, Hysteresis, Electromagnets and permanent magnets.
Reflection and refraction of light at plane and spherical surfaces, mirror formula, Total internal reflection and its applications, Deviation and Dispersion of light by a prism, Lens Formula, Magnification, Power of a Lens, Combination of thin lenses in contact, Microscope and Astronomical Telescope (reflecting and refracting) and their magnifyingpowers. Wave optics: wavefront and Huygens' principle, Laws of reflection and refraction using Huygen's principle. Interference, Young's double slit experiment and expression for fringe width. Diffraction due to a single slit, width of central maximum. Resolving power of microscopes and astronomical telescopes, Polarisation, plane polarized light; Brewster's law, uses of plane polarized light and Polaroids.
Propagation of electromagnetic waves in the atmosphere; Sky and space wave propagation, Need for modulation, Amplitude and Frequency Modulation,Bandwidth of signals, Bandwidth of Transmission medium, Basic Elements of a Communication System (Block Diagram only).
SECTION –B
UNIT 21: EXPERIMENTAL SKILLS
Familiarity with the basic approach and observations of the experiments and activities: and time.
4. Metre Scale - mass of a given object by principle of moments.
5. Young's body liquid by method of mixtures.
11. Resistivity of the material of a given wire using metre bridge.
12. Resistance of a given wire using Ohm's law.
13. Potentiometer –
(i) Comparison of emf of two primary cells.
(ii) Determination of internal resistance of a cell.
14. Resistance and figure of merit of a galvanometer by half deflection method.
15. Focal length of:
(i) Convex mirror
(ii) Concave mirror, and
(iii) Convex lens
using parallax method.
16. Plot of angle of deviation vs angle of incidence for a triangular prism.
17. Refractive index of a glass slab using a travelling microscope.
18. Characteristic curves of a p-n junction diode in forward and reverse bias.
19. Characteristic curves of a Zener diode and finding reverse break down voltage.
20. Characteristic curves of a transistor and finding current gain and voltage gain.
Fundamentals of thermodynamics: System and surroundings, extensive andintensivesublimation, phase transition, hydration, ionization and solution.Second law ofthermodynamics; Spontaneity of processes; DS of the universe and DG of the system as criteria for spontaneity, Dgo (Standard Gibbs energychange) and equilibrium constant.
specific.
UNIT 9 : CHEMICAL KINETICS
Rate of a chemical reaction, factors affecting the rate of reactions:concentration, temperature, pressure and catalyst; elementary and complex reactions, order and molecularity of reactions, rate law, rate constant and its
units, differential and integral forms of zero and first order reactions, their characteristics and half - lives, effect of temperature on rate of reactions – Arrhenius theory, activation energy and its calculation, collision theory of
Modes of occurrence of elements in nature, minerals, ores; Steps involved in the extraction of metals - concentration, reduction (chemical and electrolytic methods) and refining with special reference to the extraction of Al, Cu, Zn and Fe; Thermodynamic and electrochemical principles involved in the extraction of metals.
UNIT 13: HYDROGEN
Position of hydrogen in periodic table, isotopes, preparation, properties and uses of hydrogen; Physical and chemical properties of water and heavy water; Structure, preparation, reactions and uses of hydrogen peroxide; Hydrogen as a fuel.
UNIT 14: S - BLOCK ELEMENTS (ALKALI AND ALKALINE EARTH METALS)
Group - 1 and 2 Elements
General introduction, electronic configuration and general trends in physical and chemical properties of elements, anomalous properties of the first element of each group, diagonal relationships. Preparation and properties of some important compounds - sodium carbonate and sodium hydroxide; Industrial uses of lime, limestone, Plaster of Paris and cement; Biological significance of Na, K, Mg and Ca.
UNIT 15: P - BLOCK ELEMENTS
Group - 13 to Group 18 Elements
General Introduction: Electronic configuration and general trends in physical andchemical properties of elements across the periods and down the groups; unique behaviour of the first element in each group. Groupwise study of the p – block elements
General methods of preparation, properties, reactions and uses. Amines: Nomenclature, classification, structure, basic character and identification of primary, secondary and tertiary amines and their basic character.
Diazonium Salts: Importance in synthetic organic chemistry.
UNIT 25: POLYMERS
General introduction and classification of polymers, general methods of polymerization-addition and condensation, copolymerization; Natural and synthetic rubber and vulcanization; some important polymers with emphasis on their monomers and uses - polythene, nylon, polyester and bakelite.
Part - I Awareness of persons, places, Buildings, Materials.) Objects, Texture related to Architecture and build~environment. Visualising three dimensional objects from two dimensional drawings. Visualising. different sides of three dimensional objects. Analytical Reasoning Mental Ability (Visual, Numerical and Verbal).
Part - tre es, plants etc.) and rural life.
Note: Candidates are advised to bring pencils, own geometry box set, erasers and colour pencils and crayons for the Aptitude Test.
Haryana Public Service Commission invites applications from eligible candidates for to the following 151 Administrative and Executive posts :
1. HCS (Executive Branch) : 30 posts
2. Dy. S.P. : 09 posts
3. E.T.O. : 38 posts
4. District Food and Supplies Controller: 01 post
5. Tehsildar 'A' Class :16 posts
6. Assistant Registrar Co-Operative Society:08 posts
7. Assistant Excise & Taxation Officer : 05 posts
8. Block Development and Panchayat Officer : 17 posts
9. Traffic Manager: 03 posts
10. District Food & Supplies Officer :03 posts
11. Assistant Employment Officer: 21 posts
How 27/12/2011. (Last date is 03/01/2011 for the candidates of far-flung areas)
Monday, 28 November 2011
Online/ Offline application are invitedfor Himachal Pradesh, whose applications are received by post from these areas is 10/01/2011 :
How to Apply : Apply Online at HPPSC website on or before 26/12/2011 or Application in the prescribedOMR application form should be sendto the Controller of Examinations, Himachal PradeshPublic Service Commission, Nigam Vihar, Shimla-2, on or before26/12/2011.
How to Apply : Application in prescribed format should be sent in an envelope superscribed with bold letters as "Application for the posts of .................... " on or before 16/12/2011 (23/12/2011 for candidates from far-flung areas) toOffice of the Regional Director, Staff Selection Commission, (Western Region) 1ST Floor, Pratishtha Bhavan, 101, MK Road, Mumbai - 400020.
Application Fee: Rs.500/- (Rs.50/- for SC/ST/PWD), should be paid at any branch of the Syndicate Bank in the prescribed payment challan. Keep original counterfoil of the challan with you as it is to be produced at the time of written test along with call letter.
How to Apply: Apply online at Syndicate Bank website only from 25/11/2011 to 15/12/2011.Take a printout for future references as this is to be submitted at the later stage
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The Math Department offers a curriculum that ranges from Algebra 1-2 through advanced mathematics concepts. Courses prepare students for future careers. Skills such as reasoning and problem solving are emphasized in all levels of mathematics.
Courses Offered: (For more details about each course check the current course guide.)
Algebra 1-2
Geometry 1
Advanced Algebra 3-4
Advanced Algebra 3-4: Accelerated
Preliminary Math Studies
IB Math Studies SL
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Math 8 starts out the year developing the basic math skills needed for all of the units to be studied through June.
Equation Solving
Word Problems
Geometry
Graphing
Lines & Angles
Students will be expected to participate appropriately in class by taking guided notes which will directly correlate to their homework for the night. Homework will be assigned at the end of each class - students will receive a copy of the guided notes attached to their homework. The expectation is that the notes they take in class will stay in their binders, while the notes copy attached to their homework will be used at home to complete the assignment. IF HOMEWORK IS NOT COMPLETED, IT WILL BE EXTREMELY DIFFICULT TO PASS MATH 8.
Students will be preparing in each unit for the NYS Math 8 Exam, which will be given in mid April.
»Online Textbook This link will take you to the online textbook we are using this year. Occasionally, we may have assignments which could be done through the website. Each student has a specific login username (their student ID) and were given a password at the beginning of the year (math08). Passwords should be changed once a student has logged in for the first time. This link can be used for review as it offers online tutorials for a quick refresher.
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This course provides students with mathematical tools and problem- solving skills needed to move comfortably and confidently into Mathematics 075, 101 and 105. The concepts explored include Number Systems, Ratio, Proportion, Percent, Measurement, Algebra, Graphing and Geometry. This course does not carry credits toward graduation.
25-075.INTRODUCTION TO ALGEBRA. 3:3:0
The course provides students with a solid foundation in algebra and problem-solving skills needed to move comfortably and confidently into College Algebra, Survey of Mathematics, or Mathematics for Primary and Middle Grade Teachers. Topics include the applications of linear and quadratic equations and inequalities to real world problems, graphing, rational and radical expressions, and systems of linear equations. This course does not carry credits toward graduation.
25-101. SURVEY OF MATHEMATICS I. 3:3:0
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25-102. SURVEY OF MATHEMATICS II. 3:3:0
A course designed to acquaint students with consumer mathematics, geometry, mathematical systems, introduction to probability and statistics, and an introduction to computers. Prerequisite: Mathematics 101. Credit: three hours.
25-105. MATHEMATICS FOR TEACHERS I. 3:3:0
This course is designed to acquaint prospective PK-8, vocational and special education teachers with the structure of the real numbers system, its subsystems, properties, operations, and algorithms. Topics include problem solving, logic, number theory, and mathematical operations over the natural, integer and rational numbers. The course emphasizes heuristic instruction of students with different learning styles. Prerequisite: Two years of high school Mathematics, including Algebra and Trigonometry. Credit: three hours.
25-106. MATHEMATICS FOR TEACHERS II. 3:3:0
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25-121. COLLEGE ALGEBRA. 3:4:0
A course designed to expose students to polynomials, factoring, rational expressions, complex numbers, rational exponents, radicals, solutions of equations, linear and quadratic inequalities, functions and graphs, and synthetic division. A graphing calculator is used for learning and discovery in this course. Prerequisite: a minimum of three (3) units of college preparatory mathematics. Credit: three hours; four contact hours.
25-122. TRIGONOMETRY. 3:3:0
A course designed to prepare students for calculus. Topics include exponential and logarithmic functions, trigonometric functions and graphs, trigonometric identities, trigonometric equations, inverse trigonometric functions, laws of sines and cosines and applications, matrices and determinants, and systems of equations. Prerequisite: Mathematics 121. Credit: three hours.
25-125. FINITE MATHEMATICS. 3:3:0
The course is designed to prepare students for business calculus and quantitative business data analysis. Topics include counting techniques and series, systems of linear equations and inequalities, matrix algebra, linear programming, and exponential and logarithmic functions. Prerequisite: Mathematics 121. Credit: three hours.
25-203. COLLEGE GEOMETRY. 3:3:0
A course designed to prepare teachers in geometry. Topics include: axiomatic systems, methods of proof, formal synthetic Euclidean geometry, measurement, transformations, introduction to non-Euclidean geometries, and geometry within art and nature. Course emphasis will additionally be placed upon geometry education, problem-solving heuristic, and pedagogy. Prerequisite: Mathematics 122 or its equivalent. Credit: three hours.
25-204. NON-EUCLIDEAN GEOMETRY. 3:3:0
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25-205. MATHEMATICS FOR TEACHERS III. 3:3:0
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25-213. DISCRETE MATHEMATICS I. 3:3:0
An introduction to discrete mathematical structures for computer science with emphasis on logic, counting techniques, set theory, mathematical induction, relations, functions, and matrix algebra. Prerequisite: Mathematics 122. Credit: three hours.
25-214. DISCRETE MATHEMATICS II. 3:3:0
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25-225. CALCULUS FOR BUSINESS AND SOCIAL SCIENCES I. 3:3:0
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25-226. CALCULUS FOR BUSINESS AND SOCIAL SCIENCES II. 3:3:0
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25-241. ELEMENTARY STATISTICS. 3:3:0
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25-251. CALCULUS I. 4:4:0
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25-252. CALCULUS II. 4:4:0
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25-253. CALCULUS III. 4:4:0
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25-313. LINEAR ALGEBRA. 3:3:0
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25-341. PROBABILITY. 3:3:0
This course is a treatment of probability theory with stochastic processes. Topics include sample spaces, probability measures, discrete and continuous random variables, sums of independent random variables, law of large numbers, and the Central Limit Theorem. Markov chain models and their applications in the social and natural sciences are included. Prerequisite: Mathematics 251, and 313. Credit: three hours.
25-351. ORDINARY DIFFERENTIAL EQUATIONS. 3:3:0
A treatment of the solutions and applications of first order linear, homogenous and non-homogenous linear nth order differential equations. A presentation of the power series solutions, Laplace transform, linear systems of ordinary differential equations, and methods of numerical solutions. Prerequisites: Mathematics 252, and 313. Credit: three hours.
25-403. METHODS OF TEACHING MATHEMATICS IN THE SECONDARY SCHOOLS. 3:3:0
A study of the methods and materials used in teaching high school mathematics. This course introduces current educational theory, reform organizations and research methodologies. Topics include NCTM standards, effective teaching models, lesson plans, classroom management, professionalism, technology in the classroom, and current issues and trend. Prerequisite: Mathematics 252. Credit: three hours.
25-411. ALGEBRAIC STRUCTURES I. 3:3:0
A study of set theory, functions, integers, groups, matrices, permutation and symmetric groups, LaGrange theorem, normal and factor groups, and homomorphisms. Prerequisite: Mathematics 252 and 214 or its equivalent. Credit: three hours.
25-412. ALGEBRAIC STRUCTURES II. 3:3:0
A continuation of Mathematics 411 covering rings, integral domains, ideals, polynomial rings, principal ideal domains, and unique factorization domains. Prerequisite: Mathematics 411. Credit: three hours.
25-431. NUMERICAL ANALYSIS. 3:3:0
An introduction to the solutions of equations in one variable, direct methods and matrix techniques for solving systems of equations, interpolation and polynomial approximation, numerical differentiation and integration, and the initial value problems for ordinary differential equations. Prerequisite: Mathematics 252 and Computer Science 240 or 262 or other programming language. Credit: three hours.
25-451. ADVANCED CALCULUS I. 3:3:0
A treatment of vector spaces, differentiation of vector valued functions, and functions of several variables, partial derivatives, maximum and minimum of functions of several variables, Taylor's formula and applications, line and double integrals, Prerequisite: Mathematics 253. Credit: three hours.
25-452. ADVANCED CALCULUS II. 3:3:0
A continuation of Mathematics 451 covering curve and double integrals, Green's Theorem, triple and surface integrals, Divergence Theorem in 3-D space, Stoke's Theorem, Differentiability and the Change of Variable Theorem for functions from Rn into Rm, the Jacobian Matrix, the inverse mapping and implicit function theorem. Prerequisite: Mathematics 451. Credit: three hours.
25-461.INTRODUCTION TO REAL ANALYSIS. 3:3:0
An introduction to ordered and Archimedean fields, the theory of limits and continuity of functions, topological concepts, properties of continuous functions, the theory of differentiation and integration, and selected topics from power series and functions of several variables. Prerequisite: Mathematics 451. Credit: three hours.
25-471. COMPLEX ANALYSIS. 3:3:0
An introduction of complex numbers, Cauchy-Riemann equations, analytic and harmonic functions, elementary functions and their properties, branches of logarithmic functions, inverse trigonometric functions, the Cauchy-Goursat theorem, the Cauchy integral formula, Monera's theorem, Maximum Modula of functions, Taylor and Laurent series, residues and poles, linear fractional transformations. Prerequisite: Mathematics 452. Credit: three hours.
25-491. HISTORY OF MATHEMATICS. 3:3:0
A study of the evolution of mathematics. Topics include the scope and history of the Egyptian geometry, Greek and Arabic mathematics, the mechanical world, probability theory, number theory, non-Euclidean geometry, and set theory. Prerequisite: Mathematics 203 and 253. Credit: three hours.
25-498. TOPICS IN MATHEMATICS. 3:3:0
A treatment of selected topics in mathematics. (This is a senior capstone course.) Prerequisite: Approval of the Department of Mathematics. Credit: three hours.
25-499. SEMINAR IN MATHEMATICS. 3:3:0
A treatment of selected topics in mathematics augmented by invited guest speakers and student presentations. Prerequisite: Approval of the Department of Mathematics. Credit: three hours.
Department Homepage
Delaware State University Applied Mathematics Research Center (AMRC) was initially funded by the Department of Defense (DoD) in 2003. AMRC is designed to create a research environment where multidisciplinary groups work together to solve applied mathematics problems in military and other areas. The research center consists of faculty of Mathematics, Computer Science, Electrical Engineering, and Biotechnology, research associates, visiting professors and an administrative assistant.
The major goals are:
to establish a permanent research base at Delaware State University which produces new knowledge and quality, publishable, peer-reviewed research relevant to DoD research goals
to enhance participation and substantial involvement of minority graduate (M.S. and Ph.D.) and undergraduate students and faculty in Science and Mathematics research
to provide additional training in mathematics and sciences to minority female high school students by involving them a summer program (GEMS), and therefore to prepare more minority students (especially women) in sciences and mathematics
to foster long-term research collaboration among scientists with Army Research Laboratories, and other national government and academic institutions; and 5) to ensure long term sufficient research funding
MAIN RESEARCH AREAS
Ground Penetrating Radar Imaging
Buried object detection using GPR has attracted tremendous attention in the past decades because of its important military, such as mine detection, and commercial applications. Our current work aims to use vector multiresolution representation for the antenna array receiving data in multifrequency ground penetrating radar (GPR), and solves the inverse scattering problem, and then uses the hidden Markov model (HMM) in the wavelet transform domain for the target detection. We plan to expand our GPR imaging research in three aspects:
continuing to investigate our current research targets;
developing algorithms for 3-D GPR imaging; and
processing real land mine GPR data with new algorithms.
The NURBS methods of Computer geometric design in automatic representing 3D objects
NURBS is the most popular and widely used method and tool in the field of computer geometric design in representing and manipulating 3D objects. The objectives of the project are to study the following problems in reconstruction of smooth surfaces, which are:
producing polygonal model from scattered and unstructured 3D data, and/or even from 2D data;
mesh quadrilaterization of the polygonal model; and
the representation of the parametric surfaces on each quadrilateral patch, and the construction of NURBS surface model.
Image Registration
The research task is to develop software in C or MATLAB that will create a unified image from a sequence of smaller images. The dyadic combination of images is the basic operation; the recursive implementation of this combination will constitute the desired algorithm. A data set of the Blossom Point test range will be used as the data source. We will identify relevant features that allow images to be merged. It is expected that these features will also be applicable to similar images. This software will be developed with the expectation that it will be enhanced to include problems associated with scaling, and then 3D image reconstruction.
Signal Processing in Data Mining
The ultimate goal of the proposed research is to provide advances in technology towards successful development, testing, refinement and application of intelligent, self-adaptive software systems. The approaches integrate computer vision systems, soft computing and evolutionary computational paradigms, complex adaptive software structures and robust machine learning algorithms. In addition, we aim towards practical design, development, prototyping and evaluation of a knowledge-based software system that will integrate theoretical aspects of the proposed techniques into user-friendly application equipped by advanced user interface and enhanced data base management capabilities.
Biotechnology
The research focuses on nucleotide sequence and chromatin structure requirements for integration. We will also deal with the scientific, social, and ethical issues related to the field of Biotechnology, present the elements of biostatics and numerical methods needed for quantitative data analysis and interpretation, and provide practical experience with the use of software and databases in the investigation of problems critical to biotechnology and molecular biology to our undergraduate students.
Other Research Areas
Inverse Ill-Posed Problems, Numerical Analysis, Partial Differential Equations, Integral Equations, Wavelets and Image Analysis, Scientific Computation, and Mathematical Physics.
Outreach
Delaware State University (DSU) will conduct the pre-college program Girls Explorations in Mathematics and Science (GEMS). GEMS is a three-week summer residential program involving hands-on explorations in mathematics, biology, and information technology with research activities. This project will offer 20 motivated high-potential female high school students entering tenth and eleventh grades an opportunity to integrate and apply concepts from these disciplines to problem solving. GEMS program is designed to stimulate and extend students' interest in these fields and encourage them to investigate careers in mathematics, biology, and information technology. This addresses the problem of under-representation of women, in particular minorities, in these fields. Three college professors and three high school teachers, who are assisted by six undergraduate/ graduate female students, conduct the project. The curriculum has been carefully designed to expose students to research methodology, to enable them to see the connections between mathematics, biology, and information technology. The participants work in small groups and use computers extensively to explore and discover mathematical and biological concepts.
Department Homepage
Rightbar:
Faculty
ETV Building Room 107
Ph: 302-857-7051
Fax: 302-857-7054
Body:
Overview
The objectives of the Mathematical Sciences Department are to provide opportunities for students to develop functional competence in mathematics; an appreciation for the contributions of mathematics to science, engineering, business, economics, and the social sciences; and the power of critical thinking. The Department strives to prepare students to pursue graduate study and for careers in teaching, government, and industry.
The Department aims to provide the student with a course of study directed toward an understanding of mathematical theory and its relation to other fields of study. This study includes an emphasis on precision of definition, reasoning to precise conclusions, and an analysis and solution of problems using mathematical principles.
