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...Algebra 2/3 develops advanced algebra skills such as systems of equations, advanced polynomials, imaginery and complex numbers, quadratics, and concepts and includes the study of trigonometric functions,logarithmic and exponential equations, and introduces matrices and their properties. Areas to...
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Harwood Heights GeometryIt goes further by establishing efficient methodologies for solving systems of equations which can be done by hand using pencil and paper (for small systems) or which can be readily automated and executed on computers and calculators. The main objective is finding values of variables satisfying
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Mathematics: A Practical Odyssey - 7th edition
Summary: MATHEMATICS: A PRACTICAL ODYSSEY, 7E demonstrates mathematics' usefulness and relevance to students' daily lives through topics such as calculating interest and understanding voting systems. Well known for its clear writing and unique variety of topics, the text emphasizes problem-solving skills, practical applications, and the history of mathematics, and unveils the relevance of mathematics and its human aspect to students
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Mathematics provides mathematically sound and comprehensive coverage of the topics considered essential in a basic college math course. The Aufmann Interactive Method ensures that students master concepts by actively practicing them as they are introduced. This approach is ideal for traditional and returning students in both classroom and distance-learning environments.For the Sixth Edition, topics from geometry have been integrated into the text, using verbal explanations. In addition, coverage of simple interest (Chapter 6) has been expanded.The Aufmann Interactive Method helps students learn and understand math concepts by doing the math. Every objective contains one or more sets of matched-pair examples. Students first walk through a worked-out example and then solve a similar "You Try It" example. Complete solutions to these examples are available in an appendix.An Integrated Learning System organized by objectives helps students understand what they're learning and why as they apply new concepts throughout the chapter. Each chapter begins with a list of goals that form the framework for a complete learning system. These objectives are woven throughout the text, in Exercises, Chapter Tests, Cumulative Reviews, as well as the print and multimedia ancillaries.An Instructor's Annotated Edition provides reduced pages from the Student Edition to leave space for the following features: Instructor Notes; In-Class Examples; Concept Checks; Discuss the Concepts; Special presentation of new Vocabulary/ Symbols/Formulas/Rules/Properties/Equations; Special review of these same features; Optional Student Activities; Quick Quizzes; Answers to Writing Exercises; Suggested Assignments; and Answers to all exercises.AIM for Success, a special student preface, offers techniques and support for student success.Prep Tests at the beginning of each chapter assess students' prerequisite skills. Students may check answers in an appendix, which refers them back to a previous objective for review, if necessary.Go Figure challenge problems follow the Prep Test to engage students in problem solving.Updated data problems, designed to show students the relevance of mathematics across the disciplines and in daily life, reflect current data and trends.Additional and revised Projects and Group Activities enable students to see the connections between abstract concepts and real-life situations.Strong emphasis on applications demonstrates the value of mathematics as a real-life tool. Chapter openers have been updated with new photos and captions illustrating a specific application from the chapter.Focus on Problem Solving features and active learning strengthen problem-solving skills.Unlike most textbooks, this series simultaneously introduces verbal phrases for mathematical operations and the operations themselves. Exercises then prompt students to make a connection between a phrase and a mathematical process.
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Brand new. We distribute directly for the publisher. Proofs without words are generally pictures or diagrams that help the reader see why a particular mathematical statement may ...be true, and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought.The proofs in this collection are arranged by topic into six chapters: Geometry and Algebra; Trigonometry, Calculus and Analytic Geometry; Inequalities; Integer Sums; Sequences and Series; and Miscellaneous. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematicsJust what are "proofs without words?" First of all, most mathematicians would agree that they certainly are not "proofs" in the formal sense. Indeed, the question does not have a simple answer. But, as you will see in this book, proofs without words are generally pictures or diagrams that help the reader see why a particular mathematical statement is true, and also to see how one could begin to go about proving it true. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. Proofs without words bear witness to the observation that often in the English language to see means to understand, and in "to see the point of an argument."
Proofs without words have a long history. In this collection you will find modern rendition of proofs without words from ancient China, classical Greece, twelth-century India- even one based on a published proof by a former President of the United States! However, most of the proofs are relatively more recent creations, and many are taken from the pages of MAA journals.
The proofs in this collection are arranged by topic into six chapters: Geometry and Algebra, Trigonometry, Calculus and Analytic Geometry; Inequalities; Integer Sums; Sequences and Series, and Miscellaneous. Teachers will find that many of the proofs without words in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.
Editorial Reviews
Choice
"By acquiring a knack for explaining in words what they already understand, students will be better prepared to seek their own explanations.... The book offers models of the sort of visual thinking that is often woefully neglected in the classroom."
Crux Mathematicorum
"This book is a nice collection of results which certainly will enhance one's geometric sense and stimulate mathematical thought."
The Matheamtics Teacher
"Teachers who desire to give their students visual mathematical insights will find a great deal of value in this book... I found this book to be a great source for both teachers and their students at the high school level. For those teachers who are striving to satisfy the NCTM's call to reach all students, including those with different writing styles, this book will be an outstanding tool to help students who are visual learners."
The Mathematical Gazette
"Every time I have shown this book to a colleague, I have been asked how to get hold of it. It is an absolute delight.... Buy a copy today."
Booknews
Although not considered proper proofs, this collection of pictures helps students to visualize why a particular theorem is true and how one might go about proving it. Dr. Nelsen has gathered his pictures from many sources, including former President James Garfield, and Nicomachus of Gerasa (A.D. 100). Theorems are taken from geometry and algebra, trigonometry, calculus and analytical geometry, inequalities, integer sums, and sequences and series. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Table of Contents
Introduction
See (se) v. saw, seen, seeing. - v.t.
5. to perceive (things) mentally; discern; understand: to see the point of an argument.
- The Random House Dictionary of the English Language (2nd Ed.) Unabridged
"Proofs without words" (PWWs) have become regular features in the journals published by the Mathematical Association of America- notably Mathematics Magazine and the College Mathematics Journal. PWWs began to appear in Mathematics Magazine about 1975, and, in an editor's note in the January 1976 issue of the Magazine, J. Arthur Seebach and Lynn Arthur Steen encouraged further contributions of PWWs to the Magazine. Although originally solicited for "use as end-of-article fillers," the editors went on to ask "What could be better for this purpose than a pleasing illustration that made an important mathematical point?"
A few years earlier Martin Gardner, in his popular "Mathematical Games" column in the October 1973 issue of the Scientific American, discussed PWWs as "look-see" diagrams. Gardner points out that "in many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance." This dramatically illustrates the dictionary quote above: in English "to see" is often "to understand."
In the same vein, the editorial policy of The College Mathematics Journal throughout most of the 1980s stated that, in addition to expository articles, "The Journal also invites other types of contributions, most notably: proofs without words, mathematical poetry, quotes,..." (their italics). But PWWs are not recent innovations- they have long history. Indeed, in this volume you will find modern renditions of proofs without words from ancient China, classical Greece, and India of the twelfth century.
Of course, "proofs without words" are not really proofs. As Theodore Eisenberg and Tommy Dreyfus note in their paper "On the Reluctance to Visualize in Mathematics" [in Visualization in Teaching and Learning Mathematics, MAA Notes Number 19], some consider such visual arguments to be of little value, and "that there is one and only one way to communicate mathematics, and 'proofs without words' are not acceptable." But to counter the viewpoint, Eisenberg and Dreyfus go on to give us some quotes on the subject:
[Paul] Halmos, speaking of Solomon Lefshetz (editor of Annals), stated: "He saw mathematics not as logic but as pictures." Speaking of what it takes to be a mathematician, he stated: "To be a scholar of mathematics you must be born with... the ability to visualize" and most teachers try to develop this ability in their students. [George] Polya's "Draw a figure..." is classic pedagogic advice, and Einstein and Poincare's views that we should use our visual intuitions are well known.
So, if "proofs without words" are not proofs, what are they? As you will see from this collection, this question does not have a simple, concise answer. But generally, PWWs are pictures or diagrams that help the observer see why a particular statement may be true, and also to see how one might begin to go about proving it true. In some an equation or two may appear in order to guide the observer in this process. But the emphasis is clearly on providing visual clues to the observer to stimulate mathematical thought.
I should note that this collection is not intended to be complete. It does not include all PWWs which have appeared in print, but is rather a sample representative of the genre. In addition, as readers of the Association's journals are well aware, new PWWs appear in print rather frequently, and I anticipate that this will continue. Perhaps some day a second volume of PWWs will appear!
I hope that the readers of this collection will find enjoyment inn discovering or rediscovering some elegant visual demonstrations of certain mathematical ideas; that teachers will want to share many of them with their students; and that all will find stimulation and encouragement to try to create new "proofs without words
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...
Show More equations, vector analysis, and applied complex analysis. Students are guided through a series of laboratory exercises that present cogent applications of the mathematics and demonstrate the use of Mathematica as a computational tool to do the mathematics. Relevant applications along with discussions of the results obtained combine to stimulate innovative thinking from the students about additional concepts and applications. An "Instructor's Manual" (ISBN 0-07-052172-2) is also available81
Your Savings:$6.32
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Basic Technical Mathematics - 7th edition
ISBN13:978-0201730753 ISBN10: 0201730758 This edition has also been released as: ISBN13: 978-0201356649 ISBN10: 0201356643
Summary: Technical mathematics is a course pioneered by Allyn Washington, and the seventh edition of this text preserves the author's highly regarded approach to technical math while improving on the integration of technology in the text. The book is intended for a two or three-semester course and is taught primarily to students who plan to pursue technical fields. The primary strength of the text is the heavy integration of technical applications, which aids the student purs...show moreuing a technical career by showing the importance of a strong foundation in algebraic and trigonometric math.
Allyn Washington defined the technical math market when he wrote the first edition of Basic Technical Mathematics over thirty years ago. His continued vision is to provide highly accurate mathematical concepts based on technical applications. The course is designed to allow the student to be simultaneously enrolled in allied technical areas, such as physics or electronics. The material in the text can be easily rearranged to fit the needs of both instructor and students. Above all, the author's vision of this book is to continue to enlighten today's students that an understanding of elementary math is critical in many aspects of life.
Features :
NEW! Graphing Calculator. The graphing calculator is used throughout the text in examples and has been more heavily integrated and emphasized than the previous edition, although it is still not required for the course. This integration includes over 140 new graphing calculator screens pictured in the text. Pg. 98
NEW! Design. A new, more open design is an important improvement and feature of the seventh edition. The more spacious layout allows for additional graphing calculator displays in the margin, which gives students a visual representation of the mathematics. Pg. 110
NEW! Applications. Over 200 new technical applications have been added to the seventh edition. A hallmark strength of the Washington text, the applications challenge students to apply the mathematics to technically-based problems, reinforcing the relevancy of mathematics in the technical fields. Pg. 256
NEW! Writing Exercises. The number of writing exercises has been increased by more than 40%. A new graphical icon highlights writing exercises in the text. These exercises reinforce student understanding as they require students to verbalize their answers using words rather than numbers.
NEW! Word Problems and Solutions. Throughout the text, approximately 70 examples present complete solutions to word problems. These examples are clearly indicated in the margin by the phrase "solving a word problem." In addition, the text includes over 700 word problems within exercise sets. Pg. 257
NEW! Exercises and Figures. The seventh edition includes over 1,000 new exercises, many of which illustrate technical applications. Over 140 new figures have been added to help students visualize applications and concepts. Pg. 9
Flexibility of Material Coverage. An important and critical feature to the Washington approach to technical math is the flexibility of the Table of Contents. The chapters of the text are easily adapted to the specific needs of the students as well as the instructor. Certain sections or chapters may be omitted without loss of continuity, and chapters may be reordered for a customized syllabus. Notes and suggestions on how to reorder the organization of the material are contained in the Answer Book.
Introduction to Functions. More About Functions. Rectangular Coordinates. The Graph of a Function. Graphs on the Graphing Calculator. Angles.
4. The Trigonometric Functions.
Angles. Defining the Trigonometric Functions. Values of Trigonometric Functions. The Right Triangle. Applications of Right Triangles.
5. Systems of Linear Equations; Determinants.
Linear Equations. Graphs of Linear Equations. Solving Systems of Two Linear Equations in Two Unknowns Graphically. Solving Systems of Two Linear Equations in Two Unknowns Algebraically. Solving Systems of Two Linear Equations in Two Unknowns by Determinants. Solving Systems of Three Linear Equations in Three Unknowns Algebraically. Solving Systems of Three Linear Equations in Three Unknowns by Determinants.
6. Factoring and Fractions.
Special Products. Factoring: Common Factor and Difference of Squares. Factoring Trinomials. The Sum and Difference of Cubes. Equivalent Fractions. Multiplication and Division of Fractions. Addition and Subtraction of Fractions. Equations Involving Fractions.
7. Quadratic Equations.
Quadratic Equations; Solution by Factoring. Completing the Square. The Quadratic Formula. The Graph of the Quadratic Function.
8. Trigonometric Functions of Any Angle.
Signs of the Trigonometric Functions. Trigonometric Functions of Any Angle. Radians. Applications of Radian Measure.
9. Vectors and Oblique Triangles.
Introduction to Vectors. Components of Vectors. Vector Addition by Components. Applications of Vectors. Oblique Triangles, the Law Of Sines. The Law of Cosines.
Basic Definitions. Basic Operations with Complex Numbers. Graphical Representation of Complex Numbers. Polar Form of a Complex Number. Exponential Form of a Complex Number. Products, Quotients, Powers, and Roots of Complex Numbers. An Application to Alternating-Current (AC) Circuits.
13. Exponential and Logarithmic Functions.
The Exponential and Logarithmic Functions. Graphs of y = b^x and y = logbx. Properties of Logarithms. Logarithms to the Base10. Natural Logarithms. Exponential and Logarithmic Equations. Graphs on Logarithmic and Semilogarithmic Paper.
14. Additional Types of Equations and Systems of Equations.
Graphical Solution of Systems of Equations. Algebraic Solution of Systems of Equations. Equations in Quadratic Form. Equations with Radicals.
Chapter 15. Equations of Higher Degree.
The Remainder Theorem and the Factor Theorem. Synthetic Division. The Roots of an Equation. Rational and Irrational Roots.
16. Determinants and Matrices.
Determinants; Expansion by Minors. Some Properties of Determinants. Matrices: Definitions and Basic Operations. Multiplication of Matrices. Finding the Inverse of a Matrix. Matrices and Linear Equations NOT
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Each Learning Math course includes sequentially organized problems, video viewing, interactive activities, readings, and homework. The multimedia elements of the course create an exciting environment for probing mathematics content. The course can be taken entirely on the Web, followed in a print guide, or completed using a combination of Web and print. You can watch the videos online via Video on Demand, or on videocassette/DVD.
The following sequence of activities will give you a sense of what you will do as a student using Learning Math:
1. Watch the session video in its entirety. You can watch the video before you begin the session to become comfortable with the material, or you can view the video after completing the session (so as not to view answers to problems).
2. Do problems sequentially. Each session is divided into several parts indicated in the tabs along the top of the page. The problems are numbered within each part. (e.g., Problem A1)
3. If you are having difficulty with a problem, click on the Tip button.
4. Check the solutions by clicking on the Solution buttons.
5. If you want a more rigorous challenge, try out a Take It Further problem.
6. Read the Notes as you go along, to establish a context for the content and for suggestions on doing the activities in groups.
7. Watch video segments strategically placed throughout the session by fast-forwarding or skipping to the approximate time code indicated. To locate the segment, zero your VCR/DVD at the spot when the Annenberg Media logo appears.
8. Do homework problems and readings (available as PDF files online) at the end of each session to reinforce your learning.
Ways To Take Learning Math Learning Math was flexibly designed for a variety of users and situations. You may choose to work through the sessions on your own, in a study group, or as part of a facilitated, face-to-face, graduate-level course for credit.
Teacher-Talk
Go to Teacher-Talk to join an email discussion group and converse with other teachers taking this course.
Taking Multiple Learning Math Courses
The five Learning Math courses are designed to be independent of one another. You can take just one course, several courses, or all five courses in the order that fits your needs or the needs of your group. The courses also complement one another, with some topics discussed in more than one course but approached differently depending on the focus of that course. Taking several of these courses will increase your own conceptual understanding and ultimately that of your students.
Facilitating the Course
You can prepare for facilitating the course by reading through each session and its "Notes" section prior to meeting with your group. Reading through the material will help you become clear about the activities, plan how much time you need to spend on each one, and pull together necessary materials. The course is designed for use by an individual, but the Notes may suggest ways for groups to work through the sessions.
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Mathematics for Economists
9780393957334
ISBN:
0393957330
Pub Date: 1994 Publisher: Norton, W. W. & Company, Inc.
Summary: An abundance of applications to current economic analysis, illustrativediagrams, thought-provoking exercises, careful proofs, and a flexibleorganization-these are the advantages that Mathematics for Economists brings to today's classroom.
Simon, Carl P. is the author of Mathematics for Economists, published 1994 under ISBN 9780393957334 and 0393957330. Four hundred ten Mathematics for Economists textbooks ar...e available for sale on ValoreBooks.com, fifty nine used from the cheapest price of $66.87, or buy new starting at $163.40393957334-1-0-3 Orders ship the same or next business day. Expedited shipp... [more]
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A college level study of vector (multivariable) calculus which includes polar coordinates, analysis of vector-valued functions, analysis of functions of several variables, multiple integrals, and analysis of vector fields. This course emphasizes computational techniques, geometry, theoretical structure, and creative problem solving. Upon successful completion of the course, the student will receive 4 credit hours from the Central Virginia Community College.
Course Materials:
Textbook: Calculus, by Larson, Hostetler, and Edwards (4th edition). We will also use software packages and graphing calculators.
Course Content (and Tentative Schedule):
Week of
Coverage in textbook
HW due on Fri
Topics
1/6- 1/10
11.1 - 11.5
1
Parametric Eqs, Polar Coords, & Calculus
1/13 – 1/17
12.1-12.5
2
Vectors, Lines, planes
1/20 – 1/24
13.1 -13.3
3
No School Monday, Tuesday.
vector-valued funs & Calculus
1/27 – 1/31
13.4-13.5,14.1
4
Calculus of Vector-valued functions
Functions of several variables
2/3 - 2/7
14.2, 14.3, 14.5
5
Limits/continuity,Partial Derivs,Chain Rules
2/10 – 2/14
Review, Test 1,14.6
none
Test 1 on Weds, Directional derivatives
2/17 - 2/21
14.7-14.8
6
No school Monday Tangent planes, Max/Min problems
2/24- 2/28
14.9 - 14.10
7
Max/Min & Lagrange Multipliers,
3/3 - 3/7
15.1 - 15.3
8
Double Integrals, including Polar Coords
3/10 - 3/14
Review, Test
none
Test 2 on Thursday. Double Integrals in Polar Coordinates. Applications. No school Monday
3/17 – 3/21
15.4, 15.6, 12.7
9
Applications and Triple Integrals Cyl and Sph Coordinates
3/24 – 3/28
15.7,16.1
10
Triple Integrals in Cyl and Sph Coordinates
Vector Fields Thursday is Middle School Day
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This is a short eBook that describes how to get free high school Algebra 1 help online without having to spend any money, buy anything, join any free trials, or anything like that. Free High School Algebra 1 Help Online | Algebra 1 Help.org.
A short ebook explaining a simple way to subtract integers for people who have trouble subtracting integers. This uses a method based on simply changing a subtraction problem to an addition problem based on helping people with algebra. How to Subtract Integers Without Getting Confused | Algebra 1 Help.org
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El Cerrito ACT MathMy approach is holistic, letting each field inform others and looking for points of intersection. For example, I have found that most students better understand and appreciate mathematical concepts if they consider not only the "what" (i.e., rules) but also the "why" (historical development and ...
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The main goal of this project is to improve student understanding of the geometric nature of multivariable calculus concepts,...
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The main goal of this project is to improve student understanding of the geometric nature of multivariable calculus concepts, i.e., to help them develop accurate geometric intuition about multivariable calculus concepts and the various relationships among them.To accomplish this goal, the project includes four parts:· Creating a Multivariable Calculus Visualization applet using Java and publishing it on a website: web.monroecc.edu/calcNSF· Creating a series of focused applets that demonstrate and explore particular 3D calculus concepts in a more dedicated way.· Developing a series of guided exploration/assessments to be used by students to explore calculus concepts visually on their own.· Dissemination of these materials through presentations and poster sessions at math conferences and through other publications.Intellectual Merit: This project provides dynamic visualization tools that enhance the teaching and learning of multivariable calculus. The visualization applets can be used in a number of ways:- Instructors can use them to visually demonstrate concepts and verify results during lectures.- Students can use them to explore the concepts visually outside of class, either using a guided activity or on their own.- Instructors can use the main applet (CalcPlot3D) to create colorful graphs for visual aids (color overheads), worksheets, notes/handouts, or tests. 3D graphs or 2D contour plots can be copied from the applet and pasted into a word processor like Microsoft Word.- Instructors will be able to use CalcPlot3D to create lecture demonstrations containing particular functions they specify and/or guided explorations for their own students using a scripting feature that is being integrated with this applet.The guided activities created for this project will provide a means for instructors to get their students to use these applets to actively explore and "play" with the calculus concepts.Paul Seeburger, the Principal Investigator (PI) for this grant project, has a lot of experience developing applets to bring calculus concepts to life. He has created 100+ Java applets supporting 5 major calculus textbooks (Anton, Thomas, Varberg, Salas, Hughes-Hallett). These applets essentially make textbook figures come to life. See examples of these applets at Impacts: This project will provide reliable visualization tools for educators to use to enhance their teaching in calculus and also in various Physics/Engineering classes. It is designed to promote student exploration and discovery, providing a way to truly "see" how the concepts work in motion and living color. The applets and support materials will be published and widely disseminated through the web and conference presentations.
Demos with Positive Impact is a collection of quick classroom demos that enhance the learning of mathematics content through...
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Demos with Positive Impact is a collection of quick classroom demos that enhance the learning of mathematics content through animations, experiments etc. Each demo comes with stated objective, prerequisites, instructor notes and platform info, plus the level of the demo and credits. This setup appears conducive to quick inclusion into a class. To view a video of the award winning author, go to target=״_blank״>Demos with Positive Impact - the Mathematics Award Winner 2008 videoThe author also participated in the MERLOT Classics Series on Elluminate: " target=״_blank״
This site provides an extremely large encyclopedia-style collection of material related to mathematics at the college level...
see more
This site provides an extremely large encyclopedia-style collection of material related to mathematics at the college level and beyond. Much of the material deals with advanced topics. A large number of animated GIFs and java applets are presented as visual aids and the site has won numerous web awards. The World of Mathematics is hosted by Wolfram Research, Inc., and is offered as a free service to the mathematics community.
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This book aims to explain the basics of graph theory that are needed at an introductory level for students in computer or information sciences. To motivate students and to show that even these basic notions can be extremely useful, the book also aims to provide an introduction to the modern field of network science. Mathematics is often unnecessarily difficult for students, at times even intimidating. For this reason, explicit attention is paid in the first chapters to mathematical notations and proof techniques, emphasizing that the notations form the biggest obstacle, not the mathematical concepts themselves. This approach allows to gradually prepare students for using tools that are necessary to put graph theory to work: complex networks. In the second part of the book the student learns about random networks, small worlds, the structure of the Internet and the Web, peer-to-peer systems, and social networks. Again, everything is discussed at an elementary level, but such that in the end students indeed have the feeling that they: 1.Have learned how to read and understand the basic mathematics related to graph theory. 2.Understand how basic graph theory can be applied to optimization problems such as routing in communication networks. 3.Know a bit more about this sometimes mystical field of small worlds and random networks. There is an accompanying web site from where supplementary material can be obtained, including exercises, Mathematica notebooks, data for analyzing graphs, and generators for various complex networks.
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More About the Author
Product Description
About the Author
Maarten van Steen is full professor at the Computer Science department of VU University Amsterdam, The Netherlands. He mainly teaches in the field of distributed systems, computer networks, and operating systems. Together with Andrew Tanenbaum he has co-authored a well-known textbook on distributed systems. Confronted with the difficulties that undergraduates in computer science have with mathematics, he set out to design a course on graph theory and complex networks that for most students would be less intimidating and much more fun than regular mathematics courses. His research concentrates on extreme distributed computer systems: very large systems consisting of thousands to hundreds of thousands of computers, be they connected through wired or wireless networks. Graph theory and complexity are topics that coincide naturally with his research. Maarten van Steen considers himself an experimental computer scientist, meaning that ideas and designs are validated by real-world experiments and systems prototyping. This approach has widely shaped his attitude toward theoretical work, which he believes obtains true value if it can be tied to real-world systems.
Customer Reviews
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
1 review
6 of 8 people found the following review helpful
graph theory16 Aug 2012
By
technocrat
- Published on Amazon.com
Format: Paperback
Verified Purchase
The book is written in an easy to understand format.The coverage on graph theory is quite expansive.The theories are accompanied by proofs.The applications of graph theory in different practical segments are highlighted.I would highly recommend this book to anyone looking to delve into graph theory.
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Master Math: Pre-Calculus (Master Math Series)
Click to enlarge
Author
Debra Anne Ross
Manufacturer
Cengage Learning PTR
PublicationDate
2009-05-21
RRP:$17.99 Buy New:$9.30 as of 2014-11-25 23:05:47 You Save:$8.69(48Get ready to master the principles and formulas of pre-calculus! Master Math: Pre-Calculus is a comprehensive reference guide that explains and clarifies pre-calculus and introductory calculus principles in a simple, easy-to-follow style and format. Beginning with the most basic fundamental topics and progressing through to the more advanced topics that will help prepare you for introductory calculus, the book helps clarify pre-calculus using step-by-step procedures and solutions, along with examples and applications. A complete table of contents and a comprehensive index enable you to quickly find specific topics, and the approachable style and format facilitate an understanding of what can be intimidating and tricky skills. Perfect for both students who need some extra help or rusty professionals who want to brush up on their basic math skills, Master Math: Pre-Calculus will help you master everything from sets and functions to derivatives and integrals.
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Algebra and Trigonometry
Includes problem solving and mathematical modeling that provides students with a foundation in the principles of mathematical thinking. This book ...Show synopsisIncludes problem solving and mathematical modeling that provides students with a foundation in the principles of mathematical thinking. This book also provides coverage of the function concept, and integrates a significant amount of graphing calculator material to help students develop insight into mathematical ideas840068132-5Good. Hardcover. May include moderately worn cover, writing,...Good. Hardcover. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9780840068132-4Fair. 0840068131 -used book-book appears to be recovered-has...Fair. 0840068131 -used book-book appears to be recovered-has some used book stickers-free tracking number with every order. book may have some writing or highlighting, or used book stickers on front or back
Description:Fair. 0840068131 Used books do not include any supplemental...Fair. 0840068131 3rd Edition. Used-Good. Used books may have used stickers...Good. 3rd Edition. Used-Good. Used books may have used stickers on the cover, and do not include online codes or other supplements unless noted. n
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Background
The latest math technology need for the blind is a talking graphing calculator with the sophistication of the Texas Instruments series. The use of a graphing calculator is now an integral part of advanced mathematics classrooms across the U.S., and they are a requirement in many statewide assessments.
The Accessible Graphing Calculator (AGC) is a computer software program and was developed by the esteemed Science Access Project at Oregon State University, directed by Dr. John Gardner. This group is dedicated to the development of methods for making science, math, and engineering information accessible to people with print disabilities. "Print disabilities" include low vision, blindness, and dyslexia. In April 2000, I began beta testing the AGC. By the summer of 2000, students were being introduced to the AGC as well. During the 2000/2001 school year, all of my Algebra I and ATTAM (Adaptive Tools and Technology for Accessible Math) students were taught the use of the AGC. On March 7, 2001, ViewPlus Software Inc. (exclusive distributor) announced the availability of the AGC to the general public.
As you know from previous evaluations, I am always looking for the "best buy" in any math technology. However, although my definition of best buy includes price affordability - user-friendliness, features, and reliability are equally important.
Affordability
You may download a free 30-day fully functional copy of the AGC from the web at Then, check it out for yourself to make sure that it is the right product for your needs. When purchased on-line, the cost of a single copy license is just $75. CD copies are also available at a cost of $10 each, but this is not a necessity. Substantial institutional quantity discounts are available as well.
User-Friendliness
The AGC was developed from the ground up to be a universally usable Windows 95/98/ME/NT/2000 computer program that features a graphing calculator capable of displaying graphs both visually and audibly as a tone graph. With technology specifically designed for the blind, we often find that although it may be user-friendly for the blind student, there is an extensive learning curve for their sighted teacher. Since the AGC is truly accessible by both the blind and sighted, teachers, parents, and peers do not need to learn to use a special device in order to teach or assist these students.
In fact, the regular ed math teacher may very well wish to use the AGC with the entire class. In this day and age when math anxiety is rampant, and there is an emphasis on multiple modality input, the math teacher is always looking for any tool that will capture the attention of and increase understanding in all her students.
The AGC is a complex program and requires some practice before a student will become proficient and totally independent in its use. However, I have noticed that those of my students already technologically proficient in the use of JAWS (or other screen reader) are the quickest to learn how to navigate in the self-voiced AGC. In fact, these students are so intrigued with the AGC features; they take the initiative and beg to use their own after school time to practice. Everyone wants to have his or her own copy for home use. I promise this is really true and not just the ravings of an over-enthusiastic math teacher.
Also, it is not necessary that the student learn all of the features of the AGC at once in order to benefit from its use. I feel that various features should be slowly introduced as needed, and the AGC should never replace the student learning how to graph manually. My best students know how to use all the various tools in their toolbox.
The AGC comes with an HTML and a self-voiced user manual, getting started instructions, specific instructions regarding the use of screen readers and magnification, and help both off and on-line.
Features
The AGC has a scientific keypad calculator; an expression evaluator with the ability to define or import constants and expressions; two data set pages that permit the user to compute expressions, import and edit data tables, and compute a number of standard statistical properties; and the ability to plot either data set, their sum or difference, or their first derivative. However, you cannot plot two or more expressions on the same graph (no parent functions), nor can you do computations with matrices. There are several display options for tone-graph audio plots, and it is self-voicing for usability by people who are blind or dyslexic or kinesthetic learners.
Navigating the AGC is actually pretty user-friendly. Using the arrow, space bar, tab, and shift-tab keys let one move around fairly quickly, but many items can also be selected by using a hot key shortcut. The speech rate, pitch, and volume controls on the Speech tab page can be easily adjusted to the individual user's satisfaction. The AGC screen can also be magnified repeatedly and then decreased again. The domain, range, use of grid lines, tick marks, or none, and thickness of the graph can be adjusted to the user's specific requirements from the Plot tab page, allowing for further individualization.