Students who select a major in the Department must complete the general education program which is required of all students. Request more information
Curriculum Options for Majors
MATHEMATICS:
The requirements for a major in Mathematics are: Mathematics 191,192, 213, 214, 251, 252, 253, 313, 341, 351, 411, 451, and 498; One of 412, 452; Physics 201 and 202; and a minimum of six (6) hours selected from Mathematics courses numbered 300 or higher, excluding 403. With departmental approval, three hours may be submitted from Physics 311-312 and 404.
MATHEMATICS WITH COMPUTER SCIENCE:
The requirements for a major in Mathematics with Computer Science are: Mathematics 191,192, 213, 214, 251, 252, 253, 313, 341, 351, 431 and 498; Physics 201, 202; Computer Science 240, 261, 262, 360, 461 and 495; and a minimum of twelve (12) hours selected from Mathematics courses numbered 300 or higher, excluding 403.
MATHEMATICS EDUCATION:
The requirements for a teaching major in Mathematics are: Mathematics 191,192, 203, 213, 241, 251, 252, 253, 313, 341, 403, 411 and 491; Education 204, 313, 318, 322, 357, and 412; Physics 201 and 202; Psychology 201; and Computer Science 261. Students must take and pass PRAXIS I and apply for admission to the TPE prior to the start of their junior year. Students must pass PRAXIS II prior to student teaching.
OPTION FOR MINORS
To provide an opportunity for students to obtain a minor concentration in mathematics, the Department of Mathematical Sciences offers the following option:
Minor in Mathematics:
Twenty-one (21) hours distributed as follows: Mathematics 251, 252, 253; and nine (9) additional hours selected from Mathematics courses at the 300 level or higher, excluding 403.
Leftbar:
Free Student Tutoring Resources
The Department of Mathematical Sciences offersfree mathematics tutoringin the Mathematics Laboratory (ETV 128). Tutoring sessions are available for any student who needs assistance in their mathematics courses. Mathematics Laboratory tutors are responsible students with a 3.3 GPA or higher. Tutoring session times are flexible to accommodate any student's schedule.
Typical hours of operation are Mondays through Fridays with times varying from 9 a.m. to 8 p.m.. Actual hours of operation with specific tutor information are posted on the door of the Mathematics Laboratory each semester.
If you have any questions, please contact the Department of Mathematical Sciences at ext. 7051.
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Algebra
Age 15+ Time 2h. Students find transforming functions one of the most demanding topics in mathematicsat this level. In particular, the effect a has on the function, f(x) for y=af(x) and y=f(ax) and understanding just what a stretch is. This activity documents the most succesful approach I've had with this topic. It approaches the idea from the angle of transforming shapes, looking at the effect on the coordinates, then applying the same transformations to graphs. [Show][Hide]
This is a very complete activity that makes use of Geogebra and includes ready made applets and help videos for teachers who may have little experience or confidence in using technology in the classroom. Watch the following video (no sound) to get an overview of the activity:
Age: 14+ Time: 2h. This is a perfect activity to discover the properties of quadratic graphs. An investigation to 1) describe the axis of symmetry, 2) find the vertex form and 3) describe the zeros of a quadratic function. It includes fun quizzes and is concluded with a firefighter game where Sam must aim the water jet correctly to put out the fire. Great fun! Click show to see short video overview of activity [Show][Hide]
Age: 14+ Time: 1h Questions start off easy (one or two vert/horiz inequalities) to ensure all students can be engaged - will they save the eggs from the Pterodactyls? The aim of the activity is to focus student attention on how coordinates relate to the inequality and hence facilitate a better understanding of which side of an inequality students should shade. Playable on ipad etc. also.
Age: 14+ Time: 1h Students have to modify the inequalities to trap each ghost in turn within their "laser fields" (no software required). Care is required because if their inequalities aren't precise they could easily burn the baby! Levels increase in difficulty, from one to three ghosts, but only using linear inequalities. Playable on ipad also.
Age: 15+ Time: 1hr + This activity introduces students to the concept of even and odd functions, i.e. functions with properties f(x) = f(-x) and f(x) = -f(-x). There follows an investigation into the properties of adding, multiplying and finding composites of these functions e.g. even function + even function =?
Age 11+ Time: 1h Students take the orders at Luigi's or Taj's Waiter of the Year competition using a single letter to abbreviate each starter, main etc. Simplify the algebra and substitute in the prices to finalise the bill. This leads into letters as variables: Spin the fruit machine to select a number target before rolling a die to substitute in. Self-checking exercise to finish or for use as a homework. Lots of human interaction!
Age 13+ Time: 2h This is a very complete activity to get students factorising quadratic expressions for the first time. It includes 2 arcade games to practise expanding brackets, a product and sum puzzle and a self-checking spreadsheet for factorising. Watch the following video for an overview[Show][Hide]
Age: 14+ Time: 1h+ This activity will challenge high achieving students to learn about the properties of exponential functions and their transformations. Interactive applets and quizzes get the students to discover the properties for themselves then there are a couple of games to challenge them to 'copy the function'. Watch the short video below for a quick overview.[Show][Hide]
Age: 14+ Time: 1-2h+. Students use Geogebra to plot, then try and find a function to fit Olympic winning data for the men and women's 100m, High Jump, Show jumping and men's weightlifting from 1896 to the present. What are the limits of human physical abilities? This is a great activity to develop students' mathematical modelling: who will predict most accurately the winning times for the forthcoming Olympics?
Age: 12+ Time: 1h What changed during the Renaissance? This activity looks at the revolution in using algebra to describe geometries, graphs, 3D perspective and the introduction of decimal notation. It can be used as part of a Renaissance School Day where students make links between subjects and then present their findings in a whole school assembly. Overview of this day, lead by History department, available here.
Age: 15+ Time 1.5 hr + This activity gets students to produce families of trigonometric functions (like the one on the right) using dynamic geometry software. By exploring the effect of changing parameters they really get a deep understanding of the properties of the main transformations: translations and stretches. Get ready for "Oos and Ahhs"!
Age: 12+ Time 1 hr + A computer with internet access is required for this set of five interlinked activities where students are introduced to the equation of a straight line. A structured investigation is followed by a bowling game where students are required to enter the correct equation in order to be able to bowl over the pins and get a strike. A really entertaining way to learn about gradient and y intercept.
Age: 13+ Time: 1-2h. Estimation is a key skill in all areas of maths, but perhaps particularly so in Trial and Improvement. Using mini-whiteboards, paper, in pairs or teams students use what they know to estimate square and cube roots of numbers they don't know. They then use Excel to try and hone their answers to 1, 2 or 3 d.p. accuracy. Students can also create their own Excel questions and solutions.
Age: 15+ Time 1 hr. This
Age: 15+ Time: 30mins-1h. Students use geometry software to model wave pictures from real-life objects and situations. In doing so, students will investigate the effects of the coefficients for sine and cosine waves e.g. y = a cos[b(x-c)]+d asking themselves: "What Changes?", "What Stays the Same?". No software is required
Age: 15+ Time 1-2 hrs Using Autograph or the free Geogebra or Microsoft Maths 4.0, students investigate the functions of the sine and cosine graph. Students record the key, defining points in a pre-prepared table: coordinates of the maximum and minimum and x-intercepts, as they change different parameters using the constant controller or sliders. Without technology, students then have to predict [Show][Hide]
Age: 15+ Time 1h This activity introduces sine and cosine graphs using the video of the construction of a Ferris wheel that demonstrates the link with triangles. Students then sketch the graph of their movement on the Big Wheel. The aim is to link the sine and cosine ratios to a circle. Students use calculators to plot the graphs exactly (spotting symmetries to save them calculation time!). VM also available.
Age: 11+ Time: 1hr+ This activity gets students to explore the ideas of factorising simple linear expressions. However, it does it in a way that never mentions factorising! Students will need to think critically to solve some puzzles about multiplying out number grids. By turning the questions around, students will then discover the rules for factorising. Students should be able to [Show][Hide]
multiply simple algebraic expressions before they attempt this activity.
Age: 11+ Time: up to 1hr. Practise programming spreadsheets with simple formulae. Use the spreadsheet to examine the relationships and patterns between the numbers in magic squares. Do all of this while you get lost in this fantastic challenge! Create a 7 x 7 magic square with a 5 x 5 magic square inside it and a 3 x 3 one inside that!
Age: 12+ Time: 1h. In this activity, students are given a target and have to choose expessions that correspond to the target e.g. even number: 2n-2. They then make up their own targets and/or cards to match. In the second activity students match a series of formulae to their symbolic meaning, word meaning and physical world context. All activities focus on the concept of letter as "variable". The last activity [Show][Hide]
develops students effective internet and textbook etc. research skills.
Age: 12+ Time: 2 hours. In this investigation, students explore the sums of consecutive numbers and their divisors with the hope of discovering and proving that the sum of n consecutive numbers is divisible by n when n is odd. This is a gentle introduction for young students to the idea of proof! Using algebraic terms to represent unknown numbers and very simple algebraic manipulation, [Show][Hide]
students see the power of algebra. It therefore provides them with a reason and motivation to learn more about this often elusive topic. Before attempting this activity, I would expect students to have had a little exposure to adding simple algebraic expressions together.
Use card games to get students practising and revising solving equations. Playing in pairs, threes or fours students roll a die, in combination with the cards, to win their partner's cards. There are many possible games using these cards, as well as a range of levels from Apprentice to Mathmagician. Age: 12+ Time: 30mins to 1h
Age 14+ Time 30-40 minutes. Match the waves with their functions! The discussions and reasoning that take place during this type of activity can be incredibly valuable and effective. It is a simple idea, but so often the simple ideas can be the most effective. It is also a nice alternative to a traditional exercise. When well practised, this is not a desperately difficult concept and it can be very satisfying [Show][Hide]
to be able to quickly make the link and either deduce a function from the graph or the other way round. This simple activity lends itself to group work and presents the kind of challenge that usually engages students
This group activity gets students to match a physical world scenario e.g. pressure exerted by an elephant of 400kg mass, with its associated data (a number relation), the equation that defines this relationship, a graph and the nth term rule. This provokes student discussion to air and refine students' conceptions of the relationship between these topics. Age: 14+ Time 1 hr.
Age: 15+ Time 1 hr. Challenge students to really understand the concept of a function. Match a set of input values with a function and a corresponding set of output values. There are eight sets of three to make and only one correct solution. This activity is 'old meets new'. Students work with cut out bits of paper but can use calculators/computers to help them solve the puzzle!
Age: 12+ Time: 1-2 hours. This activity is another great example of a puzzle whose solutions can be modeled by an algebraic sequence (linear). The puzzle provides an engaging introduction and an incentive to generalise, which helps students with this traditionally difficult idea. The puzzle can be modeled by a linear sequence and broken down into a series of different linear sequences that combine to form the overall model. [Show][Hide]
As such this activity has lots of scope for relating sequences to physical situations, breaking them down in to parts and seeing how algebraic manipulation links the different solutions together. This is a good deep problem that only involves linear sequences.
Age: 12+ Time: 1-2 hours Bring life to this classic sequences problem by getting students out of their chairs and jumping around to solve the problem. This is a terrific problem for generating and investigating a quadratic sequence. It can be looked at from a number of angles and demonstrating the way they link together gives a very satisfying result. This problem has been around for a while and this activity is really about [Show][Hide]
A card game to introduce students to quadratic equations. Playing in pairs, threes or fours students roll a die, in combination with the cards, to win their partner's cards. There are many games possible using these cards. Age: 12+ Time: 10-30 minutes
This immediately absorbing and engaging activity requires students to use graphing software. The aim is to explore the basic transformations of a function, e.g. y=f(x-a), y=f(ax) for the quadratic function. However, the questions are disguised in videos of moving graphs that students are asked to reproduce. This challenge provides a great incentive to explore, experiment and share ideas. Age: 15+ Time: 1h
This activity is about linking the graphing of quadratics with the equations themselves by looking at their key features. Students match pieces of information with different graphs using logical deduction. This practical group activity leads to being able to sketch graphs from their equations. Age: 15+ Time: 1h
In one hour students should have worked out how to "factorise quadratics" for themselves using patterns in the factorisations given by CAS software, such as TiNspire, Geogebra, WolframAlpha or Derive. "How to" videos are included for those inexperienced in using these programmes. A second activity relates factorising to the "Grid Method" of multiplication including the use of an online virtual manipulative. Age: 13+ Time: 1-2h
This is a great introductory lesson to linear graphs. Students will act as coordinates on a huge grid. Holding A3 sheets of white paper up when a rule requires it, they will plot coordinate pictures and straight line graphs following instructions such as, "Hold up your sheet is your x and y coordinates add together to make 9!" A webcam and a projector can add an extra dimension to this practical activity. Age: 9+ Time: 30m to 1hr
A real game that is fun to play and, when investigated, generates a great example of an exponential sequence. Ideal activity for exploring sequences in general and for introducing these functions. It is a practical activity that can be enhanced with access to computers. Age: 13+ Time: 1 hour
In this activity students will use a graphing package to explore the link between geometrical patterns, sequences and their graphical representations. There are 3 levels of difficulty starting with linear sequences moving on to quadratic, then other more challenging sequences. Age: 12+ Time: 1-2 hours
Use Excel or any other spreadsheet to explore the patterns in linear or arithmetic sequences. Students are quickly drawn to striking patterns and the teacher's role is careful questioning aimed at asking students to articulate the whats? and whys? Age: 11+ Time: 1h
Use dynamic geometry software to find the quadratic equations that model some photographs of real-life objects. This activity will get students to understand the effect of changing the parameters in the general equation y = a(x - b)² + c. Three Geogebra files are provided and are ready to use. No software is needed. Age: 14+ Time: 1h
By the end of the hour students should have worked out how to "factorise" for themselves by looking for patterns in the factorisations given by CAS software such as TiNspire and Derive. "How to" videos are included, for those inexperienced with the technology, to help ensure teacher and student time is focused on the mathematics. Age: 12+ Time: 1h
Re-arrange simple formulae with this matching pair activity. 32 cards are cut out and matched up to give 16 pairs of equivalent formulae with different subjects. This activity promotes much discussion and helps iron out fallacies. Age : 14+ Time : 1 hr
Students get practice in finding the nth term of arithmetic and geometric sequences. Sequences are presented in a graphical form and students are required to find their nth terms. Ti Nspire calculators are recommended to get the most out of this activity and allow students to play with and test their own conjectures. Age: 15+Time: 1hr
How many ways to win a 3D game of three in a row? A real physical game situation that leads to algebraic sequences. There are many ways to investigate this problem and this makes a great project for Algebraic Investigation. Age: 14+Time: 1hr to a whole week.
Who's the fastest in your class? How do you know they are "fast"? What does "fast" mean exactly? Student's discuss the above, then race 100m and use the distance, speed, time formulae to work out: If they maintained this speed, could they set a new marathon record?! Age : 12+ Time: 2hrs
Formulae often seem so abstract to students, expressed as they are using algebra, yet they are one of the most applied area of mathematics! Students are asked to search Google images and find one or two images to go with each formula. Students then share their pictures with the rest of the class and discuss what each letter represents and how it describes a relationship. Age: 12+ Time: 1-2hrs
Students all too often do not realise that functions are all around them: on the dance floor, in the swaying of the branches of a tree . . . . and in people holding their hands in the air in joy! This activity gets them to use their body to feel the transformation! Age: 15+ Time: 5mins to 1h (use sections as starters/plenaries or full resource in a single lesson).
Bend a wire to "feel" the shape of the different functions such as sinx, cosx, x3 etc. and their transformations e.g. sin(x-90), Cos3x, etc. Given an equation/function, can you draw the graph on a mini-whiteboard? Age: 15+ Time: 20mins to 1h (starter/plenary or full lesson)
Many marks can be lost in exams because of a lack of precision in the exact coordinates of a transformation. Students are taken outside the classroom to give them a physical experience of how functions define coordinates. The discussion between students is useful for drawing out student misconceptions. Careful questioning can challenge these misconceptions. Age:15+ Time: 20mins to 1h (starter or full lesson)
Many students find the symbols and meanings used in equations difficult to understand. This activity uses the excellent "balancing scales" manipulative to give students an intuitive understanding of how to solve equations - through experiment and discovery. Age: 11+ Time: 1h
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Synopsis
This book is packed with practice questions for students taking the AQA GCSE Foundation level Modular Maths course. It thoroughly covers all the topics for the current exams with a range of exercises to test your maths skills. The answers come in a separate book (9781841465807). Matching study notes and explanations are also available in the CGP Revision Guide (9781841465432
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The author presents his approach to how undergraduate students in mathematics, business, computer science, and engineering should be introduced to the science of decision making. The material is
designed to prepare the student for more advanced topics. The level of mathematics required is deterministic mathematics at an elementary level, including linear equations and graphs. Introductory probabilistic notions
are assumed, but they are not used extensively and can be introduced by the instructor. The target audience is juniors, seniors, and advanced lower-division students. The text is for a one-semester course.
You may copy this unique Krieger Book Number into the Quote and Information Form, for quick processing, if you're interested in this book
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Provides a clear and comprehensive overview of the fundamental theories, numerical methods, and iterative processes encountered in difference calculus. Explores classical problems such as orthological polynomials, the Euclidean algorithm, roots of polynomials, and well-conditioning.
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This book is the first English translation of the classic long paper Theorie der algebraischen Functionen einer Veränderlichen (Theory of algebraic functions of one variable), published by Dedekind and Weber in 1882. The translation has been enriched by a Translator's Introduction that includes historical background, and also by extensive commentary embedded in the translation itself.
The translation, introduction, and commentary provide the first easy access to this important paper for a wide mathematical audience: students, historians of mathematics, and professional mathematicians.
Why is the Dedekind-Weber paper important? In the 1850s, Riemann initiated a revolution in algebraic geometry by interpreting algebraic curves as surfaces covering the sphere. He obtained deep and striking results in pure algebra by intuitive arguments about surfaces and their topology. However, Riemann's arguments were not rigorous, and they remained in limbo until 1882, when Dedekind and Weber put them on a sound foundation.
The key to this breakthrough was to develop the theory of algebraic functions in analogy with Dedekind's theory of algebraic numbers, where the concept of ideal plays a central role. By introducing such concepts into the theory of algebraic curves, Dedekind and Weber paved the way for modern algebraic geometry.Undergraduate and graduate students and research mathematicians interested in algebra, algebraic geometry, and the history of mathematics.
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MATH 772 Applied Math
COURSE DESCRIPTION:
A course in elementary mathematical skills for
technicians. Topics covered include fundamental operations with whole numbers,
fractions, decimals, and signed numbers ; percents; geometric figures and basic
constructions; area and volume formulas; English/Metric systems; measurements;
and the interpretation of graphs and charts.
COURSE COMPETENCIES: During this course, the student will be
expected to:
2. Compute with whole numbers, fractions, decimals, and
integers in real world and mathematical solving.
2.1 Apply the four arithmetic operations ( add , subtract ,
multiply , and divide ) to whole numbers.
2.2 Apply the four arithmetic operations to fractions.
2.3 Apply the four arithmetic operations to decimals.
2.4 Apply the four arithmetic operations to integers.
2.5 Apply the four arithmetic operations to complex fractions .
2.6 Demonstrate the use of exponential notation in computation.
2.7 Demonstrate the use of scientific notation in computation.
6.1 Construct:
a. an angle bisector
b. congruent angles
c. line segment bisectors
d. perpendicular bisector of a line
e. parallel lines
f. perpendicular to a line from a point on the line
g. perpendicular to a line from a point off the line
h. inscribed regular triangle
i. inscribed regular square
j. inscribed regular hexagon
k. inscribed regular pentagon
l. congruent triangles
m. a triangle given three sides
n. altitude of a triangle
o. center of balance of a triangle
p. inscribed circle in a triangle
q. a circumscribed circle about a triangle
8.1 Calculate the measure of an angle in both degrees and
radians.
8.2 Calculate the area and volume of plane figures.
8.3 Calculate lateral surface area, total surface area and volume of geometric
solids (prisms, cylinders, pyramids, cones, and spheres).
9.1 Identify the units in the English and Metric systems.
9.2 Convert within the English System.
9.3 Convert within the Metric System.
9.4 Convert between Metric and English Systems.
9.5 Model dimensional figures.
9.6 Calculate answers to dimensional figures.
10. Use appropriate units and tools to measure to the
degree of accuracy required in a particular situation
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UCD Mat 67: Linear Algebra
Table of contents
No headers
1.1 Introduction to MAT 67 This class may well be one of your first mathematics classes that bridges the gap between the mainly computation-oriented lower division classes and the abstract mathematics encountered in more advanced mathematics courses. The goal of this class is threefold:
You will learn Linear Algebra, which is one of the most widely used mathematical theories around. Linear Algebra finds applications in virtually every area of mathematics, including Multivariate Calculus, Differential Equations, and Probability Theory. It is also widely applied in fields like physics, chemistry, economics, psychology, and engineering. You are even relying on methods from Linear Algebra every time you use an Internet search like Google, the Global Positioning System (GPS), or a cellphone.