The tab pages define the functionality of the AGC and each page has links to example exercises relating to that tab page. They include the calculator, speech, evaluator, wave, plot, and two data set pages.
Reliability and Flexibility
The AGC is accessible to all. The on-screen graphics are easily seen by a low vision student, and the graph can be listened to by using the audio wave feature. Print copies can be made using any standard printer using a variety of fonts including braille. The print copies with braille fonts can be copied onto swell paper and run through a tactile imaging machine to create a raised line graphic. However, the best way to create a tactile graphic is to emboss directly from the AGC to a TIGER (braille/graphics embosser) from ViewPlus Technologies.
A student listens to the audiograph sound of the parabola as she follows along on paper.
John Gardner assures me that they are working on adding matrix math to the AGC, and he now has a better understanding of why I have been so insistent on this. Work with matrices used to be shoved to the back of the Algebra II book because working with them manually was just too tedious for high school students. Now, with the advent of graphing calculators, work with matrices appears in Chapter 1 of Algebra I. As soon as we have the matrix situation under control, perhaps we can work on parent functions! I have always found John to be most cooperative, supportive, and greatly appreciative of all input, so I foresee the AGC adding even more features in the future, insuring that blind persons have equal access in all areas of mathematics.
Recommendations
I definitely recommend this calculator program for students taking high school algebra and beyond. WARNING: After exposure to the AGC, 99% of students are not satisfied to just graph linear functions. They are compelled to try and graph the most difficult functions their minds can conceive, especially becoming addicted to exponential and trigonometric functions.
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Systems and their mathematical description play an important role in all branches of science. This book offers an introduction to mathematical modeling techniques. It is intended for undergrad students in applied natural science, in particular earth and environmental science, environmental engineering, as well as ecology, environmental chemistry, chemical... more...
Updated and expanded, this second edition satisfies the same philosophical objective as the first -- to show the importance of problem posing. Although interest in mathematical problem solving increased during the past decade, problem posing remained relatively ignored. The Art of Problem Posing draws attention to this equally important act and is... more...
A provocative collection of papers containing comprehensive reviews of previous research, teaching techniques, and pointers for direction of future study. Provides both a comprehensive assessment of the latest research on mathematical problem solving, with special emphasis on its teaching, and an attempt to increase communication across the active... more...
This book looks at the process of human cognition and the way complex problems are solved by decomposing them into a list of strategic objectives, before focusing individually on each objective to plan for a tactical solution. This process has been formulated by military planners in the form of the Standard Operating Procedure, by which problem solving... more...
Convex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical foundation for convex optimization, having deep knowledge of convex analysis helps students and... more...
Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly... more...
Intends to set the modern foundations of the theory of generalized curvature measures. Following a historical and didactic approach, this book introduces the mathematical background of the subject, curves and surfaces, convex subsets, smooth submanifolds, subsets of positive reach, polyhedra and triangulations, and surface reconstruction. more...
A guide to concept mapping in mathematics. It provides the reader with an understanding of how the meta-cognitive tool, namely, hierarchical concept maps, and the process of concept mapping can be used innovatively and strategically to improve planning, teaching, learning, and assessment at different educational levels. more...
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When I heard about the Life of Fred series, I decided to start by reviewing the Geometry text since the homeschool market has a bigger lack of practical options in this area than in any other area of math.
Two features immediately make this appealing to many families: low cost and a course design suitable for independent study. But there's much more to the Life of Fred books! The books are written by Dr. Stanley Schmidt, a retired math teacher who loves math and wants to share his enthusiasm with students. Part of his strategy is to build his math books around the adventures of Fred, a very young (six years old in the Geometry text) genius who is a math teacher at KITTENS University. The stories shift from silly to serious, outlandish to edgy, and they are likely to be very appealing to learners who prefer something more than "dry" math. Fred's adventures are the jumping off point for math lessons (e.g. Fred plays with his food and creates a polygon), or Fred might be pondering something mathematical, or teaching, or discussing a math topic with friends or students....
The page illustration from the book (above) shows [an] example. In addition, Dr. Schmidt digresses into side comments, footnotes, and "conversations" such as one concerning Harry S Truman and the fact that his name is frequently misspelled with a period after the "S" in official government usage. All of this makes the text much more user-friendly than most others. It also adds a bit to the size of the book—542 pages for the Geometry text.
Surprisingly, the story line and discursions are not used to dumb down the course. The geometry content is actually quite traditional, even though the presentation is not. The content is high level and challenging with proofs introduced in chapter one. Chapter eleven teaches constructions using a compass and a straight edge. There are six "extra" chapters (chapters 5 1/2, 7 1/2, 8 1/2, 11 1/2, 12 1/2, and 13 1/2) that can be skipped or included depending upon the student's ability and rate of progress.
Each lesson teaches a concept, albeit sometimes in a roundabout fashion through the story. Then there's a "Your Turn to Play"—practice problems with complete solutions. Students should work through every one of these problems rather than just jumping ahead to the solutions. There are a number of lessons with practice problems within each chapter.
At the end of each chapter are six sets of problems, each set labeled with the name of a city. Students should complete the first two "cities" (for which all the solutions/answers are available in the student text). They should also complete the odd-numbered problems in the next two cities for which solutions/answers are also supplied. The remaining problems can be used for tests. A separate, very inexpensive answer key is available for the remaining problems. This allows students to work independently for the most part, but still provides a practical way to ensure they are actually studying and learning the material. And if students get stuck and parents can't help, you are welcome to call the author!....
At least a few references to the Bible and churches indicate that the author likely has a Christian worldview, but there aren't actually any directly religious statements that I spotted....
It is difficult to convey the full "flavor" of this text in a review, but Dr. Schmidt does a marvelous job of helping students see the real value and applications of math.
After reviewing Geometry, I liked the series enough to follow up with reviews of the other Life of Fred texts as they've been published. Middle school students who have already completed Life of Fred:Decimals and Percents should continue with Pre-Algebra 0 with Physics,Pre-Algebra 1 with Biology and Pre-Algebra 2 with Economics.
These three texts treat physics, biology and economics just as they treat math, jumping from topic to topic with unusual connections to the storyline about Fred. Pre-algebra is covered in a scattered fashion along with a few more advanced concepts such as functions, calculating the molecular weight of sucrose, and balancing chemical equations. The Biology text touches on topics such as seed germination, life cycles, teeth brushing, photosynthesis, eyes and vision, the circulatory system, breathing, bones and calcium, dermis and epidermis, chromosomes, DNA, genes, and alleles. In Economics, Dr. Schmidt teaches some basic concepts along with some "conservative" ideas. He discusses the need for sufficient capital when starting a business, the value of tools in increasing production, the law of comparative advantage, demand curves, and other topics of basic economics....
Beginning Algebra obviously follows these texts. Beginning and Advanced Algebra serve as first and second year Algebra courses and cover traditional content at a relatively high level. Both of these texts and the Trigonometry text have an optional Fred's Home Companion book that I highly recommend. Fred's Home Companion outlines lesson plans for the core text, including which "cities" of questions students should do, making it easier for students to pace themselves if they are working independently. The core text has answers to some of the "cities" problems, and Fred's Home Companion provides solutions to the rest of them. In addition, there are extra problems (with their solutions) for students to solve.
Parents have urged Dr. Schmidt to create more problem solving practice for algebra, so he has produced supplements titledZillions of Practice Problems for Beginning Algebraand Zillions of Practice Problems: Advanced Algebra.
Beginning Algebra allows but does not require the use of a basic calculator. For Advanced Algebra through Statistics, students will need a scientific calculator but not a graphing calculator.
Trigonometry should be taken between Geometry and Calculus, serving to some extent as a Precalculus course.
The Statistics course really is college level. However, it is so engagingly written that it actually makes me want to study statistics. It might be possible for a high school student to work through this text, then test for college credit, but I haven't investigated those possibilities. This text might be unique in that it includes a chapter (Chapter 4 1/2) on moral guidelines for the use of statistics and statistical devices.
There is also a new Elementary Physics course written for students to use before tackling high school math. It might be used as early as sixth grade. (I have not yet reviewed it.)
The story of Fred is very much a part of all the courses and the teaching method is pretty much the same from Fractions through Statistics. Most students should be able to work through all the books independently.
All the Life of Fred texts are hardcover books, printed in black-and-white. There are no separate teacher guides or answer keys to purchase although you might want the Fred's Home Companion for those courses where it is available.
....
Throughout the series, Dr. Schmidt tries to teach for conceptual understanding rather than mere memorization of formulas and strategies. Students often see the practical application of a math concept before they learn how to solve the problem. Students are likely to begin thinking about math more like solving puzzles or critical thinking exercises than lists of problems to solve. The story of Fred is an important part of this approach. The story does take up significant space within in each text. And while it sometimes meanders into "entertainment" unrelated to the math topic at hand, most of the time it stimulates students to consider how math might be used to deal with a real life situation.
One other factor important to many families is the low cost of these texts. Texts range in cost from $19 to $49. Home Companions are $14 each. There are no other teacher manuals, answer keys, or anything else to buy. In addition, the texts are non-consumable and might be used for a number of students.
Life of Fred: Elementary Physics
Instant Key
Suitable for: independent study; might appeal most to Sociable Sue because of the story line.
Audience: grades 4-12
Need for parent/teacher instruction: minimal
Prep time needed: 0 Need for Teacher's Manual: Not available although Home Companions have some solutions/answers
Religious perspective:
secular but "Christian friendly"
All reviews and articles on this site belong to Cathy Duffy unless otherwise identified. No review or article may be copied or reprinted without permission except for a single copy of a review made for temporary use AND not shared with others. Our organization does not engage in any solicitation activities in California specifically targeting potential customers residing in California (including distributing flyers, newsletters and other promotional materials, sending emails, initiating telephone calls or making referrals in person) that refer potential customers to the retailers with whom we have links.
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Mathematics Methods for Physicists - 6th edition
Summary: This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition.
Updates the leading graduate-level text in mathematical physics
Provides compreh...show moreensive coverage of the mathematics necessary for advanced study in physics and engineering
Focuses on problem-solving skills and offers a vast array of exercises
Clearly illustrates and proves mathematical relations
New in the Sixth Edition:
Updated content throughout, based on users' feedback
More advanced sections, including differential forms and the elegant forms of Maxwell's equations
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31Algebra For College Students
Eduspace Registration and Enrollment Guide Pass Code: For Students
Eduspace Student Registration And Enrollment Guide
Summary
Designed to support first-year developmental math students taking an intermediate-level algebra course, this new text offers the hallmark features developed by the best-selling Larson team: abundant high-quality applications, the use of real data, the integration of visualization (many figures and graphs) throughout, and extensive opportunities for self-assessment. The authors' goal is for students to come away from the course with a firm understanding of algebra and how it functions as a modern modeling language. What You Should Learnorients students to each section by listing the main objectives. Why You Should Learn Itprovides a motivational explanation for learning the given objectives. What Did You Learn?following each chapter highlights key mathematical terms and concepts. Integrated Review Exercisesappear before section exercises in every section. Eduspace, powered by Blackboard, for the Larson/HostetlerAlgebra for College Studentscourse features algorithmic exercises, test bank content in question pools, an online study guide, interactive tutorials for appropriate sections and video explanations.
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Main menu
Advanced Quantitative Reasoning
AQR Press publishes innovative mathematics textbooks, including Common
Core and Texas editions of Advanced Quantitative Reasoning. This textbook
teaches quantitative literacy, statistics, and modeling. It meets a need for
many high school seniors. Advanced Quantitative Reasoning is designed for
students who have completed Algebra I, Geometry, and Algebra II, or
Integrated Mathematics I, II, and III.
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CliffsStudySolver workbooks combine 20 percent review material with 80 percent practice problems (and the answers!) to help make your lessons stick.CliffsStudySolver Algebra I is for students who want to reinforce their knowledge with a learn-by-doing approach. Inside, you'll get the practice you need to tackle numbers and operations with problem-solving tools such asStraightforward, concise reviews of every topicPractice problems in every chapter — with explanations and solutionsA complete chapter on story problemsA diagnostic pretest to assess your current skillsA full-length exam that adapts to your skill levelBeginning with the basics of algebraic symbols and vocabulary, this workbook ventures into signed numbers, polynomials, inequalities, quadratic equations, and more. You'll explore integers, prime numbers, linear equations, functions and relations, plus details aboutWorking with the associative property of addition and multiplicationAdding, subtracting, multiplying, and dividing algebraic functionsFactoring binomials, trinomials, and other polynomialsGraphing points, quadrants, lines, and curves such as parabolasDealing with coin and interest story problemsPractice makes perfect — and whether you're taking lessons or teaching yourself, CliffsStudySolver guides can help you make the grade.
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Spring 2014 Math 121 Trigonometry (4 units)
Section # 4444 Begins 1/21/14 Ends 5/23/14
Course Description
This course will cover the mathematical uses and implications of triangles with its focus on the six trigonometric functions, the inverse trigonometric functions, and their graphs. Students will learn to solve triangles, apply trigonometry to physical phenomena, and work with the trigonometric functions in an algebraic setting.
Textbook: Trigonometry by Ratti and McWaters ISBN 0321614704. Approximate cost new $200 OR online access to text ISBN 032119991X (approx. $100) available from Pearson when you access the course (choose only one of these options).
Estimated Time per Week: Students can expect to spend approximately 12 hours per week (more if this is a difficult subject for you) reading, writing, and taking quizzes and participating in online class discussions. This course does NOT take "less time" nor is it "easier" to complete successfully than a face-to-face course (in fact, many students find that it takes more time and can be very challenging). You should consider the amount of time you can devote to the course before you register for the course.
Special Requirements: Log into Etudes the first day of class and complete the online orientation for math classes. Access the class (the same day) following the instructions in the orientation (mymathlab.com).
Assignments & Tests: Assignments will consist of reading, watching online instructional videos, practice exercises, journal responses, and discussion board activities. Exams will be conducted online. You will be required to submit your written work for the final exam within one week of the course ending date.
Additional Comments The entire course will be conducted online through the MyMathLab program and email contact with the instructor. Etudes will only be used for orientation to the MyMathLab program. Students are required to have regular, reliable Internet access, an active email account, the ability to use word processing, conduct Internet searches, attach files, send emails, and work independently. This course is NOT self-paced (there are due dates similar to what you would find in a face-to-face course).
New to ETUDES:
Here is an
Online Orientation (Flash presentation opens in a new window)
that will show you the basics of how to use ETUDES. Here is a
flash
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The most helpful favorable review
The most helpful critical review
4 of 5 people found the following review helpful
5.0 out of 5 starsLoves to WatchPublished on May 27, 2010 by K. Freeman
15 of 16 people found the following review helpful
1.0 out of 5 starsNot educational, not worth the money...
teach about them at all-- skip this one!
This excellent, educational Disney DVDs helps make basic algebra accessible to young people. This is a "classroom edition" DVDs particularly ideal for use in public or private schools (or home schooling). Bill Nye's Solving For X: Pre-Algebra, Volume 1 covers infinite fractions, exponents, signed numbers & proportional reasoning. Enhancing the colorful presentation featuring ways in which mathematics is directly useful in real life, the Solving for X DVDs also includes an interactive whiteboard assessment game that students can play independently, in teams, or as an entire class, as well as a downloadable educator's guide with additional resources and activities, and correlations to National Curriculum Standards. Due to its step-by-step, user-friendly format, this DVDs is also useful for teens and adults who need a refresher in algebra basics! Highly recommended.
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Practicing College Learning Strategies, 5th Edition
PRACTICING COLLEGE LEARNING STRATEGIES, Fifth Edition, is a straightforward text with ample exercises and a "Survival Kit" — a quick roadmap that provides an overview of keys to academic success. This roadmap is perfect for the first few days of class, because it helps you gain confidence as a new college student. You're in the driver's seat and this book will teach you how to use the tools that are at your disposal. Structured activities and exercises guide you in the reflection process to make the information personal and useful and to provide practice opportunities.
The Fifth Edition features a revised appendix, Principles of Studying Math. Organized around the learning strategies presented in the text, the appendix gives you concrete strategies for not just getting through your math class, but for becoming completely engaged in the learning102.95
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RATIONALE
The curriculum in Mathematics has been designed to cater to the specific needs of NIOS
learners. The thrust is on the applicational aspects of mathematics and relating learning to the
daily life and work situation of the learners. The course is modular in nature with – eight
compulsory modules forming the core curriculum and four optional modules out of which the
learner is to choose one optional module. An attempt has been made to reduce rigour and
abstractness.
Argand Diagram
- Representation of a complex number by
a point in a plane.
Quadratic Equations
- Solution of quadratic equation with real
coefficients using the quadratic formula
- Square root of a complex number
- Cube roots of unity
Extended Learning
Polar representation of a complex
number
Quadratic equations with complex
coefficients
NOTE :
- "Division by zero is not allowed in
complex numbers" to be stressed.
- Lack of order in complex numbers to be
highlighted.
- The fact that complex roots of a
quadratic equation with real coefficients
occur in conjugate pairs but the same
may not be true if the coefficients are
complex numbers is to be verified using
different examples.
Module 2: Determinants and Matrices
Study Time: 15 hrs. Max. Marks: 10
Pre-requisites : Knowledge of number
systems; solution of system of linear
equations.
Content and Extent of Coverage
Determinants and their Properties
- Minors and Cofactors
- Expansion of a determinant
- Properties of determinants
Algebra of matrices
- Multiplication of a matrix by a number
- Sum and difference of matrices
- Multiplication of matrices
Inverse of a square matrix
- Minor and cofactors of a matrix
- Adjoint of a matrix
- Inverse of a matrix
Solution of a system of linear
equations
- Solution by Cramer's Rule
- Solution by matrix method
NOTE:
- The properties of determinants to include
the following:
1. If any two rows or columns of a
determinant are interchanged, then the sign of the determinant is
changed.
2. If each element of a row (or column)
of a determinant is multiplied by a
constant, the value of the
determinant gets multiplied by.
3. If k times a row (or column) is added
to another row (or column) the value
of the determinant remains
unchanged.
- The number of equations and variables to
be restricted to three only.
Extended Learning
Cramer's Rule for four or more
equations
Determinant as a function
Matrix as a function
Matrices over complex numbers
Hermitian and Skew Hermitian
Rank of a Matrix
Inverse by elementary row
transformations
Solution of 4 or more than 4 linear
equations in 4 more than 4 variables
Pre-requisites : Permutation, Combination
and concept of a function, Exponential
functions, Logarithmic functions and their
properties, and graphs.
Content and Extent of coverage
Arithmetic Progression
- Concept of a sequence
- A.P as a sequence
- General term of an A.P
- Sum upto 'n' terms of an A.P.
Geometric Progression
- G.P as a sequence
- General term of a G.P
- Sum upto 'n' terms of a G.P.
- Sum upto infinite terms of a G.P. Series
- Concept of a series
- Some important series, etc. using method of
differences and mathematical induction
Exponential and Logarithmic Series
- Representation of x e and log(1+ x) as
series.
- Properties of x e and log(1+ x)
Straight Line
- Equation of a straight line in
- Slope-intercept form
- Two point form
- Point-slope form
- Parametric form
- Intercepts form
General equation of first degree and its
relationship with straight line
Parallel and Perpendicular Lines
- Angle between two lines
- Parallel lines
- Perpendicular lines
- Distance of a point from a line
- Distance between two parallel lines
- Family of lines
Circle
- Equation of a circle whose radius and
centre are given.
- Equation of a circle in terms of
extremities of its diameter.
- General equation of a circle
- Equations of tangents and normals
- Parametric representation of a circle.
Conic Sections
- Acquaintance with equation of parabola
and ellipse in standard form
- Eccentricity, directrix and focus
NOTE:
- Problems on lines to include questions of
the type ' l +l l = 0
- Conic sections to be introduced through
examples of loci and not as a section of a
cone.
Extended Learning
Locus
- Advanced examples of loci
System of Circles
- Equation of a family of circles passing
through the intersection of two circles
- Condition for orthogonality of circles
- Radical axis of two circles
Sections of a cone (Conic sections)
- Derivation of equations of parabola, ellipse
and hyperbola in standard form
- Condition for y = mx + c to be a tangent to
these conics
- Point of tangency
General second degree equation in two
variables
Condition for it to represent :
- A pair of straight lines
- A circle
- Different conic sections
MODULES 7: Differential Calculus
Study Time: 45 hrs. Max. Marks: 17
Pre-requisites: Trigonometry and Exponential
and Logarithmic series
Content and Extent of Coverage
Limit and Coverage
- Notion of limit (left hand and right hand
limits)
- Continuity of functions at a point
- Continuity of functions in an interval
Definite Integrals
- Idea of definite integral as limit of a sum
- Geometrical interpretation of definite
integrals in simple cases.
- Properties of definite integrals
- Application of definite integrals in finding
area under a curve
Differential Equations
- Notion of differential equation, its order and
degree
- Solution of first order, first degree
differential equations
NOTE:
The fact that integral is called primitive, antiderivative
to be specified.
Probability
- Concept of probability
- Use of permutation and combination in
probability
- Probability as a function
- Conditional Probability and independent
events
- Random variable as a function on sample
space.
NOTE:
- Probability to be explained as the ratio of
number of cases favourable to an event and
the total number of cases.
- Venn diagrams to be used as frequently as
possible to give a pictorial representation of
the concepts
- Use of addition theorem when product of
event is easily identifiable.
Vectors
- Scalars and vectors
- Vectors as directed line segments
- Magnitude and direction of a vector
- Null vector and Unit vector
- Equality of vectors
- Position vector of a point
Algebra of vectors
- Addition and subtraction of vectors and their
properties
- Multiplication of a vector by a scalar and
their properties
Resolution of a vector
- Resolution of a vector in two dimensions.
- Resolution of a vector in three dimensions
- Section formula
Co-ordinates of a point
- Co-ordinates of a point in space.
- Distance between two points
- Co-ordinates of a division point.
- Direction cosines and projection.
- Condition of parallelism and
perpendicularity of two lines.
The Plane
- General equation of a plane.
- Equation of a plane passing through three
points.
- Equation of a plane in the normal and
intercept form.
- Angle between two planes.
- Plane bisecting angles between two planes.
- Homogeneous Equations of second degree
representing two planes.
- Projection and Area of a triangle.
- Volume of tetrahedron.
The Straight Line
- Equation of a line in symmetrical form.
- Deduction of the general equation into
symmetrical form.
- Perpendicular distance of a point from a
straight line.
- Angle between a line and a plane.
- Condition of coplanarity of two lines.
The Sphere
- Equation of a sphere : Centre-radius form.
- Equation of a sphere through four non
coplanar points.
- Diameter form of the equation of a sphere.
- Plane section of a sphere and sphere through
a given circle.
- Intersection of a sphere and a line
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I want to graph some vectors but I'm not able to in the regular student version. The lab book we have says to refer to the electronic version to be able to graph vectors. Can anyone tell me what the ''electronic copy'' of a lab is?
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This course is designed to enable the student to recognize, understand and apply various mathematical concepts and principles that are the foundation for many things that we take for granted in our everyday lives, such as Voting, Traveling, Finances, Government and the wonders of Nature. Satisfies GER/GEP requirement for CPLS students only. Open to CPLS students only.
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Excursions in Modern Mathematics - 7th edition
Summary: Excursions in Modern Mathematics, Seventh Edition, shows readers that math is a lively, interesting, useful, and surprisingly rich subject. With a new chapter on financial math and an improved supplements package, this book helps students appreciate that math is more than just a set of classroom theories: math can enrich the life of any one who appreciates and knows how to use it contain some highlighting. Supplemental materials may not be included. We select best copy available. - 7th Edition - Hardcover - ISBN 9780321568038
$39.52 +$3.99 s/h
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Cheryls-Books Vinemont, AL
2009-01-07 Hardcover 7th Good Hardback book in good condition, but missing dust jacket if issued one. No CD if issued one. Small amount of torn paper inside the front cover.
$39.97 +$3.99 s/h
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Nivea Books Lynnwood, WA
Hardcover Fine 0321568036 Like New copy, without any marks or highlights. Might have minor shelf wear on covers. This is Student US Edition. Same day shipping with free tracking number. A+ Customer...show more Service! ...show less
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Nivea Books Lynnwood, WA
Hardcover New 0321568036 New Copy with minor shelf wear. This is Student US Edition. May be publisher overstock. Same day shipping with free tracking number. Expedited shipping available. A+ Custom...show moreer Service! ...show less
Hardcover Fine 0321568036 Like New. May have highlights/underlines and/or textual notes with only a few pages. STUDENT US EDITION. Packaged carefully. Ships IMMEDIATELY with tracking number. Excell...show moreent Customer Service. All Orders Backed by Hassle-Free Returns. ...show less
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Used - Very Good Book. Shipped from US within 4 to 14 business days. Established seller since 2000
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Excursions in Modern Mathematics
9780131001916
ISBN:
0131001914
Edition: 5 Pub Date: 2003 Publisher: Prentice Hall
Summary: Excursions in Modern Mathematicsis, as we hope the title might suggest, a collection of "trips" into that vast and alien frontier that many people perceive mathematics to be. While the purpose of this book is quite conventional--it is intended to serve as a textbook for a college-level liberal arts mathematics course--its contents are not. By design, the topics in this book are chosen with the purpose of showing the ...reader a different view of mathematics from the one presented in a traditional general education mathematics curriculum. The notion that general education mathematics must be dull, unrelated to the real world, highly technical, and deal mostly with concepts that are historically ancient is totally unfounded. The "excursions" in this book represent a collection of topics chosen to meet a few simple criteria. Applicability.The connection between the mathematics presented here and down-to-earth, concrete real-life problems is direct and immediate. The often heard question, "What is this stuff good for?" is a legitimate one and deserves to be met head on. The often heard answer, "Well, you need to learn the material in Math 101 so that you can understand Math 102 which you will need to know if you plan to take Math 201 which will teach you the real applications," is less than persuasive and in many cases reinforces students' convictions that mathematics is remote, labyrinthine, and ultimately useless to them. Accessibility.Interesting mathematics need not always be highly technical and built on layers upon layers of concepts. As a general rule, the choice of topics in this book is such that a heavy mathematical infrastructure is not needed--by and large, Intermediate Algebra is an appropriate and sufficient prerequisite. (In the few instances in which more advanced concepts are unavoidable, an effort has been made to provide enough background to make the material self-contained.) A word of caution--this does not mean that the material is easy! In mathematics, as in many other walks of life, simple and straightforward is not synonymous with easy and superficial. Age.Much of the mathematics in this book has been discovered within the last 100 years; some as recently as 20 years ago. Modern mathematical discoveries do not have to be only within the grasp of experts. Aesthetics.The notion that there is such a thing as beauty in mathematics is surprising to most casual observers. There is an important aesthetic component in mathematics and, just as in art and music (which mathematics very much resembles), it often surfaces in the simplest ideas. A fundamental objective of this book is to develop an appreciation for the aesthetic elements of mathematics. Hopefully, every open-minded reader will find some topics about which they can say, "I really enjoyed learning this stuff!" Outline The material in the book is divided into four independent parts. Each of these parts in turn contains four chapters dealing with interrelated topics. Part 1 (Chapters 1 through 4). The Mathematics of Social Choice.This part deals with mathematical applications in social science. How do groups make decisions? How are elections decided? What is power? How can power be measured? What is fairness? How are competing claims on property resolved in a fair and equitable way? How are seats apportioned in the House of Representatives? Part 2 (Chapters 5 through 8). Management Science.This part deals with methods for solving problems involving the organization and management of complex activities-that is, activities involving either a large number of steps and/or a large number of variables (routing the delivery of packages, landing a spaceship on Mars, organizing a banquet, scheduling classrooms at a big university, etc.). Efficiency is the name of the game in all these problems. Some li
Tannenbaum, Peter is the author of Excursions in Modern Mathematics, published 2003 under ISBN 9780131001916 and 0131001914. Four Excursions in Modern Mathematics textbooks are available for sale on ValoreBooks.com, two used from the cheapest price of $4.89, or buy new starting at $48
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Pre-Calculus Guide
Description
Calculus may not seem very important to you but the lessons and skills you learn will be with for your whole lifetime!
Calculus is the mathematical study of continuous change. It helps you practice and develop your logic/reasoning skills. It ...Read more
Description
Calculus may not seem very important to you but the lessons and skills you learn will be with for your whole lifetime!
Calculus is the mathematical study of continuous change. It helps you practice and develop your logic/reasoning skills. It throws challenging problems your way which make you think. Although you may never use calculus ever again after school or college, you will definitely hold on to the lessons that calculus teaches you.
Things like time management, how to be organized, how to accomplish things on time, how to perform under pressure, how to be responsible are just some of the things Calculus helps you become proficient in. Traits that will help you succeed.
Calculus plays a big role in most universities today as students in the fields of economics, science, business, engineering, computer science, and so on are all required to take Calculus as prerequisites.
Our Pre-Calculus guide is a preliminary version of Calculus containing over 300 rules, definitions, and examples that provides you with a broad and general introduction of this subject. A valuable pocket reference to have on your phone.
Even if you dont use Calculus, this app sure is a cool way to show-off some high IQ!
Like all our 'phoneflips', this fast and lightweight application navigates quick, has NO Adverts, NO In-App purchasing, never needs an internet connection and will not take up much space on your phone!
Portrait & Landscape mode supported.
Thank you!
App Questions
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App Details
UPDATED ON: May 12, 2011
GRÖSSE: 1,363,148
INSTALLATIONS: 1,000 - 5,000
LATEST VERSION: 2
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...
More About
This Book
problem. You'll also memorize the most frequently used equations, see how to avoid common mistakes, understand tricky trig proofs, and much more.
100s of Problems!
Detailed, fully worked-out solutions to problems
The inside scoop on quadratic equations, graphing functions, polynomials, and more needed a refresher!
Taking calculus for the first time in years and decided to use this to refresh my memory and it worked very well! It really did explain all of the topics very well, the only problem I had was with some of the explanations to the answers of the practice problems. I couldn't answer some of the reasons why the answers were what they were. But the book did it's job in reminding me the basics for the course.
1 out of 1 people found this review helpful.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
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Summary: Joseph Gallian is a well-known active researcher and award-winning teacher. His Contemporary Abstract Algebra, 6/e, includes challenging topics in abstract algebra as well as numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings that give the subject a current feel and makes the content interesting and relevant for students.