You will acquire computational skills to solve linear systems of equations, perform operations on matrices, calculate eigenvalues, and find determinants of matrices.
In the setting of Linear Algebra, you will be introduced to abstraction. We will develop the theory of Linear Algebra together, and you will learn to write proofs.
The lectures will mainly develop the theory of Linear Algebra, and the discussion sessions will focus on the computational aspects. The lectures and the discussion sections go hand in hand, and it is important that you attend both. The exercises for each Chapter are divided into more computation-oriented exercises and exercises that focus on proof-writing.
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Course Description: Limits and Continuity. Derivatives and applications. Differentiation of polynomial, rational, trigonometric, logarithmic and exponential functions. L'Hopital's Rule. Prerequisite: acceptable placement score (or ACT math score of at least 28), or at least 3 years of high school algebra and trigonometry with at least a B average, or a grade of C or better in MATH 180. Recommended as a general education liberal studies elective course.
CORE SKILL OBJECTIVES 1. Thinking Skills: A. Uses reasoned standards in solving problems and presenting arguments. 2. Communication Skills: A. Reads with comprehension and the ability to analyze and evaluate. B. Listens with an open mind and responds with respect. C. Information and communicates using current technology. 3. Life Values: A. Analyzes, evaluates and responds to ethical issues from an informed personal value system. 4. Cultural Skills: A. Understands culture as an evolving set of world views with diverse historical roots that provides a framework for guiding, expressing, and interpreting human behavior. B. Demonstrates knowledge of the signs and symbols of another culture. C. Participates in activity that broadens the student's customary way of thinking. 5. Aesthetic Skills: A. Develops an aesthetic sensitivity.
NCTM Goals: The NCTM (National Council of Teachers of Mathematics) gives the following set of overall goals for mathematics education in general, which are worth including here: 1. Learn to value mathematics. 2. Learn to reason mathematically. 3. Learn to communicate mathematically. 4. Become confident in your mathematical ability. 5. Become problem solvers and posers.
COURSE OBJECTIVES 1. Thinking Skills: A. Understands the "big problems" in the development of differential calculus, the tangent problem and the velocity problem. B. Understands the mathematical concept of Limit. C . Explores differentiation formulas for a variety of functions, including exponential and logarithmic, trigonometric and inverse trigonometric, hyperbolic and inverse hyperbolic functions. D. Investigates a wide variety of applications of differentiation, such as finding maximum and minimum values of functions, and instantaneous rates of change. 2. Communication Skills: A. Collects a portfolio of one's work during the course and write a reflection paper. B. Does group work (labs and practice exams) is done throughout the course, involving both written and oral communication. C. Uses technology - graphing calculators and Maple V in the computer lab - to solve problems and to be able to communication solutions and explore options. D. Improves one's ability to write logically valid and precise mathematical proofs and solutions. 3. Life Value Skills: A. Develops an appreciation for the intellectual honesty of deductive reasoning. B. Understands the need to do one's own work, to honestly challenge oneself to master the material. 4. Cultural Skills: A. Develops and appreciation of the history of calculus and the role it has played in mathematics and in other disciplines. B. Learns to use the symbolic notation correctly and appropriately. 5. Aesthetic Skills: A. Develops an appreciation for the austere intellectual beauty of deductive reasoning. B. Develops an appreciation for mathematical elegance.
Objectives: This is a list of more specific outcomes this course should provide. The student should... 1. ... gain a better understanding of the concept of a function. 2. ... use graphs to estimate related values, relative rates, extreme values, limits, and derivatives. 3. ... develop a concept of limit. 4. ... understand the derivative. 5. ... apply concepts and techniques to calculus to analyze functions and find relative rates, extreme values. 6. ... use numerical methods to evaluate derivatives and use calculators and computers efficiently as tools. 7. ... model problems from geometry and other disciplines using calculus concepts.
COURSE POLICIES AND PROCEDURES:
Probably the best single piece of wisdom I can pass on to you as you begin this course is: "Mathematics is not a spectator sport!" You need to view yourself as the LEARNER – and "learn" is an active verb, not a passive verb. I will do what I can to help structure things so that you have an appropriate sequence of topics and a useful collection of problems, but it is up to YOU to DO the problems and to READ the book and THINK ABOUT the topics. You must develop a system that works for you, but let me suggest that it might include finding a study group or coming to me with your questions or going to tutoring sessions in the learning center. In any case you should expect to spend at least the traditional expectation of 2 hours outside of class for each hour in class – this is important! Class time is for exploring the topics and answering questions you might have, but you simply can't master the material without putting in the time alone to really engage in the mathematics. We are in the process of phasing in a new textbook and more than ever it is important that you actually READ the BOOK! The authors attempt to force the reader to think about the material and to develop an intuitive sense of what is going on; there is much emphasis on solving problems and much reliance on graphing technology as well as on symbolic manipulation.
READING THE TEXT: Because it is so important that you read the book, I am going to ask you to OUTLINE the text. You can't read a mathematics text like you might read a novel – it is important that you actually understand what you are reading! Each week I will take a brief look at your growing outline and will check off your name for acceptable work. This will be worth 5 points per week.
HOMEWORK: In a nutshell, working problems is one of the key ways you will learn Calculus. Attending class is important, of course, but without doing problems you will not develop a solid foundation in the material. I will give you daily assignments and will expect that you will do as many as time allows (which I take to be roughly 2 hours per class period). I will not generally collect these assignments but I do see them as testing your understanding and as raising questions for you to ask in class.
QUIZZES: There will be an occasional quiz or problem set in addition to the exams.
EXAMS: There will be exams after each of the first 3 chapters – these will be in two parts, a group practice problem set worth 20 points and then an individual exam worth 80 points, 100 points in total. The final exam will be cumulative and worth 150 points (25 on the group part, 125 on the individual part). Because chapter 4 will take us up to the end of the course, there will not be a separate exam on that chapter, but the final will more heavily emphasize that final chapter than the previous three – this is very reasonable in a course like this, in which the material builds in such a sequential manner. By the way, I do not expect you to memorize the various formulas – you are allowed a page of notes for each exam, and you can bring all four pages in for the final exam.
GRADING POLICY: In general I use the rather traditional 90% of possible points for an "A", 80% for a "B", 70% for a "C", and 60% for a "D". I will try to make enough points available in non-test situations that "test-anxiety" should not entirely kill your chances for success, but I am a very firm believer in putting students through the exam experience so that I can see whether you, not your study group, understand the material.
AMERICANS WITH DISABILITIES ACT
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Algebra I is a course of study primarily designed to prepare students for Algebra II. The 2007 Saxon Textbook Series is used and emphasizes constant review of topics that have been covered in the past. These topics include solving equations, graphing, various word problems, factoring, area and volume problems, fractions, solving systems, radicals, exponents and scientific notation. The course is structured to introduce a new topic each day. Assignments generally include 4-5 new problems and 25 review problems from past lessons. (Students who fail to maintain a "C" or higher average in Algebra I will have great difficulty passing Algebra II.)
This is a study of traditional algebra concepts integrated with the study of geometry. First and second degree equations, conic sections, trigonometry, logarithms, and problem solving are some of the concepts taught. The correct use of the calculator is emphasized. Prerequisite: This course is offered to ninth grade students who have had Algebra I in middle school, and are recommended by the middle school faculty.
This is a study of traditional algebra concepts integrated with the study of geometry. First and second degree equations are studied in depth and there is a heavy emphasis on problem solving. Trigonometry is introduced and the correct use of the calculator is taught. Of the thirty problems assigned nightly, only three or four are of the newly introduced lesson. The remaining problems are review problems. Half of the instructional period is spent in teacher assisted work on these problems. Tests are given following each fourth lesson.
This course is an advanced study of Euclidean Geometry. In addition to the topics covered in the regular geometry course, this course will emphasize proof and deductive reasoning. The class will move at a more rapid pace and will provide an in-depth study of each concept. Prerequisite: This course is offered to tenth grade students who desire to study four years of math in high school and who have been recommended for Honors Mathematics classes.
The students in Pre-Calculus Honors should be juniors who are on tract to take AP Calculus during their senior year. The content of the curriculum will be much the same as the other Pre-Calculus courses offered at DLHS. The main difference in the honor's course is that all students will be assumed to take AP Calculus. Effectively, this class will be the first year of a two year sequence. More emphasis will be given to interpreting problems verbally, numerically, graphically, as well as analytically. The students will be expected to transfer knowledge to various situations in an effort to prepare them for AP Calculus and the AP Calculus exam.
This course is designed primarily for seniors, or for juniors who plan to take Statistics in their senior year. Early in the year, much emphasis will be given to analytical geometry and the study of functions. The TI83+ or TI89 will be used extensively by the students and teacher via computer projection equipment to study the relationships between functions and graphs. The "reform" movement in mathematics gives much more emphasis in studying functions analytically as well as through tables and graphs. Technology improvements have dramatically changed the way Pre-Calculus is taught. Nearly a third of the year will then be given to the study of trigonometry. Circle trigonometry goes beyond the geometric concept of an angle. Circular representations of angles allow us to study many real world phenomena that are periodic in nature. Triangle trigonometry uses the geometric concepts to find distances and areas given any polygonal region. Logarithms will be studied to be able to solve problems with exponential variables as is often the case in Chemistry as well as Economics. Conics and their interesting reflective properties will be studied. As time allows, some topics of discrete mathematics including sequences will be studied. Elementary probability will give students a concept of the likelihood of an event. These ideas would be very important as a beginning point for those taking Statistics.
Advanced Placement Calculus consists of a full high school academic year of work that is comparable to calculus courses in colleges and universities. It is required that students who take AP Calculus will seek college credit by taking the AP Exam. Most of the year will be devoted to topics in differential and integral calculus. The course emphasizes a multi-representational approach of calculus, with concepts, results, and problems being expressed graphically, numerically, analytically and verbally. Also note that a detailed course description including philosophy, goals, prerequisites, and topical outline are given at: Prerequisite – teacher approval and summer review on teacher wiki located at
This class is designed for students with grades below B- (85) in Algebra II who need to develop better math skills to prepare for college math and for students who will not require a high level of mathematics in their chosen careers. Students with grades of B-(85) or above in Algebra II should take Pre-Calculus or Statistics. Teacher recommendation will be necessary to take this class.
Statistics is the science of gaining information from numerical data. Although statistics can be extremely complicated in theory, this course will be concerned with the practice of statistics. There are three basic parts to the practice of statistics, which will be incorporated in this course. Data analysis concerns methods and ideas for organizing and describing data using graphs, numerical summaries, and more elaborate mathematical descriptions. Data production includes some basic concepts about how to select samples and design experiments. Finally, statistical inference moves beyond data in order to draw conclusions about a wide universe. In other words, we will attempt to put data in context.
This University level course will involve a quick review of equations and inequalities; functions and graphs; polynomial and rational functions; exponential and logarithmic functions; systems of equations and inequalities; sequences, series, and probability. Prerequisite: two years of high school Algebra and at least a 21 ACT or 590 SAT math score.
This University level course will involve trigonometric and circular functions; trigonometric analysis; analytical geometry of the plane and three space including the conic sections, rotation of axes, polar coordinates, polar equations of conics, plane curves and parametric equations. Prerequisite: two years of high school Algebra and at least a 26 ACT or 590 SAT math score or College Algebra.
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Polynomial Test for Algebra 50 point Algebra test that covers multiplying binomials using the FOIL method, as well as factoring polynomials. It includes finding the common monomial, factoring the difference of two squares, and factoring perfect squares. The test is comprehensive, and questions are based on four levels of Bloom's Taxonomy: knowledge, comprehension, analysis, and evaluation. Questions consist of two sections of multiple choice, several computation problems, one evaluation question, and one section of fill-in-the-blank. Work Spaces are provided for each section where computation is involved so that all of the student's work will appear on the test. A complete answer key is included. The test is not saved in a PDF format so that you can change it to meet the needs of your students. To view a sample problem from each of the six sections, download the preview version.
Word Document File
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College Mathematics I –
mth208ca
(3 credits)
This course begins a demonstration and examination of various concepts of algebra. It assists in building skills for performing specific mathematical operations and problem solving. These concepts and skills serve as a foundation for subsequent quantitative business coursework. Applications to real-world problems are emphasized throughout the course. This course is the first half of the college mathematics sequence, which is completed in MTH 209: College Mathematics II.
Fundamentals of Expressions
Apply mathematical laws and order of operations principles to solve math problems.
Evaluate expressions.
Classify real numbers.
Identify real and variable elements.
Exponents & Polynomials
Use exponents in algebraic expressions.
Apply exponential principles to scientific notation.
Use exponents and polynomials in real-world applications.
Perform polynomial operations.
Use the distribution property with polynomials.
Simplify polynomials.
Linear Functions
Use linear functions in real-world applications.
Identify slope and intercept from a linear function.
Use the midpoint formula with linear segments.
Generate graphs.
Evaluate forms of linear functions.
Identify the domain and range of a function, as expressed per set theory.
Linear Equations & Inequalities
Use linear equations and inequalities in real-world applications.
Solve linear inequalities.
Use equations to solve word problems and formulas.
Solve linear equations.
Evaluate forms of linear equations.
Fundamentals of College Algebra Review I
Analyze applications of mathematics.
Review all objectives from Weeks One through Four
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Academics
Course Descriptions
MAT 098. Mathematical Skills. (3)
A course in basic mathematical skills. Required for those students who lack the minimum competency necessary for success in Mathematics 099, 121, 122, 221, and 222. This course does NOT satisfy the Core Curriculum requirement in Area D-2 or D-3. Not open for credit to students with credit in Mathematics beyond MAT 098.
MAT 099. Algebra. (3)
Prerequisite: MAT 098 or placement by examination only.
A basic skills course in algebra designed to improve mathematical skills of those students who need, but are not ready to begin a course in precalculus, computer science, business, or statistics. This course does NOT satisfy the Core Curriculum requirement in Area D-2 or D-3. Offered every semester.
MAT 121, 122. Mathematics for the Liberal Arts. (3, 3)
Prerequisite: MAT 099 or suitable placement by examination.
A course on the methods and ideas of mathematics as they relate to the liberal arts. Topics such as sets, logic, mathematics and the fine arts, properties of functions, elementary probability and statistics, game theory social choice, financial mathematics, number theory, graph theory, and binary operations will be covered. Satisfies Core Curriculum in Area D-2 or D-3. MAT 121 offered fall semester; MAT 122 offered spring semester.
MAT 150. Precalculus Mathematics. (4)
Prerequisite: MAT 099 or suitable placement by examination.
An integrated treatment of algebra and trigonometry sufficient to prepare qualified students to begin a calculus sequence in their freshman year. Concepts of set and function are developed at the outset and used throughout the course. Satisfies Core Curriculum in Area D-2 or D-3. Offered every semester.
MAT 200. Applied Statistics. (3)
Prerequisite: MAT 099 or suitable placement by examination.
A data-oriented approach to statistics by arguing from the sample to the population. Topics include combinatorics, random variables, sampling distributions, estimation, tests of statistical hypotheses, regression, correlation, ANOVA, and nonparametric methods. Satisfies Core Curriculum in Area D-2 or D-3. Offered every semester.
MAT 211: Calculus I—Differential Calculus. (4)
Prerequisite: MAT 150 or placement by the department.
A first semester calculus course. Topics include limits, applications and methods for differentiation in a single variable, and an introduction to integration. Satisfies Core Curriculum in Area D-2 or D-3. Offered every semester.
MAT 212: Calculus II—Integral Calculus. (4)
Prerequisite: MAT 211 or placement by the department.
A second semester calculus course. Topics include techniques and applications for integration and an introduction to sequences. Satisfies Core Curriculum in Area D-2 or D-3. Offered every semester.
MAT 221. Basic Concepts of Mathematics. (3)
A study from the early childhood and elementary school teacher's point of view of the structure of numbers, numeration systems, fundamental operations and set theory. Required of all Early Childhood and Elementary Education majors.
A grade of "C" or better is required for Elementary Education majors. Does NOT satisfy Core Curriculum requirements for Areas D-2 or D-3. Offered fall semester.
MAT 222. Geometry for Early Childhood/Elementary Teachers. (3)
A study to develop geometric intuition and insight of such concepts as congruence, measurement, parallelism, and similarity. Required of all Early Childhood and Elementary Education majors.
A grade of "C" or better is required for Elementary Education majors. Does NOT satisfy Core Curriculum requirements for Areas D-2 or D-3. Mathematics 222 will meet Core Curriculum requirements, Area D-2, for only Early Childhood/Elementary Education majors. Offered spring semester.
Prerequisite: MAT 212. (PHY 213 may be taken concurrently with MAT 300.)
A study of infinite series and linear algebra treatment of multivariable calculus.
MAT 334. Linear Algebra. (3)
Prerequisite: MAT 212 or permission of department.
Topics include the theory of finite dimensional vector spaces and matrices treated from the standpoint of linear transformations. Required for state teacher certification in Mathematics.
MAT 335. Modern Geometry. (3)
Prerequisite: MAT 121 or higher.
A study of modern geometry including history, current axiom systems, and alternate developments of geometry using coordinates, vectors, and groups. Required for state teacher certification in Mathematics.
MAT 336. Methods of Teaching Secondary Mathematics. (3)
Prerequisite: MAT 150 or higher.
This course is designed to give teacher candidates practical training in the teaching of mathematics on the secondary level (9-12). Teacher candidates will become familiar with the national and state curriculum standards for mathematics instruction. They will develop an understanding of instructional strategies, activities, and materials essential for effective teaching of mathematics in secondary schools. Twenty-four hours of field experience will be required. Required for teacher certification in Mathematics. Open only to students in the Teacher Education Program. Does NOT satisfy Core Curriculum requirements for Areas D-2 or D-3.
MAT 338. Vector Analysis. (3)
Prerequisite: MAT 300.
A study of the algebra of vectors and the calculus of vector-valued functions. Topics include vector identities, space curves, and the gradient, divergence, and curl of vector functions. Also considered are line and surface integrals including the Divergence Theorem, Green's Theorem, and Stoke's Theorem.
Offered at departmental discretion.
MAT 341. Differential Equations. (3)
Co-requisite: MAT 300.
Methods for the solution of differential equations of the first order and special equations of the second order.
MAT 342. Applied Mathematics. (3)
Prerequisite: MAT 341 or permission of instructor.
Topics include curvilinear coordinate systems, Fourier Series, and transforms. Boundary value problems of interest to science and mathematics students. An introduction to the calculus of residues. Laplace transforms and the inversion integral. Offered at departmental discretion.
MAT 433. Modern Abstract Algebra. (3) Prerequisite: MAT 212 or consent of the department. Topics include groups, rings, and fields. Required for state teacher certification in Mathematics.
MAT 443. Mathematical Analysis. (3)
Prerequisite: MAT 300.
Topics include the study of point sets on the line and in the plane, continuity of functions in these spaces, Stieljes integration, function spaces, and convergence. Offered at departmental discretion.
MAT 445. Complex Analysis. (3)
Prerequisite: MAT 300.
A study of the algebra and calculus of complex numbers. Specific topics include analytic and elementary functions, mappings by elementary functions, the Cauchy integral formula, Taylor and Laurent Series, and residues and poles. Offered at departmental discretion.
MAT 490. Special Topics in Mathematics. (3)
Prerequisite: Permission of instructor.
Topics to be selected by the instructor. Students may receive credit for more than one MAT 490 course, but students may not repeat the topics.
MAT 491. Independent Study. (1-3)
Independent study in a selected field or problem area of mathematics. The topic or problem to be studied will be chosen in consultation with departmental faculty under whose guidance the study will be conducted. Subject to rules and regulations on page 64 of the Catalog.
MAT 495, 496. Internship. (1-3, 1-3)
Internships or practical experience in an approved program of study.
Limited to majors in the department. Subject to regulations and restrictions on page 64 of the Catalog.
MAT 499. Senior Essay. (1-3)
A project requiring scholarly research. Topics to be selected by the instructor. Students may receive credit for more than one MAT 490 course, but students may not repeat the topics. Subject to rules and regulations on page 65 of the Catalog.
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Cambridge General Mathematics Year 11 is written by experienced teachers to address the new syllabus for this new course. Along with a focus on mathematical fundamentals, the authors have treated the course strands according to their relative emphasis in the syllabus and integrated the use of technology into each topic. Each chapter features an outline of the topics to be covered, appropriate and clearly written explanations of the coursework as well as detailed examples followed by carefully graded exercises at three levels. A summary completes each chapter. Investigations appropriate to the topic area are interspersed throughout. Cyclic revision exercises linked to the topics are featured after every three chapters.
CAMBRIDGE UNIV. PRESS
ISBN-10: 0521643783 ISBN-13: 9780521643788
PGS: N/A
List: 30.65YOUR PRICE: 30.65
Cambridge General Mathematics Year 12
Alice Thomas, Michael Brown, Norman Fish
2000
Cambridge General Mathematics Year 12 completes a series of books written by experienced teachers to guide students and teachers through the new NSW mathematics curriculum. The material presented is suited to the full range of student abilities encountered in General Mathematics. The course strands are treated according to their relative emphasis in the NSW syllabus and include: financial mathematics; data analysis; measurement; probability; and algebraic modelling. Each chapter commences with an outline of the material to be covered together with modelling applications and suggested technology use. A summary for learning and understanding, together with revision exercises, complete each chapter. Investigations appropriate to each topic area are interspersed throughout each chapter along with graphics calculator and computer spreadsheet applications of the coursework.