Motivation Definitions and Notation Free Group Generators and Relations Classification of Groups of Order up to 15 Characterization of Dihedral Groups Realizing the Dihedral Groups with Mirrors Biography of Marshall Hall, Jr.
27. Symmetry Groups
Isometries Classification of Finite Plane Symmetry Groups Classification of Finite Group of Rotations in R3
28. Frieze Groups and Crystallographic Groups
The Frieze Groups The Crystallographic Groups Identification of Plane Periodic Patterns Biography of M. C. Escher Biography of George Pólya Biography of John H. Conway
29. Symmetry and Counting
Motivation Burnside's Theorem Applications Group Action Biography of William Burnside
30. Cayley Digraphs of Groups
Motivation The Cayley Digraph of a Group Hamiltonian Circuits and Paths Some Applications Biography of William Rowan Hamilton Biography of Paul Erdös
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MERLOT Search - materialType=Tutorial&userId=21266
A search of MERLOT materialsCopyright 1997-2014 MERLOT. All rights reserved.Thu, 27 Nov 2014 03:04:22 PSTThu, 27 Nov 2014 03:04:22 PSTMERLOT Search - materialType=Tutorial&userId=21266
4434Particle Adventure
Tutorials on fundamentals of nuclear and particle physics. Many foreign language versions available.Calculus Quest
A Calculus Tutorial developed at Oregon State University. "Contains wonderful illustrations ofcalculus concepts using stories and interactive screens. Check it out. -- Karl Hahn "1-D Kinematics
This site contains an extensive set of notes on basic topics in physics. There are extensive illustrations and animations along with the text. Also included are self-quizzes, and shockwave quizzes and tutorials. Discusses the use of diagrams and graphsQuasiTiler 3.0
QuasiTiler draws Penrose tilings and their generalizations. This document explains the interesting geometryinvolved in the processes. The concepts involved are surprisingly simple. The only apparent hurdle that wehave to overcome is working in spaces with more than 3 dimensions. However in the next section we startwith examples in 2 and 3 dimensions where our intuition is useful. Then we extend the same concepts tomore dimensions. I hope that you get some insight on the geometry of higher-dimensional spaces by readingthis document and by experimenting with QuasiTiler. Includes interactive applet.Online Technical Writing
A tutorial for improving writing, with examples.Coolmath.com
A large collection of links to tutorials and references covering a wide range of mathematics topics. Calculators, games, and a daily fractal also included.HTML Goodies Tutorial
A large site that teaches the basics of HTML, Javascript, and Java applets. A lot of links to programming resources.Advice on Research and Writing
A collection of advice about how to do research and how to communicateeffectively (primarily for computer scientists).
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Developed from the author's popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also...
Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors' successful work with...
Now with an extensive introduction to fractal geometry
Revised and updated, Encounters with Chaos and Fractals, Second Edition provides an accessible introduction to chaotic dynamics and fractal geometry for readers with a calculus background. It incorporates important mathematical concepts...
Lectures on NX(p) deals with the question on how NX(p), the number of solutions of mod p congruences, varies with p when the family (X) of polynomial equations is fixed. While such a general question cannot have a complete answer, it offers a good occasion for reviewing various techniques in l-adic...
First developed in the early 1980s by Lenstra, Lenstra, and Lovász, the LLL algorithm was originally used to provide a polynomial-time algorithm for factoring polynomials with rational coefficients. It very quickly became an essential tool in integer linear programming problems and was later...
Designed for mathematics majors and other students who intend to teach mathematics at the secondary school level, College Geometry: A Unified Development unifies the three classical geometries within an axiomatic framework. The author develops the axioms to include Euclidean, elliptic, and...
Bringing the material up to date to reflect modern applications, Algebraic Number Theory, Second Edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. This edition focuses on integral domains, ideals, and unique factorization in the first...
Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page
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NOTES
1.
The study of functions, as we define it here, overlaps substantially with the topic of "algebra" traditionally taught in the United States in ninth grade, though national and many state standards now recommend that aspects of algebra be addressed in earlier grades (as is done in most other countries). Although functions are a critical piece of algebra, other aspects of algebra, such as equation solving, are not addressed in this chapter.
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PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
0 MB
PRODUCT DESCRIPTION
Explores a variety of problem solving strategies that can be applied to everyday mathematical problems. In addressing a variety of problem solving techniques and strategies, each approach is described in detail with examples. Techniques include: Guess and Check; Create a Diagram; Use a Table; Logical Reasoning; Make a Table; Find a Pattern; Work Backwards and Solve an Easier Version
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79,"ASIN":"061880076X","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":4.94,"ASIN":"0446310786","isPreorder":0}],"shippingId":"061880076X::%2B%2FLtyyaRJn2vPHTR1GVULEXh6ya7lTwip6Zt%2FAsJxRQlyT430lyxU0VCAYVILRY4jDHX2jNmcThsKDfI3ymAMa%2BjEoEZaBHp5tnktDd7xB8%3D,0446310786::OKo0Baz7orbLc3YYSMf%2BVGWhR%2BKqTK2L9qTtmczPXm9vXhalmorEc4hSVuo8%2Bg96pxIRJcnzEqLAMYm9ERtxPN%2FrIKe7vDBUbBZaGDs2 text book for my brother, and he loved it! This is a great book for students who are newly entering into middle school. There is a smooth transition b/w chapters and I love how my brother has to think a little harder for answering some challenging problems. I would definitely recommend this book to anyone who is learning pre-algebra.
This math curriculum is SO much better than the connected math we use in our school district. I haven't done math in about thirty years, so I'm going it together with my daughter and it so interesting and well-put together.
I really like it to far. It's very easy to understand and I like that it has a lot of online tools to use. Some of those would be: quizzes, outlines and even games! I would recommend this book to students in middle school or those who have a problem with pre-algebra. I myself am a college student and I am using it to catch up.
The lessons are explained in clear and logical fashion. We have no problems following them. The pages are thin and are good quality. Child is rough on his books, but we have had no tears. This will last for years.
McDougal Littell may have an e-book online as well. We had not checked at the time of the purchase.
I have a daughter who skipped a year in math and went right into pre-algebra in 6th grade. The book was challenging, but clear. It presented new concepts well, and transitioned into each chapter with smooth continuity from the previous. I had to help my daughter with her focus on details and showing all steps but conceptually she did get it. I think the book was great in helping her grasp a full understanding of pre-algebra, which included math 6, a little trig and geometry.
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Curriki Launches Free Interactive, Project-Based Algebra Course
Curriki has launched a free Algebra 1 course that addresses each of the Common Core State Standards. This algebra course was sponsored and funded by AT&T and developed by Curriki. The online project-based modular course pulls in students through real-world examples, engaging projects, interactive Web 2.0 tools, videos and targeted feedback. With its modular design it can be used as a supplementary resource, as the foundation for students' Algebra 1 curriculum, in after-school programs or in a homeschooling environment.
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Problem Solving Tips and Methods
Solving problems in mathematics and other subjects sounds practical.
There are two kinds of problems, routine and not. The solution of routine
problems may be given in class for students to apply. When a problem is
routine, routine solutions should be employed. So routine solution
methods for routine problems should be met and memorized to avoid the
extra work required for solving problems whose solution is not given. The
rule of thumb is a follows.
For Routine Problems, learn and use Routine Methods.
For non-routine problems, be combinatorial, follow strageties, and
try whatever may work, near or far.
There is a need to master or at least identify what problems are
routine. Otherwise, you will spend time in looking for and inventing
solutions for problems whose solutions should routine or automatic.
The Jigsaw Puzzle Approach
Problem solving may be like putting together a jigsaw puzzle. In solving
a jigsaw puzzle, we may begin with the sides as pieces with straight
edeges are fewer in number and must be aligned, after that the more
difficult to place inside pieces may be fitted together. Jigsaw puzzles
may be made more challenging by hiding the picture they are suppose to
form, or by assembling the pieces upside down. That being said, with the
pieces picture side up, we may put try to put them together with trial
and error as needed, but with continuity and drawn shape limiting the
trial and error. This trial and error combination of pieces that go
together may be ad hoc, opportunistic and in general combinatorial. The
trial and error requires persistence. With that, over time, more and more
of the puzzle will be solved until, if all the pieces are present, the
problem is fully solved. Unfortunately, jigsaw puzzle pieces may walk
away over time, so there no guarantee that all the effort made will lead
to complete picture to solve the puzzle. More generally, when we are
tackling a nonrouting problem or puzzle, the existence of solutions is
not always certain.
Text Book Problems and Exercises
For most textbook problems and exercises, all the pieces or elements
needed to solve the problem are likely to be present in the current or
previous chapters. They may just need to be fitted together in ways
similar to the worked problems or examples in the text or course notes.
The similarity will be close for the easiest problems and further for the
more complicated ones. Skill in following textbook patterns may become
routine or almost so with practice, with careful reading of the text or
notes, with care not to forget earlier skills and methods. In senior high
school and college mathematics and mathematical subjects, problem solving
may remain routine and feasible with time and effort to see and master
all the problem solving methods present in notes or a textbook.
Thinking Outside the Box when need-be
What is routine for one is not for another. Experience counts. Where a
student may have to think hard to solve a problem, an older student or an
instructor may tackle a problem based on past experience. Problem solving
may think out of the box or the confines of earlier problem solving
practices, when none of the latter practices apply, Thinking out of the
box means look for new angles or different perspectives for tackling or
addressing the problem. Or, it may involve tackling what appears to be a
related, similar or easier problem in the hope that experience with the
latter will make the original problem addressable. Not all certain. And
for problems from real life, solutions may be routine, solutions may be
difficult to find, or the existence of solutions may be not be known.
Some trial and error may be required with success not always certain for
the original formulation of a problem.
Real World Problems
In real world problems and questions unlike most problems and exercises
in a book, there may be no given pattern to follow. Not all is certain.
Here may be missing pieces or extra pieces, and no guarantee that the
solution can be done.
Preparing to Solve Problems
Master Logic: Again, poblem solving is like putting together a jigsaw
puzzle. In the case of textbook problems, all the pieces are present
and just need to be fitted together following the clues, and an
possible a picture showing the desired result. In the case of real
world problems, there may be missing pieces or extra pieces, and no
guarantee that the solution can be done.
Problem solving besides thinking out of the box and being opportunistic
an combinatorial in looking for clues to use alone or with others
requires precision in reading, writing and figuring. Imprecise logic and
language abilities will lead to difficulties. Precision reading and
writing, and opportunistic trial and error skills for problem solving may
be refined and developed (we hope) by reading the following chapters in
site Volumes 1A and 2.
Implication Rules (Volume 1, Part I, Pattern Based Reason)
chains of reason (Volume 1, Part I, Pattern Based Reason)
longer chains of reason (Volume 1, Part I, Pattern Based Reason)
islands and divisions of knowledge (Volume 1, Part I, Pattern Based
Reason)
painless theorem proving (Volume 2, Three Skills for Algebra)
These appetizers and lessons show how rules and patterns may fit together
to arrive at conclusions or solve SOME problems. Other problems are just
too hard. We can't prevent that.
Master Fractions
Many applied mathematics problems involving chopping and combining
lengths, areas and volumes. So you need to know how to take a
proper or improper fraction of a length, area or volume. You need to
understand that one length may be 2.5 times or 2½ times or
(5/2) times another. Any if you do calculation, you need to do it with
care or at least do it with the knowledge that an error in one step makes
all that follows wrong. The ability to figure well and precisely, so that
you answer is correct, shows or suggests the ability to follow methods,
one step at a time and one step after another in any subject, and in
problem solving as well.
Algebra Word Problems
If your interest is in solving algebra word problems at the high school
level, I would recommend learning how to solve linear equations in
several unknowns in an effortless fashion. High school students who can
solve linear equations in one unknown are often given word problems where
extra variables have to be eliminated to formulate a single equation in
one unknown quantity to solve. The trick here is to draw or extract a
single equation from the given information. But in most such words
problems, it is easier to extract or draw from the given information
several linear equations in several unknowns to solve. Each sentence in
the word problem gives an equation in one or more unknowns or quantities.
Now the algebraic way of writing and thinking can be used to eliminate
variables and to solve for the one or more quantities of interest in an
effortless fashion.
The algebraic solution of linear equations involves the elimination of
variables to obtain say one equation in one unknown. This elimination
process may be better done and recorded with algebraic notation. Going
directly to one equation in one unknown to solve a problem requires more
work to be done with words
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Math is not as daunting as it seems, it's all about following simple rules. Repeated use of these rules builds understanding and confidence. You also must pay attention and be positive of your answers and your mark.
Ad
Steps
1
Pay attention to your teacher. If you're in a fast paced math class, they'll probably only teach a concept once and move on. This means that if you don't pay attention, you've just missed your one chance to learn it.
Ad
2
Do your homework. This will help you understand the concepts more clearly. Your homework will probably be the only time you get to practice what you just learned before a test, so you need to make sure you do it! If you can't attend the class for a day, ask your teacher to give you the homework you missed as soon as possible.
3
Talk to your teacher when you don't understand something. A math class is not a class you want to only think you know what you're doing.
4
Learn the terminology. Knowing what is asked of you is half the problem. Math is its own language (solve, expand, simplify, etc.). Becoming accustomed to this will really benefit you. Highlight key words in the question to ascertain what you need to find out. Attempting past exam papers will give you a feel of what to expect; many of these are available for download from your examination board's website..
5
Buy a good calculator depending on the class you're taking. If you're taking a basic algebra class, a scientific calculator should suffice. If you're taking a calculus class, a graphing calculator will probably be necessary. Your teacher or professor should have a good idea of what's necessary as well, so asking them at the beginning of the term would be a good idea.
6
Know how to use your calculator. It doesn't matter if your calculator has lots of fancy functions; if you don't even know how to add with it, you're wasting all of its features.
7
Sit next to friendly, positive people. These should be people you can turn to when you have a question about something, or don't know what to do for a certain problem. However, make sure they won't just give you the answer.
8
Find extra learning materials. Oftentimes, different sources will be better explaining some things than others. If you can expose yourself to a different explanation of a concept, you may understand something a lot better. Only use "cheat books" to check your answer.
9
Show all your working. Most of the time, your teachers don't care as much about what you put down as an answer as the working that you show. Many will only give partial credit for the correct answer; the rest must be earned by showing your working correctly.
10
Be organized. If you aren't organized, doing all that homework will do nothing to help you. Many times, you think you're organized but to gain a true perspective on whether you are organized or not, ask someone you know that will give you an honest opinion.
Ad
We could really use your help! someone you know has taken the class before you, try talking to them for tips or notes.
Consider taking notes on the lesson if you can keep up with what the teacher is saying. This will help you remember the material better and let you go back if you forget something in time.
Do as many questions as possible, you will eventually see the steps you need to follow to solve particular problem. Going above and beyond and doing more problems than assigned will not only boost your understanding of the concept, but will put you on your teacher's good side.
Try not to forget the formulas. If you revise formulas frequently, it'll be hard to forget them easily, so keep refreshing your memory by studying math often!
Produce formulae flash cards. For example on one side you would write the question "What is the area of a triangle" and on the other side you would have "Width x Height / 2 ". Keep a pile with you and go over them when you find some free time, for instance when you're at the bus stop. In addition, if you have many flash cards, you might want to consider hole punching them and putting them on a ring.
Don't be too shy to ask questions.
Warnings
Don't sit in the back or next to the class clown, unless s/he is helpful
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An Introduction to Mathematical Modeling. A Course in Mechanics. Wiley Series in Computational Mechanics
A modern approach to mathematical modeling, featuring unique applications from the field of mechanics
An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics.
The author streamlines a comprehensive understanding of the topic in three clearly organized sections:
Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equations
Electromagnetic Field Theory and Quantum Mechanics contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory
account of quantum mechanics with related topics including ab initio methods and Spin and Pauli's principles
Statistical Mechanics presents an introduction to statistical mechanics of systems in thermodynamic equilibrium as well as continuum mechanics, quantum mechanics, and molecular dynamics
Each part of the book concludes with exercise sets that allow readers to test their understanding of the presented material. Key theorems and fundamental equations are highlighted throughout, and an extensive bibliography outlines resources for further study.
Extensively class-tested to ensure an accessible presentation, An Introduction to Mathematical Modeling is an excellent book for courses on introductory mathematical modeling and statistical mechanics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering
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Mathematics 1
Covers the parts of calculus and algebra which have proved fundamental to all of mathematics and its applications. It is the first of a pair of courses, MATH1110 and MATH1120, designed to cover a range of mathematical topics of importance to students in the Sciences, Engineering or Commerce.
In algebra, students learn concepts and symbolic manipulation when calculating with large numbers of variables. In calculus, they learn concepts used when working with continuously changing variables. Both ways of thinking are essential in the mathematics met by students in the Sciences, Engineering and Commerce.
This course has a prerequisite, either being - band 5 or better in the NSW HSC course "Mathematics" (Commonly known as "2 unit mathematics") or; - completion of extension 1 or extension 2 mathematics in the NSW HSC or; - completion of at least A Level Mathematics in UK or Singapore CGSE, or; - completion of PSB Foundation Studies Diploma including Engineering Mathematics 1 and Engineering Mathematics 2, or: - a pass in MATH1002 or; - a mark of 10/20 or better in an invigilated sitting of the MATH1110 Math Placement Test*, or; - or equivalent qualifications as approved by the Head of School, School of Mathematical and Physical Sciences.
* Please note that only one attempt at this invigilated quiz is permitted.
Not to be counted for credit with MATH1210.
Available in 2015
Callaghan Campus
Semester 1, Semester 2
UoN Singapore
Trimester 3
Previously offered in 2014
Objectives
At the successful completion fo this course students will have 1. gained the necessary background to study further university level mathematics as required in their program of study. 2. gained mathematical knowledge and skills in the areas of calculus, functions, vectors and complex numbers. 3. improved their analytical ability, in particular their skills at problem-solving.
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Learn Math
Geogebra
Reginaldo J. Santos - Apostilas. Math for Morons like Us - Formula Database. Interactive Differential Equations (IDE) — CODEE. IDE is available, for free, at When we first, in the 1990s, became acquainted with Hubert Hohn and his wonderful interactive illustrations we knew immediately that he had found a real key to making our subject (and many others) come alive--not only for students, but for ourselves and our faculty colleagues.
Hohn is a master educator.
Ordinary Differential Equations - Resources. The sources below are among some of the best locations of sites dedicated to ordinary differential equations, online and on the computer.
General Sources Math Forum: Differential Equations.
Statistics Glossary - paired data, correlation & regression. Paired Sample t-test A paired sample t-test is used to determine whether there is a significant difference between the average values of the same measurement made under two different conditions.
Both measurements are made on each unit in a sample, and the test is based on the paired differences between these two values. The usual null hypothesis is that the difference in the mean values is zero. For example, the yield of two strains of barley is measured in successive years in twenty different plots of agricultural land (the units) to investigate whether one crop gives a significantly greater yield than the other, on average.
Matematica Essencial: Superior: Calculo: Maximos e minimos: Medias aritmetica, geometrica e harmonica. Maths online. GCSE Bitesize - Maths. Video Courses on Academic Earth. On-line Tutorials. Demonstrations Project. Sistema Galileu de Educação Estatística. Matemática. Daniel Kopsas. Daniel Kopsas (pronounced "Copsis") E-mail: kopsasd@otc.edu Office Phone: (417) 447 - 8263 Twitter: I teach mathematics at Ozarks Technical Community College in Springfield, Missouri.
I was inspired by Maria Andersen from Muskegon Community College to create this site and continue to pursue the use of technology in the mathematics classroom. For each of the courses in the sidebar to the left, I have built or I am currently building math video libraries.
Math and Algebra Help - Videos from MathTV.com.
A knowledge of statistics is like a knowledge of foreign languages or of algebra; it may prove of use at any time under any circumstances. - A. L. Bowley Courses[edit]
Statistics - Wikibooks, collection of open-content textbooks. Welcome to the Wikibook of Statistics Statistics - Area of applied mathematics concerned with the data collection, analysis, interpretation and presentation.
Statistics is used in almost every field of research: the discovery of the Higgs particle, social sciences, climate research,... With this, and with its well established foundations, it is very well suited for a wikibook.
All of Statistics. All of Statistics A Concise Course in Statistical Inference by Larry Wasserman Get the book from Springer or Amazon Errata (last updated April 3 2013)
Wolfram MathWorld: The Web's Most Extensive Mathematics Resource. Dynamics of Complex Systems. New England Complex Systems Institute 238 Main Street Suite 319, Cambridge, MA 02142 Phone: 617-547-4100 Fax: 617-661-7711 Textbook for seminar/course on complex systems.View full text in PDF format The study of complex systems in a unified framework has become recognized in recent years as a new scientific discipline, the ultimate of interdisciplinary fields.
Breaking down the barriers between physics, chemistry and biology and the so-called soft sciences of psychology, sociology, economics, and anthropology, this text explores the universal physical and mathematical principles that govern the emergence of complex systems from simple components.
Teacher package: Mathematical Modelling. September 2007 This is the second installment of a new feature in Plus: the teacher package.
Every issue contains a package bringing together all Plus articles about a particular subject from the UK National Curriculum. Whether you're a student studying the subject, or a teacher teaching it, all relevant Plus articles are available to you at a glance.
Watchmath.com.
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Developmental Arithmetic (3-0-3). Credit not applicable toward degrees. Required of students whose ACT Mathematics Main score is less than 15 or COMPASS Math score of 30 or less. Fundamental topics in arithmetic, geometry, and pre-algebra.
099 Developmental Algebra (3-0-3). Credit not applicable toward degrees. Required of students whose ACT Mathematics Main score is at least 15 but less than 19 or COMPASS Math score of 31 to 58. Fundamental topics in algebra for students with insufficient knowledge of high school level mathematics. PR: ACT Mathematics Main score of 15 or grade of "S" in MATH 098.
109 Algebra (3-0-3). Real numbers, exponents, roots and radicals; polynomials, first and second degree equations and inequalities; functions and graphs. PR: ACT Mathematics main score of 19 or grade of "S" in MATH 099.
211 Informal Geometry (3-0-3). Theorems are motivated by using experiences with physical objects or pictures and most of them are stated without proof. Point approach is used with space as the set of all points; review elementary geometry, measurement, observation, intuition and inductive reasoning, distance, coordinate systems, convexitivity, separation, angles, and polygons. No field credit for math majors/minors. PR: MATH 101 or higher.
220 Calculus I (4-0-4). A study of elements of plane analytical geometry, including polar coordinates, the derivative of a function with applications, integrals and applications, differentiation of transcendental functions, and methods of integration. PR: MATH 109 and MATH 110, or GNET 116, or ACT Mathematics main score of 26 or COMPASS Trigonometry score of 46 or above.
250 Discrete Mathematics (3-0-3). Treats a variety of themes in discrete mathematics: logic and proof, to develop students' ability to think abstractly; induction and recursion, the use of smaller cases to solve larger cases of problems; combinatorics, mathematics of counting and arranging objects; algorithms and their analysis, the sequence of instructions; discrete structures, e.g., graphs, trees, sets; and mathematical models, applying one theory to many different problems. PR: MATH 109 and MATH 110 or GNET 116.
290 Topics in Mathematics (1-4 hours credit). Formal course in diverse areas of mathematics. Course may be repeated for different topics. Specific topics will be announced and indicated by subtitle on the student transcript. PR: Consent of instructor.
400 Introduction to Topology (3-0-3). A study of set theory; topological spaces, cartesian products, connectedness; separation axioms; convergences; compactness. Special attention will be given to the interpretation of the above ideas in terms of the real line and other metric spaces. PR: MATH 240.
490 Topics in Mathematics (1-4 hours credit per semester). Advanced formal courses in diverse areas of mathematics. Courses may be repeated for different topics. Specific topics will be announced and indicated by subtitle on transcript. PR: Consent of instructor.
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More About
This Textbook
Overview
This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses.
Editorial Reviews
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A new edition of the classic undergraduate text introducing abstract algebra using concrete examples. The authors ground their explanations with computational and theoretical exercises to develop the student's "power to think for himself," covering topics such as the role of careful proof in algebra, linear algebra as grounded in geometry, groups as expressions of symmetry, and subgroups and subsystems leading to lattice theory. This volume is a corrected version of the 4th edition and is offered by a new publisher
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Algebra Concepts is a tool for introducing many of the difficult concepts that are necessary for success in higher level math courses. This program includes a special feature, the Algebra Tool Kit, wh... More: lessons, discussions, ratings, reviews,...
Algebra Concepts is an interactive learning system designed to provide instruction in mathematics at the 7th grade enrichment through adult levels. The instructional goals for Algebra Concepts include
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College Algebra Demystified
Say goodbye to dry presentations, grueling formulas, and abstract theories that would put Einstein to sleep -- now there's an easier way to master the disciplines you really need to know.
McGraw-Hill's Demystified Series teaches complex subjects in a unique, easy-to-absorb manner, and is perfect for users without formal training or unlimited time. They're also the most time-efficient, interestingly written "brush-ups" you can find.
Organized as self-teaching guides, they come complete with key points, background information, questions at the end of each chapter, and even final exams. You'll be able to learn more in less time, evaluate your areas of strength and weakness and reinforce your knowledge and confidence.
The perfect book for mastering all the essentials of college algebra, with coverage of: the coordinate plane, circles, lines and intercepts, parabolas, nonlinear equations, functions, graphs of functions, exponents and logarithms, and more. less
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About the book:
This introductory text offers an introduction to the topics included on a first year undergraduate course in mathematical economics. Oriented towards the needs of the student, the text is heavily illustrated, providing numerous exercises and examples throughout. The focus on economics is always maintained as maths is not examined for its own sake, but rather for the use it may be to an economist. This concern is reflected in the structure each section takes - it begins by questioning the need for a particular mathematical skill, examines the principles of the topic and then puts the newly acquired skill to work in the context of economics. Special features of this book include its suitability for students with a limited mathematical background, as well as the more capable, student based activities occuring throughout each chapter - to help consolidate learning along with the inclusion of exercises and chapter summaries at the end of each chapter.
Softcover, ISBN 0077074076 Publisher: McGraw-Hill Publishing Co., 0077074076 Publisher: Mcgraw Hill Book Co Ltd, 1991 Mcgraw Hill Book Co Ltd, 1991 McGraw-Hill Publishing Co., 1991 Used - Good. Introductory Mathematical Methods in Economics77074076 Publisher: McGraw-Hill Publishing Co., 1991 Used - Very Good. Introductory Mathematical Methods in Economics77074076 Publisher: Mcgraw Hill Book Co Ltd, 1991 Mcgraw Hill Book Co Ltd, 1991 0077074076 Publisher: McGraw-Hill Publishing Co.,
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Introductory combinatorics
Introductory Combinatorics emphasizes combinatorial ideas, including the pigeon-hole principle, counting techniques, permutations and combinations, ...Show synopsisIntroductory Combinatorics emphasizes combinatorial ideas, including the pigeon-hole principle, counting techniques, permutations and combinations, Polya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, and combinatortial structures (matchings, designs, graphs).Written to be entertaining and readable, this book's lively style reflects the author's joy for teaching the subject. It presents an excellent treatment of Polya's Counting Theorem that doesn't assume the student is familiar with group theory. It also includes problems that offer good practice of the principles it presents. The third edition of Introductory Combinatorics has been updated to include new material on partially ordered sets, Dilworth's Theorem, partitions of integers and generating functions. In addition, the chapters on graph theory have been completely revised
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We all know how important it is to get training and be real professionals. There are lots of ways of being trained but what disadvantage most of them have is that there is no certificate verifying you have been trained! If we are realistic, then we'd better have not attended...
Equations are the formulas needed to solve certain problems for Algebra 1 concepts. They will provide a foundation and reference guide that can be used to assist any student in solving problems. Such equations relate to areas like Linear, Radicals, Absolute Values, Quadratic, Fractions, Exponential and Logarithmic concepts. They provide...
Forensic science is one of the widest programs offered by graduate schools in the United States. There are a lot of choices you can make and choose to specialize in any of them. The higher you go the more specialized you become. You can study forensic psychology, Forensic Computing criminal...
One of the most popular pastimes for many people is to play video games. These entertainment activities have grown and developed in leaps and bounds since the first days of Pong and Pac Man. With the advances in technology that have come along in the gaming world, there has been...
A large number of Christians, who are interested in studying the bible regularly, either as a group or individually, usually ask what constitutes bible study. This article touches on some important factors and ingredients of good bible study classes. Whether the study is for academia or personal knowledge, it is...
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One of the most relaxing places we have found to read a book or study is in wood fired hot tubs. Read about the advantages wood has over plastics for hot tub usage. Especially for those who live in Northern climates, you'll be happy to find out, among other things, that wood is actually a better insulator!
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Math Level H: Linear Equations, Inequalities & Graphing
Students will learn to solve simultaneous linear equations in two to four variables. Concepts of numerical and algebraic value are strengthened. Students are introduced to transforming equations, inequalities, functions and graphs.
Center Updates
2014 Award Ceremony at The Tatnall School 1501 Barley Mill Dr, Wilmington DE 19802 on Saturday November 15th at 11:30 a.m.
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Cranbury PrecalculusStudents who are forced to do hundreds of ?plug and chug? exercises often wind up hating and fearing math. Who can blame them? If you?re given rules to follow, but aren?t shown why the rules make sense, then working a lot of similar problems is just a chore
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Students learn in different ways. Many mathematical concepts require dynamic thinking for deep understanding and this can be challenging for students. The new interactive capabilities of Mathematica help make mathematics come to life. Ideas described in class or illustrated on the chalkboard now may be manipulated directly and can easily demonstrate something that would otherwise take many examples and hand gestures to explain.
I am a high school mathematics teacher, and this summer I had the opportunity to work with Wolfram Research to develop materials for high school students and teachers. In this presentation I will share interactive demonstrations that illustrate concepts from algebra, geometry, trigonometry, and calculus. These examples exhibit several of the new functions coming in the future Mathematica release.
My students also use Mathematica in lessons designed to practice concepts and in their own project presentations. Other ways I use Mathematica with my students include notebooks accompanying lecture notes, materials posted on my website and interactive pages on my a site
Please note that four of my students will also be presenting their work at this conference. Look for the presentation "Mathematica Projects by High School Students" by Ryan Chuang, Samantha Patterson, Jenny Tan, and Jeffrey Tsao.