CAMBRIDGE UNIV. PRESS
ISBN-10: 0521643775 ISBN-13: 9780521643771
PGS: N/A
List: 27.00YOUR PRICE: 27.00
Cambridge HSC General Mathematics Study Guide
Jim Stamell
2005
The Cambridge General Mathematics Study Guide is designed to assist students to conduct a thorough topic-by-topic review of concepts and techniques from both the Preliminary and HSC Mathematics courses. It encourages students to apply their knowledge and skills to solve a variety of problems. Each chapter is devoted to a single topic area and comprises: * a summary of the topic content arranged under subheadings; * worked examples which illustrate the application of this content to problem solving and the appropriate setting out of mathematical working; * a set of graded exercises for students to test their understanding and practise their skills, with worked solutions provided; * a more substantial set of graded further exercises for consolidation, with outline solutions provided. Finally, a set of two Practice papers is included. Each of the papers follows the format of the HSC examination paper for Mathematics.
This companion text to Essential Advanced General Mathematics (2nd edition) contains fully worked solutions to a large and representative selection of the analysis and application questions contained in the text book. The graphics calculator is featured in the solutions where ever this is appropriate. Full diagrams, graphs and tables relevant to the solutions are included in all cases.
CAMBRIDGE UNIV. PRESS
ISBN-10: 0521665221 ISBN-13: 9780521665223
PGS: N/A
List: 21.00YOUR PRICE: 21.00
Essential Advanced General Mathematics Third Edition with Student CD-Rom With CD, 3rd Ed.
Essential Advanced General Mathematics is designed to meet the specific needs of those students who intend to proceed to Mathematical Methods 3&4 or a combination of Mathematical Methods 3&4 with Specialist Mathematics. It features content that fully addresses the key knowledge and skills outcomes in the 2000 Mathematics Study Design. A graphics calculator supplement supported by graphics calculator questions and exercises is also featured. Students will benefit from the rich mixture of analysis exercises, multiple choice questions, applications and projects, as well as the regular revision chapters.
CAMBRIDGE UNIV. PRESS
ISBN-10: 0521664497 ISBN-13: 9780521664493
PGS: N/A
List: 23.00YOUR PRICE: 23.00
Essential General Mathematics Solutions Supplement
Sue Avery
2000
This companion text to Essential General Mathematics (3rd edition) contains fully worked solutions to a large and representative selection of the analysis and application questions contained in the text book. The graphics calculator (TI 81/82/83) is featured in the solutions where ever this is appropriate. Full diagrams, graphs and tables relevant to the solutions are included in all cases.
CAMBRIDGE UNIV. PRESS
ISBN-10: 0521775647 ISBN-13: 9780521775649
PGS: N/A
List: 24.00YOUR PRICE: 24.00
Essential General Mathematics with CD-Rom book and CD ROM, 3rd Ed.
Peter Jones, Kay Lipson, David Main, Bar
1999
The third edition of Essential General Mathematics incorporates suggestions from teachers as well as the requirements of the Mathematics Study Design. It fully addresses the key skills and knowledges detailed in the course outcomes in a structure that offers flexibility in planning an appropriate course of study to meet the needs of the diverse student group studying General Mathematics. The text includes new questions and exercises to cover all areas relating to graphics calculators. Analysis questions in each chapter ensure that students are thoroughly prepared for examinations. There are also regular revision chapters to ensure each subject is understood.
CAMBRIDGE UNIV. PRESS
ISBN-10: 0521779324 ISBN-13: 9780521779326
PGS: N/A
List: 27.00YOUR PRICE: 27.00
Essential Standard General Maths First Edition Solution Supplement
Sue Avery
2006
CAMBRIDGE UNIV. PRESS
ISBN-10: 0521612543 ISBN-13: 9780521612548
PGS: N/A
List: 22.00YOUR PRICE: 22.00
Essential Standard General Maths First Edition Teacher CD
Peter Jones, Kay Lipson, David Main, Bar
2006
CAMBRIDGE UNIV. PRESS
ISBN-10: 0521612721 ISBN-13: 9780521612722
PGS: N/A
List: 65.00YOUR PRICE: 65.00
Essential Standard General Maths First Edition with Student CD-Rom With CD
Peter Jones, Kay Lipson, David Main, Bar
2005
CAMBRIDGE UNIV. PRESS
ISBN-10: 0521672600 ISBN-13: 9780521672603
PGS: N/A
List: 30.10YOUR PRICE: 30.10
Experimental General Chemistry, 1st Ed.
Marcus
1999
"This laboratory manual can be used with any general chemistry text, including books designed for courses that cover qualitative analysis and/or a substantial amount of organic chemistry."
McGraw-Hill Science/Engineering/Math
S
ISBN-10: 0072364939 ISBN-13: 9780072364934
PGS: N/A
List: 79.50YOUR PRICE: 75.53
Field and Laboratory Methods for General Ecology, 4th Ed.
Brower
1998
"This introductory ecology lab manual focuses on the process of collecting, recording and analyzing data, and equips students with the tools they need to function in more advanced science courses. It reflects the most current techniques for data gathering so that students can obtain the most accurate samples. Balanced coverage of plant, animal and physical elements offers a diverse range of exercises. Includes exercise on writing research reports."
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Syllabus
Course Meeting Times
Description
Love math but bored in math class? This is the course for you! Combinatorics is a fascinating branch of mathematics that applies to problems ranging from card games to quantum physics to the internet.
Topics will include:
Combinations and permutations
Discrete probability
Sequences and recurrences
Graph theory, with a focus on problem solving
The only pre-requisite is basic algebra; however we will be covering a lot of material. A mathematically agile mind will be helpful. This course will be especially useful for students preparing for contests such as the American Mathematics Competition, American Invitational Mathematics Examination, and USA Mathematical Talent Search.
Grading
The emphasis in this course is on exploration of new topics in math for students in high school. No grades are given for this course.
The Program
This course was offered through the High School Studies Program (HSSP), a project of the MIT Educational Studies Program. HSSP offers non-credit, enrichment courses to 7th-12th grade students on Saturdays at MIT. This program is designed to give these students a chance to take courses in a wide variety of topics. Courses cover both academic and non-academic subjects. The classes are designed to be fun and interesting for students and to offer them an opportunity to learn about something in which they're interested.
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ideal review of formulas and tables for your mathematics, physics, engineering, or other science course
More than 40 million students have trusted Schaumís Outlines for their expert knowledge and helpful solved problems. Written by a renowned expert in mathematics, Schaum's Outline of Mathematical Handbook of Formulas and Tables covers what you need to know for your course and, more important, your exams. Step-by-step, the author walks you through coming up with solutions to exercises in math.
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Book Description: Excerpts from the back cover: Discovering Geometry: An Investigative Approach is an engaging and proven curriculum in which students explore geometry concepts and develop skills that last. This activity-based geometry gives students deeper understanding and better mathematical reasoning skills. Helps students learn geometry concepts, deductive reasoning, reasoning strategies and so much more. Pages are perforated for easy removal.
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ALGEBRA I A, the first course of a two-semester series, begins by covering the basic language of algebra: real numbers, variables, exponents, powers, expressions, and equations. Students learn about the properties of real numbers and practice applying strategies, concepts, and procedures for solving problems. The course then moves onto linear equations. Students learn to use addition, subtraction, multiplication, and division to solve equations with variables on one or both sides. They also learn to apply the distributive property. Students also learn to transform formulas, solve equations involving absolute value, and calculate measures of central tendency. Once students have mastered linear equations, the course introduces them to functions and graphs. Students will use relations and functions to model number relationships. They will learn to interpret, create, and analyze various types of graphs, rules, and tables. Students will also identify and extend arithmetic sequences, graph data on a coordinate plane, and construct stem-and-leaf plots and box-and-whisker plots. Students will also learn to graph linear equations and to write linear equations in various forms, including slope-intercept form and point-slope form. Lastly, the course teaches students to solve and graph linear equalities.
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Show More manual. Detailed solutions at the back of the book help students over obstacles to their learning and the operation of the menus and submenus are absorbed with minimal effort as the mathematics is learned. Deeper investigations are included to challenge the more capable student, and historical vignettes are introduced to add a human dimension to the mathematical excursions. This new publication has been expanded to include a more detailed treatment of linear and quadratic functions and the law of sines and cosines found in most state and provincial guidelines. The topics include finding zeros, domain and range, extrema, and singularities of polynomial and rational functions. Properties of the trigonometric, exponential and logarithmic functions are also explored. Topics also include the study of limits and asymptotic behavior, polar coordinates, parametric equations and conics
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Course Main Navigation
Bachelor of Education (Secondary)
Minor In Mathematics Education
This minor includes statistics, such as organising numerical data estimation and hypothesis testing; problem solving and analysis; mathematical modelling using differential and integral calculus and analytic geometry; and linear algebra, including matrices and matrix arithmetic.
Students will be able to plan a variety of mathematics lessons, assessments and activities, with a pedagogical focus on developing an appreciation of mathematics as a useful and creatively interesting area of study.
Minor structure
This unitset structure contains information about the units which comprise the course as well as the credit points required to successfully complete it.
Content covered in this minor includes statistics, such as organising numerical data estimation and hypothesis testing; problem solving and analysis; mathematical modelling using differential and integral calculus and analytic geometry; and linear algebra, including matrices and matrix arithmetic. Students will be able to plan a variety of mathematics lessons, assessments and activities, with a pedagogical focus on developing an appreciation of mathematics as a useful and creatively interesting area of study.
Note: Students must have passed either WACE General Mathematics 2C/2D or 3A/3B to do this minor. A satisfactory result in WACE 3C/3D is also desirable.
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Math Assessment Levels
Use this table to find which math course you should take, based on
your level on the self-assessment or the proctored placement exam.
Notice that some scores allow you to choose
among several courses. Also, you can always take a course at a lower
lever, unless you already have credit for that course.
For example, a student who got a level 5 with a major that doesn't
require calculus might prefer to take MAT118 instead of MAT131.
You can find out more about the various courses by following the links.
If you place at level 2+ and plan to take calculus, you should retake
the proctored mathematics placement exam after doing a thorough review of
the appropriate material. If your placement level is still 2+ after
having retaken the exam, and you want to study calculus, you should
take MAP103,
which will provide you with the best
possible preparation for future calculus courses.
If you place at level 3 and want a single semester overview of
calculus, you should take MAT122. If you do not need to take calculus,
and wish to do only a single semester of mathematics, you should
strongly consider MAT118, which will provide you
with a more general overview of mathematics. If you place at this
level and plan to take more than a single semester of calculus, you
should take MAT123.
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Graphic display calculators (GDC)
The British A-Level specifications allow graphical calculators in all modules apart from C1.
The calculator should have at least the following buttons for basic calculation, trigonometry and the natural logarithm function:
Other functions should be available too by using the "second function" of some of the keys.
Note, however, that the calculator must NOT have a facility for symbolic algebra, differentiation or integration (sometimes known as an in-built computer algebra system, CAS). Though there are many suitable models for mathematical study at this level, this site makes particular reference to the TI range, specifically the TI-84.
The International Baccalaureate positively encourages the use of graphic calculators throughout its diploma courses.
Many pages throughout this site make specific use of graphic calculators. To find them simple enter GDC in the SEARCH box.
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books.google.com - Iintroductory treatment emphasizes graph imbedding but also covers connections between topological graph theory and other areas of mathematics. Authors explore the role of voltage graphs in the derivation of genus formulas, explain the Ringel-Youngs theorem, and examine the genus of a group, including... graph theory
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Developmental Math Program
Since many students find that their math foundation is rusty or
nonexistent, the Math Department offers a number of courses in
Developmental Math to prepare students for degree applicable
courses. Pre-algebra,
Beginning Algebra and
Geometry are the courses
considered foundational. Three types of Pre-algebra courses are
offered for students with varying backgrounds: 1) A basic review of
Arithmetic (Math 080), 2) a basic
review of Arithmetic and Pre-algebra (Math
088), and 3) a basic review of Arithmetic and Pre-algebra
specifically designed for math anxious students (Math
089).
Some of these classes are offered with a tutoring seminar
attached. In these sections, in addition to attending class, each
student attends a three-hour seminar each week going over class
materials with a tutor. The students who recognize a need to refresh
skills and then choose to commit to a developmental math course gain
self-confidence, making success easier to attain.
Some students only need to review their foundational skills and
they opt for a one-unit computer tutorial course (see
Math 088L/090L). The
computer tutorial does NOT replace a regular course, but allows
students to practice and refresh skills at their own pace. Having
successfully completed Beginning Algebra (Math
090), a student can then enroll in Intermediate Algebra (Math
103 or 110) which applies
toward an Associates degree.
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what does pre-algebra mean?? Pre-Algebra is basically preparing you for Algebra. Pre-Algebra teaches you Order of Operations, Properties of Numbers, Rational and Irrational Numbers, Exponents, PEMDAS, ect.
Monday, August 25, 2008 at 9:11pm by Delilah
pre-algebra kk my teach told me to describe and draw things that are about pre-algebra and she told me to write what pre-algebra is... so can anyone help me??
Monday, August 25, 2008 at 9:03pm by damainmind
what does pre-algebra mean?? pre algebra is like a bunch of math that comes before algebra in middle school.
Monday, August 25, 2008 at 9:11pm by Grace
pre- algebra(MATH) I need help with pre-algebra solving equations by multiplying or dividing. Can you help me with this homework for free?
Thursday, November 5, 2009 at 6:04pm by Ketrice
pre algebra i told u pre algebra... but i had to give back the text book so i dont have any now
Sunday, June 20, 2010 at 9:38pm by lavena
HELP! pre-algebra What does this question have to do with pre-algebra? Using an online unscrambling tool, I came up with "proprietors"
Friday, September 5, 2008 at 11:27pm by drwls
Pre-Algebra I do not get this! me and my friend cannot get the "simplified" ecuation part of the homework! Pre-algebra...... tough work
Tuesday, September 15, 2009 at 11:25pm by Maddison
pre-Algebra Sorry, struggling through pre-Algebra .. :-( .. How do i figure out 5x = -20 ?
Friday, February 19, 2010 at 9:55pm by Emily
Pre-Algebra the world wobbl e contests? i dunoo pre-algebra sucks
Tuesday, September 15, 2009 at 11:25pm by marina
pre algebra i dont have a math text. i had to take it back to the teacher and plus she never thought me how to do this im in pre algebra not trigonometry
Sunday, June 20, 2010 at 9:38pm by lavena
pre-algebra so the 15 - 9=4 okay thanks ms. sue for helping me with my 7th grade pre algebra hw I will probably need more help I will jut post my other questions too.
Sunday, September 16, 2012 at 4:23pm by emily
Pre-Algebra-math Sorry I am normally great at Pre-Algebra, but this one i cannot figure out. Sorry, Kim! Good Luck!
Tuesday, September 25, 2012 at 3:51am by Delilah
what does pre-algebra mean?? i have to draw things that have to do with pre algebra but...i dont understand the meaning of it
Monday, August 25, 2008 at 9:11pm by damainmind
pre algebra my grade is 83.17 in pre algebra in college, but the final exam is worth 300 points. If I got a B or B- or a C on the final, what would my grade be overall?
Thursday, March 10, 2011 at 9:20pm by Amber shall
Pre-Algebra its my pre-algebra homework
Tuesday, January 18, 2011 at 9:23pm by TiffanyJ
pre-algebra um as in for what is pre-algebra??
Monday, August 25, 2008 at 9:03pm by damainmind
Pre Algebra random question: i have a pre-algebra unscramble and i need help to unscramble the word the word they gave me was: Seproropit can any of u help me?
Thursday, June 5, 2008 at 5:21pm by coco
Pre-Algebra ok well my pre algebra teacher copied some worksheets and its pg 40 and its about some friars in a floral shop buisness. for extra credit we do the joke which is also a way to find out if our answers were correct. there is no 3/8 in my answers and welll yeah thats it.
Tuesday, November 8, 2011 at 10:28pm by Emily
Pre-Algebra Evidently you haven't mastered pre-Algebra since your answer is WRONG. It takes him 4 hours to catch her. While she does ride for 5 hours, it only takes him 4 to catch her.
Wednesday, August 18, 2010 at 6:28pm by Joe Mama
Pre-Algebra: Help I have to do a webquest for pre-algebra and we have to make up a fundraiser thing, I need a list of things that one needs for a charity fundraiser, such as chairs, buffet tables, tables, tents, tablecloths. HELPP
Thursday, March 3, 2011 at 12:20pm by Cheryl
pre-algebra write an inequality for the sentence. The total t is greater than five. Well your answer is going to be T and the sign for greater than is simply >. So the answer would be T > 5 ok again my name is above. i was just wondering what pre-algebra was? i mean i take ...
Friday, March 9, 2007 at 8:50am by Joe
Math oh no Vitaliy, this person is in 7th grade pre-agebra or 8th grade pre-algebra.
Thursday, February 5, 2009 at 6:58pm by haha
PRE-CALCULUS THIS IS FOR ALGEBRA/PRE-CALCULUS MATH. I POSTED IT JUST AS THE TEACHER WROTE IT.
Tuesday, September 13, 2011 at 10:41pm by aLVIN
SHAY THE MATH QUESTION IS IT ALGEBRA , PRE ALGEBRA' OR GEOMETRY? Quadriatic functions. so algebra i think.
Wednesday, January 17, 2007 at 7:09pm by ROSA
Pre-Algebra Sorry, you are PRE-algebra, so you may not know how to solve for x. 8x = 10x - 10 Subtract 10x from both sides. -2x = -10 Divide both sides by -2. x = 5
Wednesday, August 18, 2010 at 6:28pm by PsyDAG
algebra 2 thats part of algebra 2 thats easy were doing that now in pre algebra
Wednesday, April 29, 2009 at 1:14pm by Tanisha
Pre Algebra Thank you so much. I have another question :) In my Pre Algebra book, I have a question like this: Draw a line from one vertex to a point on another side to create a triangle. Cut along the line. What do they exactly mean by 'cut along the line'?
Thursday, March 20, 2008 at 6:36pm by Lily
Pre-calc Pre calculus? This is stock Algebra II. put the equations in the form of ax^2+bx+c=0 then factor. for instance, c is already in that form. 2x^2+x-6=0 (2x-3)(x+2)=0 x= 3/2 x=-2 do the others the same method.
Monday, January 25, 2010 at 5:18pm by bobpursley
pre algebra You have to decide you're going to learn how to do algebra.
Wednesday, June 16, 2010 at 10:05pm by Ms. Sue
Pre-Algebra it is about math in algebra i dont know why but it is my teacher is wierd
Tuesday, September 15, 2009 at 11:25pm by Mikayla
Math (Algebra/Pre-Algebra) in finding the x-intercept let y = 0 in the equation and solve for x so what do you get for x?
Thursday, June 4, 2009 at 9:13pm by Reiny
Math (Algebra/Pre-Algebra) That is one of the choices so my guess is that that is correct. Thank you! =]
Thursday, June 4, 2009 at 8:48pm by Samantha
algebra what is the answer to pre algebra with pizzazz page 106
Sunday, May 6, 2012 at 9:13pm by Anonymous
Pre-Algebra its ok i cant figure it out i really hate algebra
Tuesday, September 15, 2009 at 11:25pm by Mikayla
pre algebra try to set up an equation im in algebra 2 so i may be able to help you
Monday, November 8, 2010 at 5:31pm by ali
pre-algebra(algebra) I might need more help i am still working on my homework
Wednesday, October 3, 2007 at 9:27pm by Stacy
Algebra 2 In Kentucky, where i am from, we do algebra and algebra two before pre-cal and calculus. I didnt realize that the problem could be solved in multiple ways and i apologise. But the solution should be done without calculus.
Thursday, February 24, 2011 at 10:33pm by AnonMath (Algebra/Pre-Algebra) What is the 23rd term in the arithmetic sequence: 11, 14, 17, 20...? All I need is the formula to find the it because I have to show work. Thanks.
Thursday, June 4, 2009 at 9:11pm by Samantha
pre algebra what's pre-algebra about this? Sounds like 3rd-grade long division. Take a visit to and you can see all the steps involved with long division
Monday, September 10, 2012 at 11:10pm by Steve
pre calc There are 3! =6 ways to order the three separate topics. For each of these ways, there are 4! ways to arrange the algebra books, 2! ways for the geometry books, and 3! ways for the pre-cal books. So, in all, there are 3! 4! 2! 3! = 6*24*2*6 = 1728 ways. Note that if the ...
Sunday, September 25, 2011 at 5:39pm by Steve
Math (Algebra/Pre-Algebra) What is the x-intercept of the line with equation 2y + 3x = 24? What is the x-intercept and how do I find it? I have to show work. Thank you!
Thursday, June 4, 2009 at 9:13pm by Samantha
Math (Algebra/Pre-Algebra) Ok I think I get it... So it would be D then? Because if you got more people in the stands you would have less empty seats. Right?
Thursday, June 4, 2009 at 9:09pm by Samantha
Math (Algebra/Pre-Algebra) if a is the first term and d is the common difference then Term(n) = a + (n-1)d
Thursday, June 4, 2009 at 9:11pm by Reiny
pre-Algebra How can you solve algebra equations? The idea is to find a way to isolate the unknown by itself. You can add, subtract, multiply, and divide both </s> sides of the equal signs to do that.
Friday, May 11, 2007 at 5:03pm by Cherlyn
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\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2013a.00933}
\itemau{Heid, M. Kathleen; Thomas, Michael O. J.; Zbiek, Rose Mary}
\itemti{How might computer algebra systems change the role of algebra in the school curriculum?}
\itemso{Clements, M. A. (ed.) et al., Third international handbook of mathematics education. Berlin: Springer (ISBN 978-1-4614-4683-5/hbk; 978-1-4614-4684-2/ebook). Springer International Handbooks of Education 27, 597-641 (2013).}
\itemab
Summary: Computer algebra systems (CAS) are software systems with the capability of symbolic manipulation linked with graphical, numerical, and tabular utilities, and increasingly include interactive symbolic links to spreadsheets and dynamical geometry programs. School classrooms that incorporate CAS allow for new explorations of mathematical invariants, active linking of dynamic representations, engagement with real data, and simulations of real and mathematical relationships. Changes can occur not only in the tasks but also in the modes of interaction among teachers and students, shifting the source of mathematical authority toward the students themselves, and students' and teachers' attention toward more global mathematical perspectives. With CAS a welcome partner in school algebra, different concepts can be emphasized, concepts that are taught can be done so more deeply and in ways clearly connected to technical skills, investigations of procedures can be extended, new attention can be placed on structure, and thinking and reasoning can be inspired. CAS can also create the opportunity to extend some algebraic procedures and introduce and assist exploration of new structures. A result is the enrichment of multiple views of algebra and changing classroom dynamics. Suggestions are offered for future research centred on the use of CAS in school algebra.
\itemrv{~}
\itemcc{U50 U70 H10 I20}
\itemut{computer algebra systems; technology in mathematics education; algebra instruction; curriculum}
\itemli{doi:10.1007/978-1-4614-4684-2\_20}
\end
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Modern cryptology increasingly employs mathematically rigorous concepts and methods from complexity theory. Conversely, current research topics in complexity theory are often motivated by questions and problems from cryptology. This book takes account of this situation, and therefore its subject is what may be dubbed "cryptocomplexity'', a kind of symbiosis of these two areas. This book is written for undergraduate and graduate students of computer science, mathematics, and engineering, and can be used for courses on complexity theory and cryptology, preferably by stressing their interrelation.
This book gives a good introduction to evolutionary computation for those who are first entering the field and are looking for insight into the underlying mechanisms behind them. Emphasizing the scientific and machine learning applications of genetic algorithms instead of applications to optimization and engineering, the book could serve well in an actual course on adaptive algorithms. The authors include excellent problem sets, these being divided up into "thought exercises" and "computer exercises" in genetic algorithm. Practical use of genetic algorithms demands an understanding of how to implement them, and the authors do so in the last two chapters of the book by giving the applications in various fields
Providing a deeper understanding of the microscopic world through quantum theory, this supplementary text is ideal for undergraduate and graduate students in quantum theory and quantum optics. It contains physical, rather than formal, explanations; mathematical formalism is kept to a minimum; and theoretical discussions are combined with experimental results. ... programming concepts like selection statements, loops, and functions, before moving into defining classes. Students learn basic logic and programming concepts before moving into object-oriented programming, and GUI programming.
Building Ideas An Introduction to Architectural Theory This book is an essential text for students of architecture and related disciplines, satisfying the demand for an accessible introduction to the major theoretical debates in contemporary architecture. Written in a lucid and user-friendly style, the book also acts as a guide and companion volume to the many primary theoretical texts recently made available in reprinted collections.
With its many examples, exercises, and full solutions to selected exercises, this book provides a gentle introduction that is ideal for self-study and an excellent preparation for applications. A distinguished feature of the book is that algebraic and geometric techniques are balanced. The beautiful theory of train tracks is illustrated by two nontrivial examples.
Provides a basic foundation on trees, algorithms, Eulerian and Hamilton graphs, planar graphs and coloring, with special reference to four color theorem. Discusses directed graphs and transversal theory and related these areas to Markov chains and network flows
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Further Mathematics is the most accessible mathematics course at the units 3 & 4
level. It is usually taken alone, but it may be taken with Mathematical Methods Units 3
&4. Any of Toorak College's Unit 1&2 maths offerings provides the necessary
mathematical prerequisites for this course.
Areas of Study
Data Analysis Core material
Applications Modules Graphs and Relations
Geometry and Trigonometry
Business related mathematics
Outcomes
Unit 3
Unit 4
To define and explain key terms and concepts as specified in 'Data Analysis' area of
study and in one of the three modules
To use mathematical concepts and skills developed in the 'Data Analysis'
To select and appropriately use technology to develop mathematical ideas, produce
results and carry out analysis in situations requiring problem-solving, modelling or
investigative techniques in the core or module.
To define and explain key terms and concepts as specified in the content from the
'Applications' areas of study, and use this knowledge to apply related mathematical
procedures to solve routine application problems.
To apply mathematical processes in contexts related to the 'Applications' area of study
and to analyse and discuss these applications of mathematics.
To select and appropriately use technology to develop mathematical ideas, produce
results and carry out analysis in situations requiring problem-solving, modelling or
investigative techniques related to the modules from the 'Applications' area of study.
Further Mathematics provides general preparation for employment or further study. It
does not provide an appropriate background for students wishing to undertake further study
in courses that are largely mathematical or scientific.
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Linear algebra is a division of algebra which includes theory of systems of linear equations and other elements such as matrices, vector spaces and determinants. Matrix can be defined as a set of numbers laid out in rows and columns which has a variety of applications in the fields of encryption, games and economics.
For any Linear And Matrix Algebra assignment help related queries, you may contact us through our LIVE CHAT facility. We are now available 24/7 online to assist you on all your Linear And Matrix Algebra
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With acclaimed titles like The Manga Guide to Physics and The Manga Guide to Calculus, the best-selling Manga Guide series from No Starch Press is changing the way students think about math and science. By combining real mathematical content with authentic Japanese manga, the Manga Guides take the sting out of learning complex topics.
The latest in the series, The Manga Guide to Linear Algebra, helps math and computer science students wrap their brains around a tricky required course—linear algebra. The book uses the story of a university student and her tutor (a wannabe karate champ) to keep readers engaged while they learn the fundamental concepts of linear algebra...
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These classes use a hybrid format. Students are required to come to the
Math Lab in the Learning Center at Bakersfield College for Orientation
and for all Proctored
Assessments. All classes are taught using the Internet-based program,
ALEKS. The student may choose to read ALEKS in English or Spanish. The
ALEKS website can be found at
Hours/Location:The Math Lab is
located in the Learning Center, in the Student Services Building, above the Counseling Offices. A
stairway is in the breezeway at either side of the building.
Hours are Monday and Thursday, 8:30 am - 5:50 PM and Tuesday and
Wednesday, 8:30am–6:50 pm and Fridays,
8:30am–12:20pm. (Summer session: Monday through Thursday,
11am–6:50pm.)
THE MATH LAB IS A CLASSROOM. AS A COURTESY TO ALL STUDENTS,
CELL PHONES MUST BE TURNED OFF OR SILENCED. NO VISITING WITH OTHER
STUDENTS, FOOD, DRINKS (OTHER THAN WATER) OR CHILDREN ARE ALLOWED.
Required
Supplies:ALEKS student
access code. The access code and workbook may be
purchased at the BC bookstore front cash register or the Delano campus after attending orientation.
It is also available for purchase online from the ALEKS website.
Course
Code:Course Code information for accessing ALEKS is given out during orientation.
Textbook:The ALEKS program is not textbook specific. Any appropriate algebra
book may be used in conjunction with the course.
Textbooks bundled with the ALEKS program, Prealgebra by Martin-Gay,
and Elementary Algebra or Intermediate Algebra by Dugoploski,
are available but not required. The Dugoploski texts are
available to download by section at no extra charge directly from
ALEKS.
Grading:Grading for the class is based solely on results of ProctoredAssessments
taken on the ALEKS program. Proctored Assessments may only be taken
at the Math Lab at Bakersfield College. Students must present a picture ID. Only the calculator
provided by the ALEKS program may be used during the Proctored Assessment.
You are required to come in at least four times during the semester to
test. If you come in four or more times to test, your highest score will
be the score that counts for a grade. If you come in fewer than 4 times
to test, we will average your two highest scores to get your grade for
the course. The grading scale for all three courses is shown below:
Math B50:100-90% = A, 89-80% =
B, 79-70% = C, 69-55% = D, 54% and below = F
Math B60:100-90% = A, 89-80% =
B, 79-70% = C, 69-55% = D, 54% and below = F
Math B70:100-90% = A, 89-80% =
B, 79-70% = C, 69-55% = D, 54% and below = F
Drop
Policy:Each student is expected to put in a minimum
of 8 hours each week (11 hrs/week for Summer session) on the ALEKS
program. To check your hours, see "Total time on the ALEKS program" under
Report. Time on the ALEKS
program may be done from any Internet-accessible computer. Student
time is checked each Tuesday morning. Excess time one week is credited
toward future weeks. Students are required to to put in 4 hours the
first week, then 8 hours per week after that. If a
student has not done 4 hours in the first week they will be dropped; if
they make up the total time during the second week they may request to
reinstate. In later weeks if the student is 11 or more hours short on
time, the student will be dropped from the course and may request a
one-time only reinstatement. If a student becomes 11 or more hours short
on time again after being reinstated, he or she will be dropped
from the course a second time and will not be reinstated without
permission from the instructor.
Tutoring:All students are strongly encouraged to come to the Math Lab to get
face-to-face, one-on-one help. We definitely do not expect you to work
on the program without the help of an instructor. The Math Lab has
faculty and staff ready to help you understand and be successful. You
may use the computers in the Math Lab when you need help, or whenever
you have some time between classes and would like to work on your ALEKS
account. If you find you are having trouble with a topic at home, make a
note of the topic or print the page and move on to a different topic.
Then come to the Math Lab and let us help you. However, we do not offer
help with math problems over the phone or by e-mail. Click "LINKS" at
the bottom of this page for online sources for math help.
Incomplete
Policy:Students may request an Incomplete grade at the end of the semester
in order to complete the class the following semester. A request form for
an Incomplete will be available at the Testing Desk in the Math Lab during the
last two weeks of class (during summer, last week only).Details
on how to qualify for an Incomplete can be found on your syllabus
(distributed during orientation). If a student fails to complete
the material the following semester, the Incomplete grade automatically
becomes an F. If you are receiving Financial Aid based on units, the units
for your class count only during the semester you originally enrolled in
the class.
Transfer
Policy: In
order to be allowed to transfer to one of the ALEKS-based hybrid Math
courses after the 60% drop date (the last day to drop a semester-length
class with a "W"), you must obtain approval from the Mathematics
department chair (MS-107E, 395-4331) with a form that can be obtained at
the Math Lab.Once
approved, the form must be returned to the Math Lab and you
must complete an orientation.At
that time, you will be provided with a transfer form totake to the Admissions & Records office for completing the
transfer process.
Disability
Services:Students with disabilities who believe they may need accommodations in
this class are encouraged to contact Disabled Student Programs &
Services in FACE 16, 395-4334, as soon as possible to better ensure such
accommodations are implemented in a timely fashion.
Academic
Dishonesty:Any form of academic dishonesty will not be tolerated and will
result in a zero for that assignment. This is the only warning you will
receive. See the Student
Handbook for possible disciplinary consequences of Student Misconduct
at Bakersfield College.
|
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01/06/2012Every Chinese character is made up of a number of strokes, or single movements of the pen or writing brush. The order and direction in which the strokes are made are very important in producing uniform characters, and learning the basic rules o
91.304 Foundations of Computer ScienceChapter 0 Lecture Notes Prof. David Martin and Prof. Giam Pecelli (with modifications by Prof. Karen Daniels)This work is licensed under the Creative Commons Attribution-ShareAlike License. To view a copy of this li
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[Go around with names] [If there are new students:] Say your name Describe your academic and non-academic interests Say why you signed up for the course Say a little about your math background (esp. calculus) Talk about your best and worst math experience
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Section 1.3: The notion of limit Stewart's first definition: We write limxa f(x) = L and say "the limit of f(x), as x approaches a, equals L" if we can make the values of f(x) arbitrarily close to L by taking x to be sufficiently close (but not equal) to
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[Hand out time-sheet; 241 too!] Revised due-date for assigment #5: 10/10 is a holiday! So it's due 10/12. Don't feel bad about making mistakes on the True/False questions! They're designed to be tricky. Better to make these mistakes now (and thereby learn
For next Wednesday, read section 2.3. Last time we looked at the function f(x) = x|x|:42-2-112-2-4which can also be described by the two-part formula cfw_x2 if x < 0, f(x) = cfw_ cfw_x2 if x 0. We showed last time that f(x) is differentiable at x
For Thursday, read section 2.4. "Paradox": "Solve x2 = 1. We get x = +1 and x = 1. So 1 = x = 1, implying 1 = 1." .?. An equation is only true (or false) in a context and in a domain of validity. Ignore the context and domain of validity and you may get n
[Hand back homework and hand out practice test solutions.] What's the main idea of section 2.6? . Implicit differentiation: To differentiate y with respect to x, you don't always need to write y explicitly in the form f(x); it can be enough to write an al
Questions about the midterm exam? Reminder: Your cheat sheet must be WRITTEN or TYPED by you. The exam will cover up through (and including) section 2.5 (the chain rule). True-false questions on pages 138139: 1. "If f is continuous at a, then f is differe
Hand back homework, collect section notes Section 2.8: Linear approximation and differentials Main idea? .?. Derivatives are good for finding approximate values of functions If f is a differentiable function in the vicinity of x = a, then: for x a, the (u
Puzzle from Monday's lecture: Does there exist an irrational number r such that rsqrt(2) is rational? Hint: The answer is in Wednesday's lecture (sort of!). Solution: We can easily prove that either r = sqrt(2) or r = sqrt(2)sqrt(2) works, but the proof w
Section 3.2: Inverse functions and logarithms (concluded) Fact: If f is an increasing function then f is one-to-one. (Note: Here "increasing" means "strictly increasing".) Proof: If x1, x2 are in the domain of f with x1 < x2, then since f is increasing, f
Last time we saw one way to compute the derivative of xx with respect to x. Another method we can apply is logarithmic differentiation: (d/dx) ln f(x) = f (x) / f(x) That is, if f(x) > 0 on some open interval I, then ln f(x) is differentiable with derivat
Section 3.4: Exponential growth and decay (concluded). Interest If you put $100 in the bank and it's compounded yearly with 12% annual interest, after 1 year you get your original $100 plus $12 interest, for a total of $100 times 1.12 = $112. If your mone
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MATH1001
Preparatory Studies in Mathematics
10 Units 1000 Level Course
Available in 2013
Callaghan Campus
Semester 1
Ourimbah
Semester 1
Previously offered in 2012, 2011, 2010, 2009
Quantitative methods are used in many areas of science and business. The course MATH1001 introduces and develops those areas of arithmetic, algebra and geometry necessary for an understanding and use of basic quantitative methods.
This course is suitable for those students who have not studied, or who have not succeeded in, mathematics courses at the HSC level.
Students cannot count MATH1001 for credit if they have previously passed MATH1002, MATH1100, MATH1110 or MATH1210.
Objectives
A student successfully completing this course will have 1. An understanding of the nature of the real number system, through well-founded skills 2. Skills in algebra and an understanding of how these are based on properties of number systems 3. An appreciation of the applicability of mathematical theory and skills 4. Knowledge of the role coordinate geometry plays in linking algebra and geometry
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320 SAT Math Problems arranged by Topic and Difficulty Level
Book Description: student can immediately find the problems he or she needs to improve in a quick and efficient manner. Using this book you will learn to solve SAT math problems in clever and efficient ways that will have you spending less time on each problem, and answering difficult questions with ease. You will feel confident that you are applying a trusted system to one of the most important tests you will ever take. Also take a look at "28 SAT Math Lessons to Improve Your Score in One Month" also written by Dr. Steve Warner. There is a Beginner course for students currently scoring below 500 in SAT math, an Intermediate Course for students currently scoring between 500 and 600 in SAT math, and an Advanced Course for students currently scoring above 600. Dr. Steve Warner has also just released "The Complete Official SAT Study Guide Companion" which contains solutions to all questions in the 10 SAT's given in the 2nd Edition of the College Board's Official Study Guide.
Buyback (Sell directly to one of these merchants and get cash immediately)
Currently there are no buyers interested in purchasing this book. While the book has no cash or trade value, you may consider donating it
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Students begin an exploration of cryptology by first learning about two simple coding methods, the Caesar substitution cipher and the Vigenere polyalphabetic cipher. Students then use matrices and their inverses to create more sophisticated codes. ORC reviewers were pleased at the wealth of coding information provided in this 2-lesson unit but were disappointed that the matrix methods were not fully developed. For this reason, they recommend this site as a content resource, a good reference for background on cryptology. Activity sheets, overheads, discussion questions, lesson extensions, suggestions for assessment, numerous links to supplemental information, and prompts for teacher reflection are included. (author/sw)
Ohio Mathematics Academic Content Standards (2001)
Patterns, Functions and Algebra Standard
Benchmarks (8–10)
C.
Translate information from one representation (words, table, graph or equation) to another representation of a relation or function.
Principles and Standards for School Mathematics
Number and Operations Standard
Understand meanings of operations and how they relate to one another
Expectations (9–12)
develop an understanding of permutations and combinations as counting techniques.
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Mathematics and Statistics - NCEA Level 1
Qualifications:
• NCEA Level 1.
• You will need at least 10 credits at Level 1 Mathematics to qualify for the NCEA Level 1 Certificate.
• You will need at least 10 numeracy credits at Level 1 or higher to gain University Entrance.
• You will need 14 credits at Merit or above for a subject endorsement. (at least 3 internal and 3 external credits).
Students will be required to have a graphical calculator (These can be purchased through the school).
Entry:
• You have achieved Level 5B or better in all strands of the Year 10 Mathematics course.
• Graphics Calculator (recommended) or a Scientific Calculator.
Information:
• This course can lead onto the MAT201 AND MAS201 courses (see entry requirements below).
• This course is the basis for students wishing to continue studies in Mathematics to NCEA Level 2 and 3. It includes a variety of internal and external assessments.
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Studying to learn is different from studying for grades. Popular study techniques
often fail to produce adequate long-term learning.
Most students spend a majority of their study time on four activities:
highlight the text
read through the examples
try the exercises
copy solutions from the answer book
These activities involve no real commitment. Passive activities such as highlighting, reading, and
copying have little long-term benefits, and trying the exercises before copying solutions is only
minimally active. This kind of study leads to the common complaint, "I 'understood' everything,
but I didn't do well on the test."
People learn mathematics best by doing mathematics and then reflecting on what
they have done.
The words "doing" and "reflecting" imply activity on the part of the learner, rather than passivity.
DOING MATHEMATICS
"Doing" mathematics means reading and working problems actively.
Active reading is done as much with the hand as the eyes. Neatly list key
definitions, ideas, and results for each topic. Stop frequently to work out details and
to rework text examples.
Writing up a few exercises neatly is just as important as doing a lot of exercises.
When you don't understand something, work to frame a specific question. Then
seek help.
Active reading and careful writing of exercise solutions takes a long time, but it is what teachers
do when they prepare to teach a course for the first time, and it is a crucial learning activity.
REFLECTING ON WHAT HAS BEEN DONE
After learning a body of material, prepare a careful summary, as though you were
going to teach the material to others.
We never really know that we understand something until we have successfully written it down or
explained it to others. Often we think we understand an idea, but we find our written or spoken
explanation inadequate. The search for a better way to say something can lead to a better
understanding.
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MATH 1323 - Quantitative Reasoning
This course is designed for curricula where quantitative reasoning is required. The course content includes critical thinking skills, arithmetic and algebra concepts, statistical concepts, financial concepts, as well as numerical systems and applications. A graphing calculator is required.
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Accuplacer Math Preparation Materials
The Accuplacer Math Preparation Materials are a complete set of
resources developed to support students, and their teachers, preparing for the
ACCUPLACER® test and for success in college mathematics.
The program recognizes the importance of tailoring instructional experiences to
address students' identified needs. The fully-searchable CD includes more than
1,400 pages of materials designed in a mix-and-match model, allowing teachers
to select appropriate lessons, activities, and components for a full course, a series
of sessions, or individual assignments. This program was piloted in "College Ready" Grant Sites and enhanced based on teacher feedback.