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Excursions in Modern Mathematics - 7th edition
Summary: Excursions in Modern Mathematics, Seventh Edition, shows readers that math is a lively, interesting, useful, and surprisingly rich subject. With a new chapter on financial math and an improved supplements package, this book helps students appreciate that math is more than just a set of classroom theories: math can enrich the life of any one who appreciates and knows how to use it Very Good 0321568036 Book is not new, but in very good condition. Overall-Minor Wear. Cover is very good with minor-wear. No markings inside. Buy with confidence...customer service is our...show more TOP PRIORITY! Quick Shipping/ Free Delivery Confirmation! ...show less
$7.99Indianapolis Indianapolislight shelf wear. Pages are clean and binding is tight. If applicable, online access, codes or supplements are not guaranteed to be included or work.
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Algebra and Trigonometry
Provides students and instructors with explanations of the mathematical concepts of algebra and trigonometry.Provides students and instructors with explanations of the mathematical concepts of algebra and trigonometry
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Quoted from the site: This Web site contains a page for each section of the book Principles of Calculus Modeling, an...
see more
Quoted from the site: This Web site contains a page for each section of the book Principles of Calculus Modeling, an Interactive Approach. A section page includes a summary of the section, an on-screen applet demonstrating the key point of the section, and what you should know after studying the material of the section. It also includes links to * additional in-depth applets, * worked examples, * videos of problems being worked out by students and teachers, * a quiz (with answers) that you can take to test your knowledge, * a link to a PDF document with of all the exercises of the section, * a link to these same exercises in interactive form with answer feedback, and * hypertext links to other supplementary materials on the Web that you might find useful, such as sample exams.
Quadratic Functions contains two applets that allow the user to change the coefficients of a quadratic equation and observe...
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Quadratic Functions contains two applets that allow the user to change the coefficients of a quadratic equation and observe the change in the corresponding graph. One applet uses the standard form of a quadratic equation to investigate the role of ?a?, ?b?, and ?c?? and the second uses the standard form for a parabola to study the role of ?a?, ?h?, and ?k??.
This applet draws the graph of y = sin(x) along with its Maclaurin polynomial (Taylor polynomial at c=0). The user can...
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This applet draws the graph of y = sin(x) along with its Maclaurin polynomial (Taylor polynomial at c=0). The user can specify the degree of approximating polynomial and then increment it with a push of a button.
Solves and graphically displays the solutions to ordinary differential equations. The user can select from an extensive list...
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Solves and graphically displays the solutions to ordinary differential equations. The user can select from an extensive list of standard "Left Hand" (homogeneous) and "Right Hand" (drive) "Sides" or graphically input a drive function. The user also graphically selects a fixed point of the solution. The solution is updated and displayed in real time as all changes are made.
The interactive WISE Confidence Interval Creation Applet allows instructors to demonstrate how sample size, alpha level, population shape, and variance affect confidence intervals. The user can generate a population distribution of interest or select a distribution from a menu, select a sample size and an alpha level.A press of the 'Sample' button displays a simulated sample and confidence interval for the population mean. The sample mean, standard deviation, and confidence interval are displayed, along with the option to display calculations for the confidence interval limits. Subsequent presses of the 'Sample' button produce new random samples with their associated confidence intervals. Up to 20 confidence intervals are displayed at one time, showing how confidence intervals differ by chance.This applet provides graphic evidence for why it is wrong to say that the population mean falls within a given confidence interval 95% of the time. Rather, 95% of confidence intervals are expected to contain the population mean IF assumptions are met. Manipulations of the population shape and the sample size easily produce situations where the assumption of normality is violated to an extent where standard procedures for constructing confidence intervals are clearly wrong. Students and instructors can have fun playing with the applet and interpreting findings.The applet is linked to a demonstration guide.
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Transitioning to Proofs
One of the challenges in becoming a math major is learning the art of mathematical proof.
It is proof that distinguishes mathematics from other academic disciplines, giving our subject a permanence and transparency which makes mathematics truly timeless. Most students come to college having already exposed to a wide range of logical thinking processes, even if they haven't been aware of them. Being able to phrase and support logical arguments, however, is a skill that takes time and effort to master. As with any new skill, it will be your commitment to frequent and careful practice that will turn this new technique into second-nature.
As you transition into a proof-based class, your best resource is the professor of your class; this person can help you learn to read and write mathematical statements, and they can give you tips on how to approach certain standard proof practices. There are also a number of books which help students understand the basic structure of proofs. This PDF was a short guideline written by Erica Dohring ('14) which gives some ideas for how students might effectively transition into a proofs-based class; it also includes some suggestions for further reading as you explore this exciting new mathematical frontier
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GAUSS in Education
GAUSS in Education
The ideal environment for learning – and leading the way.
"GAUSS, with its interactive programming platform, results in students who are better equipped to explain the theory behind their work, developing and strengthening their analytical skills for future projects"
GAUSS provides students and researchers with the high-end analytical tools needed to solve the complex problems they'll face in both academic and professional careers.
GAUSS: Advantages in education
Interactivity: The highly interactive user interface of GAUSS provides a fully-featured environment with top of the line graphics. This makes it easy to interact with data and models and provides immediate feedback along every step of algorithm development.
Customization: GAUSS has the flexibility to customize models to solve a broader range of problems. This provides the opportunity for students to extend theoretical knowledge to real-world problem solving, empowering students to work in a wide variety of positions and offer more value to future employers. A complete suite of in-house GAUSS Applications are available to provide preprogrammed procedures to help students and professors quickly tackle all computational needs. Also available are GAUSS Application Paks for various industries such as econometrics, finance, etc.
Support: Aptech, the company behind GAUSS, is dedicated to providing superb support and learning tools to facilitate growth from novice to master. Check out our resources page for the latest manuals, tutorials, training events and more.
Academic Discounts / Licenses
In addition to our new GAUSS in the Classroom license, Aptech offers an array of license types to meet the unique needs of its academic customers at a price that works for any budget. Significant academic discounts are available to students and employees at approved educational institutions. Contact us for more information and pricing.
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1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable.
6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).
7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.
8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.
9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.
10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.
11.0 Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.
12.0 Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.
13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques.
14.0 Students solve a quadratic equation by factoring or completing the square.
2.0 Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices.
3.0 Students are adept at operations on polynomials, including long division.
4.0 Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes.
5.0 Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. In particular, they can plot complex numbers as points in the plane.
6.0 Students add, subtract, multiply, and divide complex numbers.
7.0 Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator.
8.0 Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system.
18.0 Students use fundamental counting principles to compute combinations and permutations.
19.0 Students use combinations and permutations to compute probabilities.
20.0 Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers.
21.0 Students apply the method of mathematical induction to prove general statements about the positive integers.
22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series.
23.0 Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series.
24.0 Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions.
25.0 Students use properties from number systems to justify steps in combining and simplifying functions.
AP Probability and Statistics
Objectives:
1.0 Students solve probability problems with finite sample spaces by using the rules for addition, multiplication, and complementation for probability distributions and understand the simplifications that arise with independent events.
2.0 Students know the definition of conditional probability and use it to solve for probabilities in finite sample spaces.
3.0 Students demonstrate an understanding of the notion of discrete random variables by using this concept to solve for the probabilities of outcomes, such as the probability of the occurrence of five or fewer heads in 14 coin tosses.
4.0 Students understand the notion of a continuous random variable and can interpret the probability of an outcome as the area of a region under the graph of the probability density function associated with the random variable.
5.0 Students know the definition of the mean of a discrete random variable and can determine the mean for a particular discrete random variable.
6.0 Students know the definition of the variance of a discrete random variable and can determine the variance for a particular discrete random variable.
7.0 Students demonstrate an understanding of the standard distributions (normal, binomial, and exponential) and can use the distributions to solve for events in problems in which the distribution belongs to those families.
8.0 Students determine the mean and the standard deviation of a normally distributed random variable.
9.0 Students know the central limit theorem and can use it to obtain approximations for probabilities in problems of finite sample spaces in which the probabilities are distributed binomially.
10.0 Students know the definitions of the mean, median, and mode of distribution of data and can compute each of them in particular situations.
11.0 Students compute the variance and the standard deviation of a distribution of data.
15.0 Students are familiar with the notions of a statistic of a distribution of values, of the sampling distribution of a statistic, and of the variability of a statistic.
16.0 Students know basic facts concerning the relation between the mean and the standard deviation of a sampling distribution and the mean and the standard deviation of the population distribution.
17.0 Students determine confidence intervals for a simple random sample from a normal distribution of data and determine the sample size required for a desired margin of error.
18.0 Students determine the P- value for a statistic for a simple random sample from a normal distribution.
19.0 Students are familiar with the chi- square distribution and chi- square test and understand their uses.
Calculus
Objectives:
1.0 Students demonstrate knowledge of both the formal definition and the graphical interpretation of limit of values of functions. This knowledge includes one-sided limits, infinite limits, and limits at infinity. Students know the definition of convergence and divergence of a function as the domain variable approaches either a number or infinity.
2.0 Students demonstrate knowledge of both the formal definition and the graphical interpretation of continuity of a function.
3.0 Students demonstrate an understanding and the application of the intermediate value theorem and the extreme value theorem.
4.0 Students demonstrate an understanding of the formal definition of the derivative of a function at a point and the notion of differentiability.
5.0 Students know the chain rule and its proof and applications to the calculation of the derivative of a variety of composite functions.
18.0 Students know the definitions and properties of inverse trigonometric functions and the expression of these functions as indefinite integrals.
19.0 Students compute, by hand, the integrals of rational functions by combining the techniques in standard 17.0 with the algebraic techniques of partial fractions and completing the square.
20.0 Students compute the integrals of trigonometric functions by using the techniques noted above.
21.0 Students understand the algorithms involved in Simpson's rule and Newton's method. They use calculators or computers or both to approximate integrals numerically.
22.0 Students understand improper integrals as limits of definite integrals.
23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges.
24.0 Students understand and can compute the radius (interval) of the convergence of power series.
25.0 Students differentiate and integrate the terms of a power series in order to form new series from known ones.
26.0 Students calculate Taylor polynomials and Taylor series of basic functions, including the remainder term.
27.0 Students know the techniques of solution of selected elementary differential equations and their applications to a wide variety of situations, including growth-and-decay problems.
Geometry
Objectives:
1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.
2.0 Students write geometric proofs, including proofs by contradiction.
3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement.
11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.
12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems.
13.0 Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles.
14.0 Students prove the Pythagorean theorem.
15.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.
16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line.
17.0 Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles.
18.0 Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan(x) = sin(x)/cos(x), (sin(x))2 + (cos(x)) 2 = 1.
19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.
20.0 Students know and are able to use angle and side relationships in problems with special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90° triangles.
22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.
Linear Algebra
Objectives:
1.0 Students solve linear equations in any number of variables by using Gauss-Jordan elimination.
2.0 Students interpret linear systems as coefficient matrices and the Gauss-Jordan method as row operations on the coefficient matrix.
3.0 Students reduce rectangular matrices to row echelon form.
4.0 Students perform addition on matrices and vectors.
5.0 Students perform matrix multiplication and multiply vectors by matrices and by scalars.
6.0 Students demonstrate an understanding that linear systems are inconsistent (have no solutions), have exactly one solution, or have infinitely many solutions.
7.0 Students demonstrate an understanding of the geometric interpretation of vectors and vector addition (by means of parallelograms) in the plane and in three-dimensional space.
8.0 Students interpret geometrically the solution sets of systems of equations. For example, the solution set of a single linear equation in two variables is interpreted as a line in the plane, and the solution set of a two-by-two system is interpreted as the intersection of a pair of lines in the plane.
9.0 Students demonstrate an understanding of the notion of the inverse to a square matrix and apply that concept to solve systems of linear equations.
10.0 Students compute the determinants of 2 x 2 and 3 x 3 matrices and are familiar with their geometric interpretations as the area and volume of the parallelepipeds spanned by the images under the matrices of the standard basis vectors in two-dimensional and three-dimensional spaces.
11.0 Students know that a square matrix is invertible if, and only if, its determinant is nonzero. They can compute the inverse to 2 x 2 and 3 x 3 matrices using row reduction methods or Cramer's rule.
12.0 Students compute the scalar (dot) product of two vectors in n- dimensional space and know that perpendicular vectors have zero dot product.
2.0 Students are adept at the arithmetic of complex numbers. They can use the trigonometric form of complex numbers and understand that a function of a complex variable can be viewed as a function of two real variables. They know the proof of DeMoivre's theorem.
3.0 Students can give proofs of various formulas by using the technique of mathematical induction.
4.0 Students know the statement of, and can apply, the fundamental theorem of algebra.
5.0 Students are familiar with conic sections, both analytically and geometrically.
6.0 Students find the roots and poles of a rational function and can graph the function and locate its asymptotes.
8.0 Students are familiar with the notion of the limit of a sequence and the limit of a function as the independent variable approaches a number or infinity. They determine whether certain sequences converge or diverge.
2.0 Students know the definition of conditional probability and use it to solve for probabilities in finite sample spaces.
3.0 Students demonstrate an understanding of the notion of discrete random variables by using them to solve for the probabilities of outcomes, such as the probability of the occurrence of five heads in 14 coin tosses.
4.0 Students are familiar with the standard distributions (normal, binomial, and exponential) and can use them to solve for events in problems in which the distribution belongs to those families.
5.0 Students determine the mean and the standard deviation of a normally distributed random variable.
6.0 Students know the definitions of the mean, median, and mode of a distribution of data and can compute each in particular situations.
7.0 Students compute the variance and the standard deviation of a distribution of data.
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Schaum's Outline of Trigonometry - 3rd edition
Summary: Updated to match the emphasis in today's courses, this clear study guide focuses entirely on plane trigonometry. It summarizes the geometry properties and theorems that prove helpful for solving trigonometry problems. Also, where solving problems requires knowledge of algebra, the algebraic processes and the basic trigonometric relations are explained carefully. Hundreds of problems solved step by step speed comprehension, make important points memorable, and teach p...show moreroblem-solving skills. Many additional problems with answers help reinforce learning and let students gauge their progress as they go. ...show less
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Elementary & Intermediate Algebra, CourseSmart eTextbook, 2nd Edition
Description
Using authentic data to make math meaningful to students, Jay Lehmann's algebra series uses a curve-fitting approach to model compelling, real-world situations, while answering the perennial question "But what is this good for?" Beginning with interesting data sets, students are asked to find models and derive equations to fit a scenario, helping them to understand functions graphically, numerically, and symbolically. Updated exercises, labs, and graphs deepen students' understanding of core concepts and keeps them motivated to learn.
Teaching and Learning Experience
This program provides a better learning experience–for you and your students. Here's how:
Personalized learning with MyMathLab: Additionally, MyMathLab® provides a wide range of homework, tutorial, and assessment tools that make it easy to manage your course in any setting.
A curve-fitting approach incorporates brand-new data sets, an emphasis on modeling, and teaching tools that lead students through the text and build a foundation for statistical thinking.
Strong pedagogical tools build students skills–updatedactivities, exercises, and labs emphasize mathematical reasoning and highlight the text's core features, all designed to help students understand and retain skills.