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Iadecentwayto meet algebraic problems that need attention, when a "picture" needs to be filled in.Ultimately,this"picture"shouldprovidesomeunificationorbetterunderstandingofdiversephenomena,orthesolutionofareticentproblem.Lookingfororworkingonmathematical(orsimplyalgebraic)structureisjustanotherstrategyforbuildingabetterconceptualpictureofthemathematicallandscape.
I meet algebraic problems that need attention, when a "picture" needs to be filled in.
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ResultsPlus Booster is best when used along with the corresponding Pearson textbook, but serves as a great supplement to any text that might be in use.
Introducing ResultsPlus Booster
ResultsPlus Booster helps students to carry on learning and improving their skills in mathematics beyond the classroom. Traditionally, if a student gets stuck on a problem, they are not able to progress until their teacher is available to help them. By providing learning tools at every step of the way, ResultsPlus Booster allows students to help themselves and so get an improved independent learning experience.
We recommend that ResultsPlus Booster is introduced during a lesson to help get students registered on the system and used to finding their way around the product.
ResultsPlus Booster as homework
ResultsPlus Booster is matched to your textbooks, so it is easy to use alongside your other materials. There is plenty of support for homework activities to be used throughout your course. The benefit of this model of teaching is not only that it reduces your marking load, but also students achieve a better learning outcome as they receive support and feedback at the point at which they need it. Research suggests that quality of learning is improved by reducing the time between a student coming up against a problem and receiving feedback.
ResultsPlus Booster in the classroom
This approach to teaching is similar to the homework model; however, students work together in the classroom. The benefit of this model is that the teacher can be available to provide extra support as the students work through the exercises.
ResultsPlus Booster for independent study
ResultsPlus Booster can automatically set work for students and track their progress through the use of the Study Plan. After taking a diagnostic test, ResultsPlus Booster will create a customised study plan for the student, making exercises available based on students' results.
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Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Topics include applications to urban geography and planning plus comparisons to Euclidean geometry. Every principle is illustrated and clarified with numerous research problems, ex... read more
Mathematics and the Imagination by Edward Kasner, James Newman With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures.
Euclidean Geometry and Transformations by Clayton W. Dodge This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
A Vector Space Approach to Geometry by Melvin Hausner This examination of geometry's correlation with other branches of math and science features a review of systematic geometric motivations in vector space theory and matrix theory; more. 1965Problems and Solutions in Euclidean Geometry by M. N. Aref, William Wernick Based on classical principles, this book is intended for a second course in Euclidean geometry and can be used as a refresher. More than 200 problems include hints and solutions. 1968 edition.
Foundations of Geometry by C. R. Wylie, Jr. Geared toward students preparing to teach high school mathematics, this text explores the principles of Euclidean and non-Euclidean geometry and covers both generalities and specifics of the axiomatic method. 1964Product Description:
Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Topics include applications to urban geography and planning plus comparisons to Euclidean geometry. Every principle is illustrated and clarified with numerous research problems, exercises, and graphs. Selected answers to
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Find a South Elgin Algebra 2Subject Content Outcomes:
1) Use the terms, definitions, and notation of Basic Algebra
2) Identify and make use of real number properties and evaluate real number expressions
3) Sketch the Graph of a Linear Function and Identify the Slope and Intercepts
4) Perform operations with Polynomials
5) ...
...I am experienced in all of these topics and also in how to apply the TI-84 in the classroom. Algebra II is a division of mathematics that comes under a general topic known as analysis. As a result Algebra II is primarily focused on providing the knowledge and skills to analyze problems, identif...
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From time to time, not all images from hardcopy texts will be found in eBooks, due to copyright restrictions. We apologise for any inconvenience.
Description
For courses in undergraduate Analysis (an easy one) and Transition to Advanced Mathematics.
This text helps fill in the groundwork students need to succeed in real analysis—often considered the most difficult course in the undergraduate curriculum. By introducing logic and by emphasizing the structure and nature of the arguments used, Lay helps students move carefully from computationally oriented courses to abstract mathematics with its emphasis on proofs. Clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers make this text readable and student-oriented, and teacher- friendly.
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the theory of error-correcting codes to computer scientists. This theory, dating back to the works of Shannon and Hamming from the late 40's, overflows with theorems, techniques, and notions of interest to theoretical computer scientists. The course will focus on results of asymptotic and algorithmic significance. Principal topics include: Construction and existence results for error-correcting codes. Limitations on the combinatorial performance of error-correcting codes. Decoding algorithms. Applications in computer science.
Highlights of Calculus is a series of short videos that introduces the basics of calculus—how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject. The videos were created by renowned mathematics professor Gilbert Strang who has taught at MIT since 1962.
The video series reviews the key topics and ideas of calculus with applications to real-life situations and problems and then fully covers the concept of Derivatives.
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These videos are intended as educational materials for my VVC students. You MAY download the files for your PERSONAL educational use only. You may NOT change, edit or distribute these video files in any way. You may NOT upload these files to any web location without the express written permission of Stephen Toner.
You will need to have Real Player installed to view some of the video lectures. After following the link, click on the words "Get RealPlayer Free" in the Basic Player column.
Summary of all of the methods of factoring in Introductory Algebra. Common mistakes that should be avoided. This is a rather long video. You might want to right-click and choose "save as" to store this to your hard drive.
How to solve quadratic equations by factoring. Word problems involving quadratic equations. This is a rather long video. You might want to right-click and choose "save as" to store this to your hard drive.
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FLOSS Mathematical Software
GeoGebra is dynamic mathematics software that joins geometry, algebra and calculus. It is developed for learning and teaching mathematics in schools by Markus Hohenwarter and an international team of programmers.
Dr. Geo is a winning award interactive geometry software. Dr. Geo allows one to create geometric figure plus the interactive manipulation of such figure in respect with their geometric constraints. It is usable in teaching situation with students from primary or secondary level.
Essentially carmetal is great at sketching just about any graph. The user interface is easy to understand and fun to play with and it is not long before you are plotting points, sketching lines and functions on the graph with ease. You can opt to give it an equation and it sketches it or vice versa. Also, you can draw just about any shape on the grid, specify the points and you have an easily drawn graph. There is also a useful tool built in which allows you to export the graphic as a png object which can be read by word.
DeadLine is a freeware designed for students and engineers. It combines graph plotting with advanced numerical Calculus, in a very intuitive approach. Most equations are supported, including algebraic equations, trigonometric equations, and exponential equations.
DeadLine includes a fast engine that performs Math calculations. You can complete any task almost instantly, even on older systems.
Graphmonkey is essentially a function plotting tool. It is available in the Linux repositories. The program itself is very minimal in nature. It does not have the ability to export images etc. It is simply a graph sketching tool. There are no user guides, however, the program is very easy to figure out and it runs quite smoothly.
Kayali is a small program, easy to download and a very useful algebra calculation tool. It is able to easily evaluate most algebraic expressions and is very easy to use. Kayali is a Linux-based system.
SpaceTime is the most powerful cross-platform mathematics software ever developed for computers and mobile devices. With real-time graphing and MobileCAS® for computer algebra and calculus, SpaceTime is a revolution in scientific computing
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MATH2340
Algebra and Geometry
10 Units 2000 Level Course
Available in 2013
Callaghan Campus
Semester 1
Previously offered in 2009, 2008, 2007, 2006, 2005, 2004
A deeper understanding and experience in the formulation of well-reasoned mathematics is developed in this course. Topics in linear algebra and introductory analysis covered in the course will provide specific knowledge and skills for later studies in Mathematics.
The course supplements MATH1110/1120 to provide assumed knowledge equivalent to MATH1210/1220. The sequence MATH1110/1120/2340 is thus a pathway to all advanced mathematics courses offered at 2000 and 3000 level.
Objectives
At the completion of this course a student will have 1. an understanding of the role of formal processes and language in mathematics 2. experience in communicating convincing and reasoned mathematical arguments 3. skills and knowledge in linear algebra and introductory analysis
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It's not an easy to use CD. (I even can't maximize the windows!)If you're IE user, don't buy this. It requires Netscape and the version included in this CD is 4.0. Check your ISP whether you can use IE or Netscape before you use this CD.
Addison-Wesley Mathematics 1993 Teacher's Edition Grade 2
Editorial review
This is the Teacher's edition of the Grade 2 book
Activity Math: Using Manipulatives in the Classroom - Grades K-3
Editorial review
Activity Math: Using Manipulatives in the Classroom (Grades 4-6)
Reviewed by a reader
I would recommend this book for teachers who want a wealth of resources for teaching math in a meaningful way. It does not provide any problems or worksheets but instead gives you multiple ways to teach students math. I use it weekly. I u
Problem-Solving Experiences in Math, Grade 2
Editorial review
There's more than one way to solve a problem, and this invaluable resource shows students how to find the solution using multiple strategies and a systematic approach that works! Designed to supplement any math textbook, the Teacher Sourc
Linear Algebra: Application Study Guide
Reviewed by a reader
vendetta against Dr. David C. Lay considering he attended the school that Dr. Lay teaches at. John Cavalieri
Reviewed by a reader
beware,, this is addition #1 make sure you get the current edition. The current edition as of spring 99 is #2
Reviewed by a reader
While his poor textbook demands that this study guide be purchased through its own lack of thoroughness, Lay's Study Guide really doesn't help at all.
College Algebra (2nd Edition)
Editorial review
is text refers to the Paperback edition.
Reviewed by Tiger Chan, (Malaysia)
I am a Math teacher in Malaysia. I own Bittinger's "Elementaryand Intermediate Algebra" and also "Trigonometry". Judging fromthe books I am using as teaching materials, I can say that theBittinger's team has written some of the best Algeb
Shame on the authors for taking advantage of college students. This is extortion! I assume that the authors are college instructors. C'mon folks, we know you don't make that much money, but why take it out on the students? This book is an
Linear Algebra (3rd Edition)
Editorial review
Reviewed by a reader
After giving up on this book when I first learned Linear Algebra,it has turned out to be a very good reference book on the subject.If you need to, use Anton's book to learn the subject, but I keep this one on my shelf.
Reviewed by Bopape Lesiba Elias "leb25", (Ithaca, New York United States)
end of the book, so often times one has to always rely on the TA office hours to get a homework done. I do not recommend buying this text for a beginner in linear algebra, unless if it's required text for a course.
Reviewed by Nick Oostveen, (Vancouver, BC)
ng to explain it! If you are stuck with this book as a course text, I would highly recommend finding a second, more useful book if you wish to get more than a passing grade.
Reviewed by b. morrison, (PA.)
Having completed much of my Engineering curriculum (spending much time with my face in a math based text over the last few years) I have to say that this is the most useless textbook I have had to date. From a students perspective It is v
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How do structural engineers predict how much the Bay Bridge will
sway during an earthquake? How does the Federal Reserve analyze
stock market fluctuations to help determine when to cut interest
rates? What model do bio logists use to describe the rate of stem
cell growth in human embryos? The answer to all of these
questions involves mathematical objects called functions. The
study of functions is where calculus begins! We will mostly look at
functions which will be important to us in calculus namely,
polynomial, logarithmic and exponential functions.
One of the great accomplishments in modern mathematics is to
apply these functions to study real world situations. Calculus
teaches you how to use functions to study velocities and
accele rations of moving bodies, find the firing angle that gives a
cannon its greatest range, or calculate the area of irregular regions
in the plane. Calculus is a really fun subject because you will learn
to use powerful ideas that took centuries to develop. It is also a
really challenging subject because it requires solid algebra skills
and has thought provoking concepts.
Homework:
Problems will be as signed at the end of each class. It is important
for your success in the course that you attempt to do those
problems before the following class meeting. The struggle to solve
them prepares you for the following class.
You may discuss the homework by forming a group and studying
with your peers. If you need help please come to my office or go to
Sichel 105, the Academic Support and Achievement Program, and
ask for a tutor. Act fast and do not fall behind.
A completed homework assignment should be folded
lengthwise in half. On the outside front half, print your name,
the assignment number , the due date of the assignment, and
the time you spent doing the assignment. Please staple your
homework.
Attendance:
Attendance is required and roll will be taken at the
beginning of
each hour. If you are not in your seat when roll is taken, you may
be considered absent, so be on time. You are allowed to miss three
classes without affecting your grade. After your grade is dropped
one step (A- to B+, C+ to C, etc.). Thereafter, each two successive
absences your grade is dropped one step further. If there is a major
illness or incapacitation, speak to your instructor. SMC athletes are
excused to attend team commitments but are responsible for
notifying me ahead of time (see below).
Exams:
There will be three midterm examinations and a final exam.
Suppose a student receives the following grades.
First Midterm
Second Midterm
Third Midterm
Final Exam
Homework Grade
Then the lowest of the Midterm/Final Exam grades above is
dropped. If you miss a midterm exam that is the grade you drop.
The final grade for the course is the average of the remaining five
grades, in this example a B-. The Homework Grade cannot be
dropped.
Honor code:
Students are expected to abide by the SMC honor code when
taking exams and doing course work.
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Title
Patterns and Relationships
Body
Things are getting pretty exciting in mathematics! In addition to one step and two step equations. We are discovering the meaning of a function. This describes the relationship between to numbers and can be displayed in a chart, graph, and an equation. Please utilize the web links for math to practice these hot topics.
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Upcoming News
» Education
This article discusses about the latest version of openSIS, one of the most popular student information system round the globe. Recently OS4ED launched openSIS ver5.2, the developers of the product demands that this will be better, faster and more secured compared to previous versions.
A System of equations is basically a collection of Linear Equations and includes the same Set of the variables in each and every equation of the system. This system of equations is also known as the Linear System.
A number which is divided by itself and by 1 is called a prime number. Prime number can also be defined as the Odd Numbers which are not divided by any odd number except 1 and itself. Prime numbers are mainly 1, 2, 3, 5, 7, and 11 and so on.
Numbers starting with 1, 2, 3, 4.…… are called Natural Numbers. Natural numbers are denoted by 'N'. These numbers are put into different groups. The group may be of Even Numbers, odd numbers, prime numbers or even composite numbers.
When we deal with algebra, we mainly focus on equations and expression. These two terms can be defined as the heart of the algebra, as whenever we solve any problem we have to solve different equations.
The elements are subdivided into molecules which further divided into atoms. The atoms for long considered to be indivisible but with the discovery of the sub atomic particle, like electrons and protons, it was understood that there were more smallest and fundamental particles then the atom.
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Suggestions for Further Reading
The following are several books on assessment
which are not primarily concerned with assessment in
mathematics. However, they are worth reading, for they contain a
good number of assessment methods not discussed here, many
of which can be adapted to the mathematics classroom.
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First-order differential equations
This unit introduces the topic of differential equations. The subject is developed...During this unit you will:
learn some basic definitions and terminology associated with differential equations and their solutions;
be able to visualize the direction field associated with a first-order differential equation and be able to use a numerical method of solution known as Euler's method;
be able to use analytical methods of solution by direct integration; separation of variables; and the integrating factor method.
Contents
First-order differential equations
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Modern Algebra An Introduction
9780471433354
ISBN:
0471433357
Edition: 5 Pub Date: 2004 Publisher: John Wiley & Sons Inc
Summary: The author has written this book with two main goals in mind: to introduce the most important kinds of algebraic structures, and to help students improve their ability to understand and work with abstract ideas
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MAT
380
- Error-correcting Codes
Error-correcting codes play a hidden but central role in modern society, ensuring the accuracy of information stored in DVDs, hard drives and flash drives, and sent over cell phone, the internet and satellites among other digital technologies. A central problem in coding theory is devising a means to transmit information as correctly and efficiently as possible given the expected interference in channels such as wired and wireless networks. The modern-day discipline of coding theory began in 1948 when Claude Shannon proved, in a no constructive way, that there exist optimal codes that maximize both transmission rates and error-correction capabilities. Since then, theoretical mathematicians have been engaged in constructing and researching optimal codes. Topics in this pure math course include Shannon's Theorem on the existence of optimal codes, linear codes, double-error-correcting BCH codes, cyclic codes and Reed-Muller codes.
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could someone tell me more about these courses? I heard 155 is the most advanced of the two, but the course is actually easier than 150 because of teaching by real professors. I also heard 150 is rather tedious and assistants are less forgiving with grading and other stuff. I am a freshmen planning on pre-med or econ-major so which course would best serve my purpose?
take 155. its faster paced and go through more stuff but you get actual teachers so the tests are teacher specific instead of department wide. 150 you get ta's who if you do something right but not the way they would have done it they count it wrong.
I would say it depends on your major. If you're an engineer, your best bet would be to take 155a, because you'll be taking a lot more calculus afterwards. If you're pre-med or something else, and just have to take it for a math requirement, then I would take 150b.
The Vandy bookstore says that we need the Calculus Online Package by Stewart, 5th edition? What is included in the package? I already have the textbook from my sister, and I'm looking for a way not to pay the 180 something dollars!
I've heard such conflicting opinions on the 150/155 topic. I've heard on this board that 155 is more forgiving in terms of grading and that the professor makes your final exam as opposed to a common exam which you would receive for 150.
BUT then i went to saop and my advisor said i shouldn't go into 155 unless i'm premed/engineering/or really psyched about math. i'm none of those (i'm doing econ) but if it's easier to acheive a better grade, i'd be more than willing to take 155.
From what I've heard, the curve in 155 is way nicer than in 150. On the other hand, if you've done well in calc in high school, 150 should be easier since it has the people who either didn't take calc in high school or didn't do as well. The TAs really aren't bad (sometimes a little unforgiving, but generally nice), so don't let that scare you off. If you're engineering (or a math major), I would suggest taking 155. If you're premed, I don't think med schools will really care which one you take, as long as you're taking calculus.
Isn't it true that all the first year calculus courses (150a-b and 155a-b) use the same textbook? And the online bookstore isn't very helpful in describing the books in detail; is the textbook Single Variable Calculus (5e) by Stewart or Early Transcendentals Single Variable Calculus (5e) by Stewart? They both look really similar to me and I can't tell which one is used. The bookstore describes it as "Calculus Online Package" so is the CD required or something? I already have two used editions of these books but they don't have the CD.
I think the textbook is "Single Variable Calculus", 5th edition. This textbook is a two-part book (Single Variable and Multivariable, which is MATH 170 and 175), but if you buy from the Vanderbilt bookstore I think they only sell the combined edition and the multivariable edition, but not the single variable edition by itself. The ISBN for the combined 5th edition is 0-534-39339-X
so does anyone think that not taking 155 if i am premed is a bad thing? i'm starting with 150B because i have ap credit for 150A (not 155A), and i'm wondering if med schools will really look into this. i definitely want to apply to the more competitive med schools (including some ivies). i'm still in the high school mode of thinking in that colleges would rather see more advanced classes and a lower GPA than vice versa, but in terms of med school, i generally hear that a killer GPA and MCAT score are what really get your foot in the door. any knowledge on this subject would be great.
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CHOOSE YOUR PATH:
Mathematics
Calculus at Augustana
High school students who have already completed Calculus I and wish to continue their mathematical education by taking Calculus II can enroll at Augustana. Interested students can see additional details and contact Adam Heinitz to register.Click here to learn more.
Sioux Falls Area Math Teachers' Circle
Learn more about this teacher-led mathematical problem-solving experience for Sioux Falls area middle school teachers.
Wherever you are in your journey with mathematics, we have a place for you in the math department. We have courses to develop basic competence in mathematical reasoning and intermediate courses that provide the necessary support for a variety of majors. We also have a full course of study for students intending to become teachers, actuaries, researchers, or engineers — and for those who are preparing for graduate study in mathematics or related areas.
For those who elect to major in mathematics, you'll be welcomed to a department that works hard to tailor your course of study to your goals.
Math majors choose from various upper-division courses in topics as diverse as abstract algebra, topology, real analysis, and complex analysis. Courses in computer science and physics are required, and students can select other advanced courses based upon your interests, choosing from courses such as probability and statistics, discrete structures, and the history of mathematics. We can also help you design a faculty-guided independent study for a unique learning experience.
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A one year required course. This is a first year algebra course for ESL students which emphasizes important vocabulary and covers decimals, fractions, square roots and cube roots, polynomials, multiplying and factoring polynomials, sets, solving quadratic equations by factoring and iteration and basic geometry terminology.
A one year required pre-calculus course consisting of trigonometric functions, inverse trigonometric functions, trigonometric equations, trigonometric identities, right triangle trigonometry, law of cosines, law of sines, area of a triangle, polar coordinates and graphs, powers and roots of complex numbers, De Moivre's Theorem, sequences and series, introductory probability and statistics.
A one year and L'Hopital's rule.
A TI-84+ graphing calculator is required for the course.
Students are encouraged to take the Advanced Placement Calculus AB exam.
Text book: Calculus (Thomas, Finney; Addison Wesley; 12th ed.)
Math 4 - Advanced Geometry ( Lise 12 students; 5 periods per week )
A one year geometry elective which focuses on solving challenging problems. The student is expected to draw on material covered in all previous and current math courses. Students are expected to develop their abilities in analyzing and solving problems and be able to communicate clearly the steps taken to their solutions.
A one year elective designed for the student to do advanced work in probability and to get an introduction to the mathematics of descriptive and inferential statistics. It consists of probability theory, techniques of counting, numerical data, random variables, probability functions, Binomial and Normal distributions, sampling and estimation and confidence intervals.
A L'Hopital's rule,A one year calculus elective designed for students who have already passed Math 3 (AP Calculus AB) in Lise 11. This elective includes a review of the topics of Math 3 plusText book: Calculus (Thomas, Finney; Addison Wesley; 12th ed. )
Math 7 - Discrete Mathematics( Lise 12 students; 5 periods per week )
A mathematics elective consisting of mathematical induction, linear programming, map coloring, graph theory, biomathematics, matrices, linear algebra and the mathematics of social choice. Because of this diversity of topics, it is perhaps preferable to view discrete mathematics simply as the mathematics that is necessary for decision making in noncontinuous situations.
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Course Description:The course will include a review and strengthening of skills in linear and quadratic functions. Polynomial, exponential, and logarithmic functions will be discussed as well as topics in Matrix Algebra. There will be an introduction to trigonometric functions and the graphs of the sine and cosine curves. The course will conclude with a preview to counting principles and probability.
Pre-requisites: Successful completion of Algebra II & Trigonometry
Student Learning Outcomes: "Students will be able to…"
Solve linear equations and linear inequalities.
Solve quadratic functions by factoring, the quadratic formula, and a graphing calculator.
Multiply, divide and factor polynomial functions.
Solve exponential and logarithmic equations.
Use the definition of a function to solve inverse functions.
Understand matrix algebra and apply matrices to systems of equations.
Implement the use of technology such as a graphing calculator.
Methods of Assessment: Class lectures include question and answer discussions between instructor and students. Written homework assignments are given daily including a review the next class day. Students demonstrate their knowledge at the white board. Weekly exams/quizzes are given. Homework Notebook/folders are graded every interim and quarter.
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Mathematics Mission and Outcomes
MISSION
The mathematics department provides students opportunities to develop their mathematical appreciation, knowledge, skills and thinking in order to improve their quality of life and to aid in their preparation for future careers.
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Mathematics
"For the things of this world cannot be made known without a knowledge of mathematics. " – Roger Bacon, philosopher
Bacon also said that, "mathematics is the gate and key to the sciences." At St. George's, we believe the coalescence of math and science is necessary to create highly adept, numerically and scientifically literate students. An intentional and well-planned mathematics and science curriculum prepares St. George's students for an evolving and global world as well as for advanced study in college.
An integrated approach to the curriculum and its emphasis on technology seeks to combine mathematical concepts with concrete matters that are addressed in other areas of academic disciplines. High standards with regard to skill development and conceptual understanding are reinforced through project-based learning that encourages students to apply ideas in real-life settings. Through such integration the mathematical concepts being learned in the specific math classes are reinforced and enriched Students in Math 6—Honors delve deeper into topics than students in Math 6 through examining more applications and critical thinking exercises at a much faster pace The final trimester consists of students reading, analyzing, and writing about classic short stories, while honing their reading comprehension skills. Note: Same as course appearing in English section.
Pre-Algebra 7 prepares students for Algebra I and Geometry slope and y-intercept to graphs and linear expressions. In Pre-Algebra 7, visualization continues with consistent modeling of fractions, percents, mathematical operations, equations, probabilities, and algebraic expressions.
Honors Pre-Algebra prepares students for Algebra I and Geometry at a faster pace and in more depth rate of change, slope, and y-intercept to graphs and linear expressions. In Honors Pre-Algebra, visualization continues with consistent modeling of fractions, percents, mathematical operations, equations, probabilities, and algebraic expressions.
In Accelerated Algebra I, students begin learning how to use graphing calculators.
In Honors Honors Algebra I, students begin learning how to use graphing calculators. Students in Honors Algebra I delve deeper and cover topics more rapidly than students in Accelerated Algebra I Additionally, students are introduced to right triangle trigonometry and their applications in the real world. Honors students should expect a rapid pace and more in-depth coverage.
Algebra II focuses on the study of functions, their graphs, and their properties. Specific functions covered include linear, quadratic, exponential, and logarithmic. However, Algebra II also touches on a wide variety of other topics including, but not limited to, solving higher order equations and inequalities, conics, and polynomial and rational expressions. Students develop a clear understanding of the relationship between algebraic equations and their graphs. All work revolves around the process of solving a problem and the mathematical concepts rather than just "getting the answer." Problem solving through both traditional algebraic methods and graphical methods is an important component of the class.
While Algebra II Honors is a continuation of the concepts learned in Algebra I, this course will introduce the student to some of the theory behind those concepts. Honors Algebra II emphasizes the strong and integral relationship between functions and their graphs. Students will solve problems both algebraically and graphically using pencil and paper as well as a graphing calculator. Students will be asked to think beyond calculations and contemplate the roots and the derivations of the topics. Honors Algebra II is a preparatory course for PreCalculus, Advanced Algebra and Trigonometry, Statistics, and Calculus. To that end, this course covers a variety of topics such as linear and nonlinear functions, relations and systems; exponents and logarithms; conics; rational functions; radical functions. Problem solving strategies as well as how concepts are applied will be emphasized throughout the course.
This course is designed to strengthen students' understanding of concepts taught in Algebra II. Students will focus on a deeper study of functions—analyzing equations, graphs and real-world applications—and the introduction of trigonometry topics needed in advanced mathematics courses. Students will collaborate to construct and share knowledge, building their confidence in mathematics and preparing them for courses in high school and College Algebra or Precalculus at the college level.
This is a functions-based course that both reinforces and broadens concepts taught in Algebra II, and introduces new concepts, preparing students for calculus matrices, series & sequence, analytic geometry and introductory calculus.
This is a functions-based course that both reinforces and broadens concepts taught in Algebra II, and introduces new concepts, preparing the students for AP Calculus BC series & sequence, limits and derivatives. Students should expect more independent work and a faster-paced experience.
This course is divided into three sections, calculus, discrete topics, and statistics. Students will experience the concepts of derivatives and integration through applications in calculus. Discrete mathematics is an umbrella of mathematical topics. Topics include game theory and social theory, which use math to discuss human behavior and its effects. The third component, statistics, will be learned as a tool used in decision making. Students will learn to gather, analyze, interpret and report their findings in a systematic and mathematical manner.
AP Statistics is an introductory, non-calculus based college statistics course that emphasizes understanding and analyzing statistical studies. Students will explore the theory of probability, descriptions of statistical measurements, probability distributions, experimental design and statistical inference. Students will be analyzing samples and understanding populations on an ongoing basis. Graphing calculators are used throughout the course. All students enrolled in this course must take the AP exam in May.
AP Calculus AB is a college-level calculus course that is generally equivalent to a first semester college course: differentiation and integration of polynomial, trigonometric, and exponential functions. Calculators and computers are used to increase and strengthen the students' understanding of the concepts. All students enrolled in this course must take the AP exam in May.
AP Calculus BC is a college-level calculus course that is generally equivalent to the first two semesters of the college Calculus sequence all of the Calculus AB topics as well as additional topics, such as series and polar coordinates. Calculators and computers are used to increase and strengthen the students' understanding of the concepts. All students enrolled in this course must take the AP exam in May.
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Inhaltsangabe
1: Geometry in Regions of a Spaces. Basic Concepts. 2: The Theory of Surfaces. 3: Tensors: The Algebraic Theory. 4: The Differential Calculus of Tensors. 5: The Elements of the Calculus of Variations. 6: The Calculus of Variations in Several Dimensions.
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A new on-screen textbook using animations and Crocodile Mathematics models to explain concepts in a straightforward visual manner.
Students can experiment freely with relationships and transformations. Each unit has questions within the narrative, designed to check understanding of what has been covered and finishes with a summary and a set of test questions. It brings a revolutionary approach to geometry and algebra teaching, with students able to experiment with models.
Absorb Mathematics is written by Kadie Armstrong, a young author, mathematician and an expert in developing interactive online content. Her text gives a framework for the investigations and animations, making the courseware suitable either for self-study or revision, or for teaching in front of the whole class on a whiteboard or screen.
Absorb Courseware titles are collections of lesson sized units, each bringing together the best examples of computer-based learning.
Simulations, investigations, animations, videos and questions are wrapped in a narrative framework, with the aim of involving the student as much as possible.
The units can be used in a variety of ways. They are ideal for projecting on a whiteboard or screen, allowing you to take the whole class through new theory together. The interactive sections allow you to demonstrate concepts, while the investigations and questions give the ideal opportunity for class discussion. Alternatively, the structure allows for individual study - either as part of a computer-lab lesson, or to revise or catch up on missed workModels
Many of the units inAbsorb Mathematics include models created in Crocodile Mathematics. These allow free experimentation with shapes, numbers and vectors, in a mathematical environment Mathematics has 10Geometry Basics
Shapes and their Properties
The Triangle
Length, Area and Volume
Transformations
Trigonometry
The Circle
Algebra Basics
Numbers
Straight Lines, Graphs and Curves
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This is a transition course between lower divison mathematics and upper division mathematics. It involves critical thinking, creativity, and analytical reasoning. Lower divison mathematics consists mainly of repletion and memorization. Upper division mathematics is more abstract and involves proving theorems. This class serves as an introduction to various advanced topics in mathematics such as Geometery, Trigonometry, and Statistical Analysis.
Course:
Number:
Grade Level:
Prerequisites:
Credit:
Algebra 1, Part 1
3131
8, 9, 10, 11, 12
Math 8
1
Algebra 1, Part 1 provides students with the basic algebra skills necessary to move to a higher level mathematics course. This course was designed to eliminate or reduce math anxiety by teaching Algebra at a slower pace. Thus, it makes mathematics understandable and applicable to everyday life. The student will learn computation with rational numbers such as intergers, fractions, and decimals and solve application problems. The student will use applications with polynomials, equations, and inequalities.
Course:
Number:
Grade Level:
Prerequisites:
Credit:
Algebra I
3130
8, 9, 10, 11, 12
None
1
This course includes types of numbers, algebraic vocabulary, properties and operations of numbers, simplifying expressions, solving equations and inequalities, and graphing. Finding and using prime factors, square roots, repeating decimals, as well as using polynomials, rational expressions, and radicals are also part of this course. Mastery of graphing, solving equations with two variables, and solving quadratics is required.
Course:
Number:
Grade Level:
Prerequisites:
Credit:
Geometry
3143
9, 10, 11, 12
Algebra I
1
The geometry course is a one year mathematics course that includes both plan geometry and three-dimensional geometry. The course is considered necessary to demonstrate a reasonable knowledge of mathematics for students who plan to pursue a college education. Simple algebraic equations are integrated into the course and presented as a means of solving some geometry problems. Geometric proofs and problem solving develop analytical reasoning skills and improve the ability to apply logic to analysis of problems.
Course:
Number:
Grade Level:
Prerequisites:
Credit:
Algebra II
3135
10, 11, 12
Algebra I
1
Algebra II is mandatory for students seeking the Advanced Studies Diploma and for those students planning a higher education in math or science. Concepts of Algebra I are reviewed and strengthened. Emphasis will be placed on the study of complex numbers, coordinate geometry, linear systems, functions, conic sections, logarithms, and an indirection to progressions and series.
Course:
Number:
Grade Level:
Prerequisites:
Credit:
Advanced Algebra and Trigonometry
3161
11, 12
Algebra II
1
Advanced Algebra and Trigonometry is a course that includes an extensive and comprehensive treatment of trigonometry. The course includes algebra topics not covered in previous courses, such as analytical geometry; exponential and logarithmic functions; sequences and series; matrix algebra and determinants. The course is designed as preparation for math analysis or for freshman mathematics in college.
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Calculus III with Vector Fields
Teaching
Fall 2011
Spring 2012
Fall 2012
Spring 2013
Meta
Research
Lectures
Divergence Theorem, II
Friday,
Apr 20,
2012
Problems
16.9: 17, 18, 19, 22
Divergence Theorem, I
Thursday,
Apr 19,
2012
Also called Gauss's theorem. The divergence theorem connects the flux across a closed surface to the divergence of the vector field on the enclosed region. We begin by re-doing some of our earlier surface integrals using the divergence theorem
Problems
16.9: 1, 5, 7, 11, 12, 13
Stokes' Theorem, II
Wednesday,
Apr 18,
2012
A couple more examples of Stokes' theorem.
Problems
16.8: 17, 18, 19, 22
Stokes' Theorem, I
Monday,
Apr 16,
2012
Stokes' theorem is a generalization of Green's theorem to 3 dimensions.
Problems
16.8: 1,2,3,5,9
Surface integrals, III
Friday,
Apr 13,
2012
More examples.
Problems
16.7: 27, 31, 45, 47, 49
Surface integrals, II
Thursday,
Apr 12,
2012
Some more examples and the surface area
Problems
16.7: 23, 25, 28, 29
Surface integrals, I
Wednesday,
Apr 11,
2012
Restate the definition of the surface integral and work a couple of examples.
Problems
16.7: 7,9,15,19,40
EXAM 3
Monday,
Apr 09,
2012
16.1 -- 16.5, need to know the definition of conservative field, vector field, incompressible flow, irrotational flow. Need to know the statements of Green's theorem in both forms and to understand the terms simple, closed, postively oriented for curves
Flux, surface integral definition
Friday,
Apr 06,
2012
We look at the notion of flux and use it to motivate the defintion of a surface integral. We then set about giving a computational method for evaluating surface integrals over parameterized surfaces. Next time we will do a bunch of computation
Surfaces
Thursday,
Apr 05,
2012
We will parametrize some simple surfaces. This is the 2d analogue of a parametrized curve. Tomorrow we will talk about surface integrals and their relation to the flux of a vector field
Problems
16.6: 3, 13, 19, 21, 23, 24, 26, 25, 33, 37, 41, 44, 45, 48
Curl and Divergence and a digression about Navier Stokes.
Wednesday,
Apr 04,
2012
The velocity field of a fluid is called incompressible if the divergence is 0. It is called irrotational if the curl is 0.
Curl and Divergence
Monday,
Apr 02,
2012
The divergence of a vector field measures it's rate of expansion, while the curl measures its rotation. We defined these two operations on vector fields, and the way that the curl can be used to check whether a field is conservative. Next time we will look at the relation between curl and divergence and the start on surface integrals.
Problems
1, 5, 7, 9, 11, 12, 14, 15, 17, 21, 22
Green's Theorem version II
Friday,
Mar 30,
2012
The second version of Green's theorem related the line integral of the vector field and the outward normal to a certain double integral over the enclosed region. This is the divergence-flux version of the theorem. Next time we will define curl, divergence and write Green's theorem in the most elegant way
Problems
page 1089: 13, 17, 18, 19
Green's Theorem version I
Thursday,
Mar 29,
2012
Green's theorem relates the line integral of a vector field F along a closed curve to a certain double integral over the enclosed region. Today we look at the first form of Green's theorem, which we can call the *work version*, or tangential version.
Problems
page 1089: 1, 5, 6, 9, 11
Conservation vector fields
Wednesday,
Mar 28,
2012
We give a partial converse to the test for conservative vector fields and discuss simply-connected regions
Fundamental theorem of line integrals, III
Monday,
Mar 26,
2012
Basic tests for conservative fields. Some examples of non-conservative fields and the notion of simple connectivity.
Problems
page 1082: 11, 13, 19, 23, 24, 25, 36
Fundamental theorem of line integrals, II
Friday,
Mar 23,
2012
Examples of conservative fields and computations using the fundamental theorem.
Problems
page 1082: 1, 2, 3, 5, 7, 9, 15, 30
Fundamental theorem of line integrals
Thursday,
Mar 22,
2012
Conservative vector fields play a significant role in physical applications. The computation of line integrals for such fields is simplified and depends only on the endpoints of the path and the potential function.
Problems
page 1082: 29, 31, 33, 35
Line integrals of vector fields, II
Wednesday,
Mar 21,
2012
More examples
Problems
32(a), 33, 41, 42, 49, 50, 51, 52
Line integrals of vector fields, I
Monday,
Mar 19,
2012
Line integrals of vector fields allow us to compute the work done by a force field in moving a particle along a given path.
Problems
5, 13, 15, 17, 19, 29
Vector fields, II
Friday,
Mar 09,
2012
More examples, conservative fields, and streamlines
Vector Fields
Thursday,
Mar 08,
2012
We will now move on to the subject vector fields. This is the main focus of our course and we will spend the rest of the semester discussin vector fields. Today we will discuss examples and tomorrow we will consider the notion of a streamline from fluid dynamics.
Problems
page 1061: 1, 5, 11, 13, 15, 18, 22, 26, 29, 34, 35, 36
Exam 1
Wednesday,
Mar 07,
2012
Double and triple integrals. There will be one problem from each of the following sections: 15.3, 4, 6, 7, 8, 9.
Review for Exam I
Monday,
Mar 05,
2012
Review for exam I and practice integrals
Triple integrals in spherical coordinates
Friday,
Mar 02,
2012
Examples of triple integrals in spherical coordinates
Triple integrals in cylindrical coordinates
Thursday,
Mar 01,
2012
Examples of triple integrals in cylindrical coordinates
Triple integrals in cartesian coordinates
Wednesday,
Feb 29,
2012
Examples of triple integrals in cartesian/rectangular coordinates
Triple integrals
Monday,
Feb 27,
2012
Introduction to triple integrals
Problems
page 1025: 9, 14, 15, 18, 19, 23, 33, 41, 42, 54
Reminders
Do the first two webassigns on triple integrals
Cylindrical and Spherical coordinates
Friday,
Feb 24,
2012
Reminders
Read the definition of cylindrical and spherical coordinates in chapter 15.8 and 15.9
Double integrals in polar coordinates (15.4)
Thursday,
Feb 23,
2012
Reminders
Webassign on this topic is due 2/24 **Change in date**
quiz 5 is tomorrow
Double integrals in polar coordinates (15.4)
Wednesday,
Feb 22,
2012
Problems
page 1002: 23, 24, 30, 31, 36
Reminders
Webassign on this topic is due 2/24 **Change in date**
Double integrals in polar coordinates (chapter 10.3 and 15.4)
Friday,
Feb 17,
2012
Problems
page 662: 7,9,17,22,25; page 1002: 1,5,9,11,17,22,25
Reminders
Webassign on this topic is due 2/22
Read the derivation of $r dr d\theta$ in 15.4. We will talk about this on Wednesday.
Double integrals over general regions (chapter 15.3)
Thursday,
Feb 16,
2012
Problems
page 995 : 30, 47, 49, 51, 60, 63, 67
Reminders
Webassign on this topic is due 2/21
Double integrals over general regions (chapter 15.3)
Wednesday,
Feb 15,
2012
Problems
page 995 : 3, 5, 9, 21, 22, 26, 27
Reminders
Webassign on this topic is due 2/21
Quiz coming up on Friday 2/17
Iterated integrals (chapter 15.2)
Monday,
Feb 13 2/15
Iterated integrals (chapter 15.2)
Friday,
Feb 10
Double integrals over rectangles (chapter 15.1)
Thursday,
Feb 09,
2012
Problems
p.981: 5,6,9,12,13
Reminders
Webassign on this topic is due 2/14
Quiz coming up
Exam 1
Wednesday,
Feb 08,
2012
Review day
Monday,
Feb 06,
2012
Review for the exam 1
Reminders
Exam 1 is coming up
Maxima and minima
Friday,
Feb 03,
2012
We will look at the test for determining the location of local maxima and minima.
Problems
Directional derivatives and the gradient
Today we discover the connection between the directional derivative and the gradient.
Problems
p.943: 1,9,11,17,20,21,33,34
Partial derivatives and the gradient
Wednesday,
Jan 25,
2012
Today we will look at the gradient of a function of two variables.
Level curves and partial derivatives
Monday,
Jan 23,
2012
Level curves, or contour plot, provide a lot of information about a function of two-variables. Some approximations can be made from the level curves. In particular it is possible to tell whether a function is increasing or decreasing in a particular direction. We also talked about the notion of a partial derivative. Tomorrow we will talk more about this topic and do some calculations.
Problems
page 911: 3,10,11,15,19,31,33,39,53
Reminders
If you haven't passed the gateway you should come by during EI to take it again
Quiz thursday on arc-length and line integrals of scalar functions
Multivariable functions
Friday,
Jan 20,
2012
In calc I, II we've encountered functions whose domains are subsets of the real numbers. The codomains are also generally subsets of the real numbers. Parametrized curves introduce the possibility that the codomain can be two- or three-dimensional.
In calculus III we will deal with functions of several variables
Problems
page 888: 1,2,9,13,15,25,29,35,36,37,53,54
Motion in space
Thursday,
Jan 19,
2012
Continuing the projectile motion calculations form yesterdayMotion in space
Wednesday,
Jan 18,
2012
We will define, position, speed, velocity and acceleration. We will then use calculus to derive Newton's laws of motion and examine the motion of a projectile.WebAssign homework is due tonight
Line integrals of scalar-valued functions
Friday,
Jan 13,
2012
The line integral of a scalar-valued function allows, for example, to compute the mass of a wire of non-uniform density. The formula requires that we integrate with respect to the arc-length s. The parametrization of a curve in terms of its arc-length is intrinsic. In general every curve has infinitely many parametrizations.
Problems
p.1072: 3,9,10
Gateway quiz. Arc-length.
Thursday,
Jan 12,
2012
We talked about arc-length, distance traveled and speed.
Problems
p.860: 1,2,12,65
Review of calculus II: vectors
Wednesday,
Jan 11,
2012
Review vectors: length, dot and cross product, angles.
Problems
p.846: 17; p.852: 5
Reminders
There will be a gateway quiz tomorrow. **No calculators**. You must score a 90% to pass. Topics: basic differentation, integration, vectors, planes, parametric curves
Review of calculus II: differentiation and integration
Tuesday,
Jan 10,
2012
Today we will review basic differentiation and integration really quick. There will be a quiz on Thursday.
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(Previously MATH-088) Beginning algebra specifically designed for students with no algebra background. Topics include introduction to variables and signed numbers, solutions to linear equations and inequalities, simplification of algebraic expressions, evaluation and manipulation of formulas, an emphasis on word problems and graphing of linear equations. Scientific calculator required.
Prerequisite: MATH 075 with a minimum grade of C- or assessment above MATH 075 and ENGL/ 085 with a minimum grade of C (may be taken concurrently) or assessment above ENGL/ 085.
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Normal 0 false false false KEY BENEFIT: Ratti and McWaters write at a level that professors want and in a way that will engage students. Included are relevant and interesting applications; clear, helpful examples; and lots and lots of exercisesall the tools that you and your students need to succeed. KEY TOPICS: Trigonometric Functions; Right Triangle Trigonometry; Radian Measure and Circular Functions; Graphs of the Circular Functions; Trigonometric Identities; Inverse Functions and Trigonometric Equations; Applications of Trigonometric Functi... MOREons; Vectors; Polar Coordinates and Complex Numbers MARKET: For all readers interested in trigonometry. Ratti and McWaters teach the way you teach. Included are relevant and interesting applications; clear, helpful examples; and lots and lots of exercisesall the tools that you and your students need to succeed.
KEY BENEFIT: Ratti and McWaters have combined years of lecture notes and firsthand experience with students to bring professors a text series that teaches at the same level and in the style that they do. An extensive array of exercises and learning aids further complements your instruction in class and during office hours.
J.S.Ratti has been teaching mathematics at all levels for over 35 years. He is currently a full professor of mathematics and director of the "Center for Mathematical Services" at the University of South Florida. Professor Ratti is the author of numerous research papers in analysis, graph theory, and probability. He has won several awards for excellence in undergraduate teaching at University of South Florida and known as the coauthor of a successful finite mathematics textbook.
Marcus McWaters is currently the chair of the Mathematics Department at the University of South Florida, a position he has held for the last eight years. Since receiving his PhD in mathematics from the University of Florida, he has taught all levels of undergraduate and graduate courses, with class sizes ranging from 3 to 250. As chair, he has worked intensively to structure a course delivery system for lower level courses that would improve the low retention rate these courses experience across the country. When not involved with mathematics or administrative activity, he enjoys playing racquetball, spending time with his two daughters, and traveling the world with his wife.
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Find an Online Course
Math
Students who take the best math online courses can expect to gain knowledge in areas including algebra, analysis, geometry, number theory and statistical mathematics. Online classes for math will also facilitate the acquisition of various skills including logical thinking, oral and written communication, computer programming, data analysis and problem solving.
Online Math Classes
Students who earn an online degree in math can expect to gain knowledge in areas including algebra, analysis, geometry, number theory, and statistical mathematics. Online classes for math will also facilitate the acquisition of various skills including logical thinking, oral and written communication, computer programming, data analysis, and problem solving.
Online Math Classes
Mathematics is the systematic study of quantity, structure, space, and change. Students who study the subject are often interested in careers that require a lot of quantitative research, problem solving using mathematical equations, and evaluation of data.
Knowledge Gained
Online courses will teach students a variety of subjects in the field, including:
Algebra
Students will study algebraic laws that govern numbers, polynomials, matrices, and permutations. Other areas of study include solving first-degree equations, writing and graphing linear equations, solving linear inequalities and quadratics, working with radicals, as well as exploring relations and functions.
Analysis
Online courses in analysis give students the opportunity to learn about continuously changing quantities that form the basis of calculus. Emphasis is placed on integral calculus, which focuses on the measurement of lengths, areas, volumes, and other quantities as limits, as well as differential calculus, which involves derivatives.
Geometry
Courses in geometry teach students about shapes and configurations and emphasize the use of inductive and deductive reasoning. Students study points, segments, triangles, polygons, circles, and solid figures and learn to classify spaces in various mathematical concepts.
Number Theory
Courses in number theory teach students about properties of integers and rational numbers. Students learn about unique factorization and the Greatest Common Divisor (GCD), quadratic residues, number-theoretic functions, and the distribution of primes, sums of squares, the Euclidean algorithm, and congruence equations.
Statistical Mathematics
Courses in statistics teach probability and the theory of sampling. Students are exposed to frequency and probability distributions, regression and correlation, analysis of variance and covariance, and bivariate distributions.
Skills Developed
Math classes help students develop valuable skills in the following areas:
Logical Thinking
Students will develop the skills to think clearly and use reasoning to solve problems. As students become more proficient in logic, they will be able to find their solutions through pattern recognition.
Oral and Written Communication
Students will learn how to write up statistical reports as well as present their findings to their peers in presentations and written papers.
Computer Programming
Students will develop a proficiency in computer programming so that they can write clean and modular source codes. Classes will train students to address fundamental issues involved in the creation of new algorithms as well as develop applications for computer graphics.
Data Analysis
Students can expect to build their skills by investigating the different ways to organize and represent data and describe and analyze variation in the data. Through practical examples, students will also learn about the concepts of association between two variables, probability, random sampling, and estimation.
Problem Solving
Students will develop analytical thinking skills, quantitative reasoning skills, and an ability to excel in a problem-solving environment. Working with large quantities of data, students will learn how to design and conduct experiments, formulate theories, and apply them to solve problems.
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7.EE.3-7.EE.4.b
Solve Real-Life And Mathematical Problems Using Numerical And Algebraic Expressions And Equations problems will willFor four days, the teacher will demonstrate inequality concepts through videos, games, virtual manipulatives, whole-class demonstrations, and small group practice. Students will then review the concepts learned in class through videos, games, and individual practice problems assigned to be done at h... or
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Trigonometry: Functions and Applications
Book Description: 'Trigonometry: Functions and Applications' is designed for a two-quarter course at the highs school or college level. This approach imparts theory and applications in a realistic way. Students must 1) Define the function 2) Draw a representative graph 3) Figure out properties of the class of function 4) Use that kind of function as a mathematical model. Therefore, rather than simply seeing graphs of periodic phenomena, the students are expected to draw the graphs themselves. Then they must write equations for the graphs, and use the equations to make predictions and interpretations about the real-world situation they are modeling. The materials are designed to interface well with algebra studied form the functions standpoint. However, since many students have studied algebra from more traditional texts, it has not been assumed that the students have used this approach before the present trigonometry course. It is assumed that the students have studied geometry, and at least on3 semester of high school second year algebra.
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Shows science, math, and engineering students and professionals how to make the most of this top-of-the-line graphing calculator Describes step by step how to harness the calculator's 3D ... > read more
This project-based guide from Adobe will teach readers all they need to know to create engaging interactive content with Flash CS3. Using step-by-step instructions with projects that build on the
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This course enables students to develop an understanding of mathematical concepts related to introductory algebra, proportional reasoning, and measurement and geometry through investigation, the effective use of technology, and hands-on activities. Students will investigate real-life examples to develop various representations of linear relations, and will determine the connections between the representations. They will also explore certain relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.
Strands and Subgroups in the MFM1P Grade 9 Foundations of Mathematics, Applied Course
Number Sense and Algebra
Solving Problems Involving Proportional Reasoning
Simplifying Expressions and Solving Equations
Linear Relations
Using Data Management to Investigate Relationships
Determining Characteristics of Linear Relations
Investigating Constant Rate of Change
Connecting Various Representations of Linear Relations and Solving Problems Using the Representations
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Post navigation
GeoGebra
GeoGebra is software for interactive geometry. Astonishingly is it free, astonishing as it is such of such high quality and is so well supported. There are many resources available on the Internet. I have created a Diigo list of resources which includes many examples and tutorials.
(Click on the green links for each item, then back on your browser if you wish to return to the list.)
Post navigation
One comment on "GeoGebra"
First I have to express my admiration for your maths energy!! Fantastic resources right and left!!
Have you heard of Mangahigh.com?? It is a new site and I would love to get your feedback on it!!
Looking forward to hearing from you…
Mangahigh.com is a games-based learning site focusing on math.
Mangahigh has developed the first curriculum-compliant maths games, and features commercial-quality gameplay, rewarding students with achievements that celebrate their progress. Through gameplay, Mangahigh aims to provoke students to explore sophisticated math concepts and reinforce skills through repetition. The games are supported by Prodigi, the world's first adaptive math learning engine. Mangahigh.com is endorsed by well-known mathematician and Oxford Professor, Marcus du Sautoy.
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Mathematics Department
Note: Loyola requires all students to take Algebra I, Geometry, and Algebra II and strongly encourages all students to take a fourth year of math.
Algebra I and Honors Algebra I are comprehensive courses that prepare students to use algebraic skills and concepts confidently in mathematics, in related disciplines, and in real world situations. Examples of topics covered are integers and rational numbers, equations, inequalities, exponents and polynomials, factoring, graphing linear equations, systems of equations, rational expressions, and radical expressions. Problem solving is emphasized throughout all of these topics. Graphing calculators are used as teaching and learning tools throughout the course.
Geometry and Honors Geometry use investigative and inductive introductory methods and then follow with programs based on traditional theorems and postulates. Computers are used as an aid in the development of the theorems and postulates. Students first learn the language of geometry and then apply this language to such topics as congruency, similar triangles, parallelism, circles, polygons, area, volume, constructions and basic trigonometry.
Algebra II and Honors Algebra II prepare students to use advanced algebra skills and concepts. Through classroom lectures, applications, assignments, and assessment, students will develop critical thinking skills and strategies necessary for problem solving. Also, students will learn to use the TI-83/TI 84 graphing calculator.
Since no student should take a year off from math, especially the year prior to college, Loyola offers several electives with varying levels of difficulty for the fourth year of math.
Pre-Calculus is an alternative to the Honors Pre-Calculus course. The course content mirrors the topics of the Honors Pre-Calculus course; however, the students set the contents' pace and depth. This course prepares students for college math courses that most non-science/math majors must take and is a prerequisite to Calculus.
Calculus is offered for those students who do not wish to deal with the rigors of the AP Calculus courses, described below.
Advanced Placement (AP) Calculus (AB) and (BC) are first and second semester college calculus courses. The College Board dictates the curriculum for each course. Students may receive college credit depending on the AP exam score and policies of the student's college choice. AP Calculus students must be mathematically able - good math scores on the PSAT, high grades in previous math courses, and the recommendation of the student's math teachers. All students are required to take the national exam in the spring
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Hastings, Scottsbluff, Ainsworth Dates: multipleThis course will help you align your teaching with the new Nebraska standards and the new Common Core standards in mathematics by focusing on the development of "habits of mind of a mathematical thinker". The approach is to understand arithmetic (number) and (introductory) algebra as a means of communicating mathematical ideas, and will stress a deep understanding of the basic operations of arithmetic, as well as the interconnected nature of arithmetic, algebra and geometry relating to the grades 3-7 curriculum.
Audience:K123456789101112 Credit Hours: 3 Locations: Holdrege, North Platte, Lincoln Dates: multipleThis course is designed to help teachers gain a deep understanding of the concept of function and the algebra and geometry concepts taught in the middle-level (through early high school) curriculum. Studying this content at a deeper level will help teachers better prepare their students for the NeSA-M. Participants also will study measurement with an emphasis on length, area and volume. Functions, Algebra and Geometry is the second course in the Math in the Middle curriculum and has been successfully taught to both elementary and high school teachers Location: Omaha Dates: June 18-22, 8am - 5pmDevelops a fundamental understanding of the key mathematical ideas of calculus in order to broaden teachers' mathematical perspective and gain insight into concepts contained in the middle-level curriculum which are related and foundational to the development of calculus. Topics include limits, differentiation, integration, applications and the Fundamental Theorem of Calculus July 16-20, 8am - 5pmThe new Nebraska state and Common Core standards for mathematics are based largely on learning progressions. Thus, the aim of this course is to familiarize elementary teachers with mathematical learning progressions by utilizing a set of frameworks developed to provide teachers with a way to analyze student thinking and respond with instruction that guides students through the "next steps" needed to advance and deepen understanding field
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Linear Algebra With Applications
9780023698316
ISBN:
0023698314
Publisher: Prentice Hall PTR
Summary: Renowned for its thoroughness, clarity, and accessibility, this best-selling book by one of today's leading figures in linear algebra reform offers users a challenging yet enjoyable treatment of linear algebra that is infused with an abundance of applications and worked examples. Balancing coverage of mathematical theory and applied topics, the book stresses the important role geometry and visualization play in under...standing the subject, and now comes with the new ancillary ATLAS computer exercise guide.Provides modern and comprehensive coverage of the subject, spanning all topics in the core syllabus recommended by the NSF sponsored Linear Algebra Curriculum Study Group. Offers new applications in astronomy and statistics, emphasizes the use of geometry to visualize linear algebra and aid in understanding all of the major topics, and previews some of the more difficult vector space concepts early on. MATLAB computing exercises provide users with experience performing matrix computations
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Video List
Differential Equations is a vast and incredibly fascinating topic that uses calculus extensively. Although the name does not have the word 'calculus' in it, differential equations is a natural extension and application of calculus. So it is thoroughly covered on this site including discussion, videos and practice problems. This page gets you started on Ordinary Differential Equations usually covered in a first semester differential equations course. If you are looking for more detail on a specific differential equations topic, you can select a topic from the drop-down menu above or open this next panel of topic links for more targeted links to topics, videos and practice problems.
Differential Equations Topic Links
Differential Equations Topic Links
As mentioned above, this page gives an introduction to differential equations.
Here are the links to in-depth details on differential equations topics, videos and practice problems on other pages.
Differential Equations is a group of topics to teach you to solve equations that contain derivatives. That's it. That's all there is to it. The complexity happens because you can't just integrate the equation to solve it. First, you need to classify what kind of differential equation it is based on several criteria. Then, you can choose a technique to solve. Learning to solve differential equations involves learning to classify the equation you are given and then learning the technique to solve that specific type of equation. There is generally no technique that works in all cases. So, to prepare yourself, spend some extra effort learning to classify the kind of equation you have as you learn each technique. If you don't, you will be totally lost.
There are a lot of shortcuts to solving differential equations. Many instructors teach those shortcuts upfront precisely because they are easier. However, don't let yourself lose sight of where those shortcuts come from and under what conditions you can use them. Spend some time learning the basic technique before using the shortcuts. This usually involves working the first few practice problems with the basic technique. Of course, the instructions your teacher gives you take priority. But really learn these techniques, so that you will know the proper time and situation to use them. After all, that's the point, right? To be able to use this material in your job or other courses?
Notation
Notation
Constants and Variables
One of the first things you need to get your head around with differential equations is which symbols are constants and which are variables. When you see derivative notation you will mostly see \(y'\) instead of \( dy/dt \), for example. So you need to keep track of which symbols are functions, which are variables, what you are taking the derivative with respect to and what are constants.
For example, one equation I ran across in the first section of a differential equations textbook was
\(\displaystyle{ m\frac{dv}{dt} = mg-\gamma v }\)
This could have been written \(\displaystyle{ mv' = mg-\gamma v }\)
In this case, the variable is \(t\) and the function is \(v(t)\). The symbols \(m, g, \gamma\) are constants. The context of the problem is important to read and understand in order to arrive at these conclusions.
exp Notation
A second thing you need to be aware of is that some textbooks (most of the ones I've seen) use unusual notation for exponential functions. Correct notation is \( y = e^x \). However, sometimes the exponent can be very long and contain a lot of detail. So, the exponential function will sometimes be written as \( y = exp(x) \). This is only used when the exponent \(x\) is detailed. For example,
\(\displaystyle{ \mu(t) = e^{ \int_{t_0}^{t}{p(s)~ds} } }\) is difficult to read. Since there is so much detail in the exponent of \(e\) that we need to see, we usually write this
\(\displaystyle{ \mu(t) = exp\left( \int_{t_0}^{t}{p(s)~ds} \right) }\)
See how much easier the exponent is to read?
We will follow this convention on this site.
Notation For Derivatives
By now you should be comfortable with the notation \(dy/dx\) and \(y'\) for the first derivative. There are a couple of other types of notation that you may or may not have seen before, that you will probably run across on this site, in your textbook, in class and in videos.
\(D_x(y)\) where \(D\) tells you take the derivative and the subscript \(x\) is the variable of integration.
\(\dot{y}\) where the dot above the \(y\) tells you to take the first derivative.
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Some Definitions Used To Classify Differential Equations
Order
Order
Order indicates the highest derivative appearing in the differential equation. For example,
\( y' - y = 0 ~\) is a first order differential equation because the highest derivative is a first derivative. Similarly, \( y'' - y = 0 \) is a second order differential equation because the highest derivative is a second derivative.
Linear
Linear
A differential equation of the form
\(P(t) y'' + Q(t)y' + R(t)y = G(t) \)
is linear since \(P(t)\), \(Q(t)\) and \(R(t)\) are functions of \(t\) only, i.e. they do not contain any \(y\)'s or derivatives of \(y\). Analyzing nonlinear equations is relatively difficult, so it is unlikely you will encounter them in a first semester differential equations course, except under very special circumstances.
Homogeneous
Homogeneous
There are several meanings of the term 'homogeneous' used in differential equations. For this definition, assume you have a differential equation of the form \( p(t)y'' + q(t)y' + r(t)y = g(t) \).
Meaning 1 - - If \( g(t) = 0 \) in the above form, then the differential equation is said to be homogeneous. The idea is to get all the terms containing \(y\) or a derivative of \(y\) to one side of the equal sign and all other terms to the other side. If there are no terms without a \(y\) or it's derivatives, then \(g(t)\) will be zero and the equation will be homogeneous. If \(g(t) \neq 0 \), then the differential equation is said to be inhomogeneous (or nonhomogeneous). Meaning 2 - - If all of the expressions \(p(t)\), \(q(t)\), \(r(t)\) and \(g(t)\) can be written as functions of \(y/t\), then it is said to be homogeneous. In this case, we use the technique of substitution to solve this type of differential equation.
Getting Started with Differential Equations
After going through the above information you are ready to watch some videos to get started on differential equations.
Video 1 - - Here is a good introduction to differential equations. He contrasts a differential equation to a standard equation, which you should be familiar with and explains, practically, what a differential equation is.
open videoclose video
In this video, he works the example
\( y'' + 2y' - 3y = 0 \) and shows that \( y_1 = e^{-3x} \) and \( y_2 = e^x \) are solutions to this differential equation.
Then, he goes on to explain linear versus nonlinear and order.
Video 2 - - Here is another introduction video. The technique he uses is separation of variables, which is the first technique usually introduced in a differential equations course. It will help you to see this technique in the context of introducing differential equations.
open videoclose video
Video 3 - - Here is a good video showing what it means for an equation to be a solution to a differential equation. This also demonstrates how to check your answer after you have solved a differential equation.
open videoclose video
Next - - Now that you have an overview of differential equations, you are ready to begin studying specific topics. The next natural topic is slope fields. However, many instructors will go straight into separation of variables. You can also choose your own next topic by selecting from the list of topics from the menu at the top of the page. In any case, take some time to enjoy studying differential equations.
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Differential Equations Resources
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faq: What is the difference between a general solution and the particular solution?
What is the difference between a general solution and the particular solution?
Short Answer: The presence (general solution) or absence (particular solution) of an unknown constant.
Long Answer:
When you solve a differential equation, you use integration, which introduces an unknown constant.
In a general solution, the unknown constant remains and you do not have enough information to be able to determine what that constant is. Consequently, you have an infinite number of solutions.
In the particular solution, you start out by solving for the general solution but then you are given initial conditions which you use to determine the value of the constant. These initial conditions are actually points that the solution to the differential equation pass through. In the end, you have only one solution without any unknown constants.
Notice that we say a general solution but we talk about the particular solution.
general solution
particular solution
infinite number of solutions
only one solution
contains unknown constant(s)
does NOT contain any unknown constants
no initial conditions given
initial conditions given; used to solve for constants
To find a general solution, just solve the differential equation and leave any constants in your final answer. To find the particular solution, find the general solution first, then plug in the initial conditions and solve for the constants.
Notes
1. When determining the particular solution, you will be given the same number of initial conditions as the order of the differential equation. Depending on how the initial conditions are given, you may need to stop after each integration and solve for the individual constants or you may need to wait until you are completely done and solve for all the constants at once.
2. When you were first learning integration, you probably ran across initial value problems. These were actually differential equations where you were asked to find the particular solution.
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