Table of Contents
Preface
Acknowledgments
Index of Applications
1. Introduction To Modeling
1.1 Variables And Constants
1.2 Scattergrams
1.3 Exact Linear Relationships
1.4 Approximate Linear Relationships
Taking It To The Lab: Climate Change Lab * Volume Lab * Linear
Graphing Lab: Topic Of Your Choice
Chapter Summary
Key Points Of Chapter 1
Chapter 1 Review Exercises
Chapter 1 Test
2. Operations And Expressions
2.1 Expressions
2.2 Operations With Fractions
2.3 Adding Real Numbers
2.4 Change In A Quantity And Subtracting Real Numbers
2.5 Ratios, Percents, And Multiplying And Dividing Real Numbers
2.6 Exponents And Order Of Operations
Taking It To The Lab: Climate Change Lab * Stocks Lab
Chapter Summary
Key Points Of Chapter 2
Chapter 2 Review Exercises
Chapter 2 Test
Cumulative Review Of Chapters 1 And 2
3. Using Slope To Graph Linear Equations
3.1 Graphing Equations Of The Form y = mx + b
3.2 Graphing Linear Models; Unit Analysis
3.3 Slope Of A Line
3.4 Using Slope To Graph Linear Equations
3.5 Rate Of Change
Taking It To The Lab: Climate Change Lab * Workout
Lab * Balloon Lab
Chapter Summary
Key Points Of Chapter 3
Chapter 3 Review Exercises
Chapter 3 Test
4. Simplifying Expressions And Solving Equations
4.1 Commutative, Associative, And Distributive Laws
4.2 Simplifying Expressions
4.3 Solving Linear Equations In One Variable
4.4 Solving More Linear Equations In One Variable
4.5 Comparing Expressions And Equations
4.6 Formulas
Chapter Summary
Key Points Of Chapter 4
Chapter 4 Review Exercises
Chapter 4 Test
Cumulative Review Of Chapters 1—4
5. Linear Functions And Linear Inequalities In One Variable
5.1 Graphing Linear Equations
5.2 Functions
5.3 Function Notation
5.4 Finding Linear Equations
5.5 Finding Equations Of Linear Models
5.6 Using Function Notation With Linear Models To Make Estimates And Predictions
5.7 Solving Linear Inequalities In One Variable
Taking It To The Lab: Climate Change Lab * Golf Ball Lab *
Rope Lab * Shadow Lab * Linear Lab: Topic Of Your Choice
Chapter Summary
Key Points Of Chapter 5
Chapter 5 Review Exercises
Chapter 5 Test
6. Systems Of Linear Equations And Systems Of Linear Inequalities
6.1 Using Graphs And Tables To Solve Systems
6.2 Using Substitution To Solve Systems
6.3 Using Elimination To Solve Systems
6.4 Using Systems To Model Data
6.5 Perimeter, Value, Interest, And Mixture Problems
6.6 Linear Inequalities In Two Variables; Systems Of Linear
Inequalities In Two Variables
Taking It To The Lab: Climate Change Lab * Sports Lab *
Truck Lab
Chapter Summary
Key Points Of Chapter 6
Chapter 6 Review Exercises
Chapter 6 test 383
Cumulative Review of Chapters 1—6
7. Polynomial Functions And Properties Of Exponents
7.1 Adding And Subtracting Polynomial Expressions And Functions
7.2 Multiplying Polynomial Expressions And Functions
7.3 Powers Of Polynomials; Product Of Binomial Conjugates
7.4 Properties Of Exponents
7.5 Dividing Polynomials: Long Division And Synthetic Division
Taking It To The Lab: Climate Change Lab * Projectile Lab
Chapter Summary
Key Points Of Chapter 7
Chapter 7 Review Exercises
Chapter 7 Test
Making Sure You're Ready For Intermediate Algebra:
A Review Of Chapters 1—7
8. Factoring Polynomials And Solving Polynomial Equations
8.1 Factoring Trinomials Of The Form x2 + bx + c And Differences of Two Squares
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Excursions in Modern Mathematics -Std. Resource Gd - 7th edition
Summary: In addition to the worked-out solutions to odd-numbered exercises from the text, this guide contains selected hints that point the reader in one of many directions leading to a solution and keys to student success, including lists of skills that will help prepare for the chapter examsTextbooksPro Dayton, OH
7
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Bowdon Junction CalculusFrequently used Microsoft PowerPoint during MBA coursework. Can help you use templates, create appealing transitions, and link or embed various items. Tutored Prealgebra topics during high school and college.
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Student Solutions Manual for Larson/Hostetler/Edwards' Algebra and Trigonometry: A Graphing Approach and Precalculus: A Graphing Approach
Summary
This manual offers step-by-step solutions for odd-numbered text exercises and for all items in the Chapter and Cumulative Tests, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer. It also provides practice tests with answers.
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Learning Exercise
This assignment was created by Nicole McGlashan of Huron High School, Huron, South Dakota. It describes a self-directed activity for students to practice finding the transformations of functions by comparing the function to the graph of the intial function. There is a link to the National Library of Virtual Manipulatives for Interactive Mathematics and Larry Green's interactive website that the students participate in.
After having completed this lesson the student should be able to determine the initial graph of a function and be able to determine the transformations of its graph that result from transformations of the function.
Text of Learning Exercise:
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Unit tangent, normal, binormal vectors, osculating, rectifying, normal planes, Frenete (TNB) frame.
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Six failed attempts in the Hairy Ball theorem, non vanishing tangent vector field with one cowlick.
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9780534495015
ISBN:
053449501X
Pub Date: 2005 Publisher: Brooks/Cole
Summary: An increasing number of computer scientists from diverse areas are using discrete mathematical structures to explain concepts and problems. Based on their teaching experiences, the authors offer an accessible text that emphasizes the fundamentals of discrete mathematics and its advanced topics. This text shows how to express precise ideas in clear mathematical language. Students discover the importance of discrete ma...thematics in describing computer science structures and problem solving. They also learn how mastering discrete mathematics will help them develop important reasoning skills that will continue to be useful throughout their careers.
Schlipf, John is the author of Discrete Mathematics For Computer Science With Student Solutions Manual on CDROM, published 2005 under ISBN 9780534495015 and 053449501X. Three hundred sixteen Discrete Mathematics For Computer Science With Student Solutions Manual on CDROM textbooks are available for sale on ValoreBooks.com, fifty seven used from the cheapest price of $44.45, or buy new starting at $78.18
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Weston, MA PrecalculusAt the introductory level, it might be called "finite" math and include topics important for business majors, such as probability, linear programming (optimization), and matrices. Higher level courses might deal with information theory, logic, graph theory, and operations research. Before taking on a discrete math student, I need to get some idea of what level they are studying
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Books
Mathematics for the Liberal Arts provides a comprehensible and precise introduction to modern mathematics intertwined with the history of mathematical discoveries. The book discusses mathematical ideas in the context of the unfolding story of human thought and highlights the application of mathematics in everyday life.
Divided into two parts, Mathematics for the Liberal Arts first traces the history of mathematics from the ancient world to the Middle Ages, then moves on to the Renaissance and finishes with the development of modern mathematics. In the second part, the book explores major topics of calculus and number theory, including problem-solving techniques and real-world applications. This book emphasizes learning through doing, presents a practical approach, and features:
A detailed explanation of why mathematical principles are true and how the mathematical processes work
Numerous figures and diagrams as well as hundreds of worked examples and exercises, aiding readers to further visualize the presented concepts
Various real-world practical applications of mathematics, including error-correcting codes and the space shuttle program
Vignette biographies of renowned mathematicians
Appendices with solutions to selected exercises and suggestions for further reading
Mathematics for the Liberal Arts is an excellent introduction to the history and concepts of mathematics for undergraduate liberal arts students and readers in non-scientific fields wishing to gain a better understanding of mathematics and mathematical problem-solving skills.
Address:
Published features on StatisticsViews.com are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS) to whom Wiley and StatisticsViews.com express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek and Lance Mitchell.
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Mathematics Upper-Secondary 4 - Distributions and Integration
The second part of our intermediate math course continues our free online maths suite of courses. It covers binomial, normal and hypergeometric distribution, discrete random variables, and integration. This course is ideal for students preparing for an exam, or for those wanting to refresh their knowledge of mathematics completion of this course you will understand the meaning of random variables and be able to calculate the dicrete probability distribution of a set of random variables, continuous random variables and normal distribution. You will gain a good knowledge of binomial probability function, distribution, hypergeometric distribution, rules of integration and intergration applications. This course will help you to understand these calculations in an easy, step-by-step processHypergeometric distribution This free online course covers topics related to the hypergeometric distribution and calculating the mean and variance of hypergeometric distributions
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Algebra, Discrete Mathematics and Number Theory
The field of algebra, discrete mathematics, and number theory encompasses one of the primary branches of pure mathematics. Problems in this field often arise (or follow naturally from) a problem that is easily stated involving counting, divisibility, or some other basic arithmetic operation. While many of the problems are easily stated, the techniques used to attack these problems are some of the most difficult and advanced in mathematics. Algebra, discrete mathematics, and number theory have seen somewhat of a renaissance in the past couple of decades with Andrew Wiles' proof of Fermat's Last Theorem, the increasing need for more advanced techniques in cryptography and coding theory arising from the internet, as well as surprising applications in areas such as particle physics and mathematical biology. Algebra, discrete mathematics, and number theory have been featured in the motion picture Good Will Hunting, the play Fermat's Last Tango, as well as numerous episodes of the CBS hit drama Numb3rs.
Curriculum
The core courses of an algebra, discrete mathematics, and number theory concentration are matrix analysis (853) and abstract algebra I and II (851-52). Matrix analysis is a basic course in linear algebra dealing with topics such as similarity of matrices, eigenvalues, and canonical forms just to name a few. Abstract algebra I and II abstract the familiar structures of the integers, rational numbers, matrices, etc. into the concepts of groups, rings, fields, and modules. One also studies one of the crowning achievements of the subject, Galois theory. In addition to the department's broad course requirements, it is expected a student in algebra, discrete mathematics, and number theory will gain a deeper level of understanding of each of the concentrations listed below as well as taking significant advanced courses in that student's particular concentration.
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Career Research
GED Math: Algebra, Geometry & Arithmetic
This GED Math: Algebra, Geometry, & Arithmetic course prepares you for the Math section of the General Education Development (GED) tests. Watch math video lessons and learn about algebra, geometry, number sense, and arithmetic. These lessons are just a portion of our online GED video lessons.
About this Course
Study the basic operations of addition, subtraction, multiplication, and division and explore more advanced branches of mathematics through the GED Math: Algebra, Geometry & Arithmetic course. Through our brief video lessons, you'll learn to graph 1- and 2-variable inequalities, calculate mean and median, and measure volume. Our team of experienced, professional educators also will teach you to define zero and negative exponents, execute the Pythagorean theorem and use the FOIL method. This course can prepare you for the math portion of the new GED exam.
Course Topics
Category
Objectives
Foundations and Linear Equations
Learn about the different types of numbers, parts of a graph, and linear equations. Also, take a look at intercepts, standard form, and systems of equations.
Matrices and Absolute Value
Study how to take a determinant of a matrix, evaluate an absolute value expression, and how to graph an absolute value.
Inequalities
Find out about inequalities, including how to graph 1- and 2-variable inequalities. Additionally, learn about set notation, compound inequalities, and systems of inequalities.
Factoring with FOIL, Graphing Parabolas and Solving Quadratics
Discover parabolas. Learn about using FOIL and the area method.
Complex Numbers
Study imaginary numbers and learn to work with complex numbers.
Exponents and Polynomials
Examine the five main exponent properties, how to define zero and negative exponents, how to graph cubics, quartics and quintics, how to work with polynomials, and using long and synthetic division to solve polynomial equations.
Study exponential functions and logarithms, including working with practice problems.
Probability Mechanics
Find out about factorials and binomial theorem.
Sequences and Series
Take a look at mathematical sequences, summation notation, and mathematical series. Learn to classify arithmetic and geometric sequences.
Functions
Study functions in order to identify them. Also, take a look at transformations, domain and range in a function, inverse functions and applying function operations.
Arithmetic
Explore the number line to learn about absolute values, addition, subtraction, multiplication, and division. Also work with exponents and finding the square root.
Solving Math Word Problems
Learn about the vocabulary used in word problems, using multiple steps to solve a word problem and increasing your understanding of a word problem through personalization.
Math Expressions and Formulas
Find out about parenthesis in math, the order of operations and the correct way to write math problems.
Decimals and Fractions
Study decimals and how to add, subtract, multiply, and divide them. Learn about estimating and fractions, too.
Ratios, Percents & Proportions
Take a look at ratios and rates, proportion, percents, and solving problems that include these things.
Data, Statistics, and Probability
Learn about probability of independent and dependent events, calculating mean, median, mode, and range, and working with tables, schedules, bar graphs and pie charts.
Measurement and Geometry
Study standards units of measure, the metric system, points, lines, and angles. Also learn about parallel, perpendicular, and transversal lines, the properties of shapes, the Pythagorean theorem, and how to measure volume.
GED (General Educational Development) is a registered trademark of the GED Testing Service, which is not affiliated with Education Portal.
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ISBN: 0130084514 / ISBN-13: 9780130084514
Linear Algebra
This book presents a treatment of principal topics of linear algebra and illustrates the importance of the subject through a variety of applications. ...Show synopsisThis book presents a treatment of principal topics of linear algebra and illustrates the importance of the subject through a variety of applications. The topics include vector spaces, linear transformations and matrices, elementary matrix operations and systems of linear equations, determinants, diagonalization, inner product spaces, canonical forms. In addition there are applications to differential equations, economics, geometry, physics and probability. The second edition uses Gaussian elimination instead of Gauss-Jordan method, reduces the dependence of direct sums, shortens and reorganizes the coverage of diagonalization, develops unitary diagonalization via Schur's theorem as opposed to the more abstract invariant subspaces, interchanges canonical forms and inner product spaces, and features a new subsection which develops motions in the plane.Hide synopsis
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Description:New. 0130084514 Premium Publisher Direct Books are Like New or...New. 0130084514 0130084514 New Condition *** Right Off the Shelf | Ships...New. 0130084514
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La Marque AlgebraMath is progressive, that is one needs to have a firm grasp on previous math instruction in order to progress successfully in later math courses. This is especially true of calculus and its foundation of algebra. For instance, if one has a complicated fraction, it may be nearly impossible to fi
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The cornerstone of Elementary Linear Algebra is the authors' clear, careful, and concise presentation of material--written so that students can fully understand how mathematics works. This program balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system.The Sixth Edition incorporates up-to-date coverage of Computer Algebra Systems (Maple/MATLAB/Mathematica); additional support is provided in a corresponding technology guide. Data and applications also reflect current statistics and examples to engage students and demonstrate the link between theory and practice.
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Companion Products
Product Description
The Student Workbook is designed for additional students using the sold-separately AGS Math Pre-Algebra Homeschool Curriculum, and provides the reinforcement and practice necessary for students to master Pre-Algebra. Workbook pages are clearly linked to the chapter and lesson in the student text for easy usage. Examples and a variety of problems are included with short directions. 122 non-reproducible pages, softcover.
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Rest Haven, GA Geometry a very powerful tool in multiple situations, so it's well worth the effort to make it work for you. Repeat - work for you - not scare you. Algebra 2 kicks in with much more powerful analysis tools to describe and evaluate real-life situations in hundreds of scientific disciplinesT. She
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Assets= Liabilities + Owners Equity. The understanding and comprehension of this equation is fundamental to grasping the concepts and principles of accounting. Concepts that I can share my expertise are:
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Product Details
Stock #
13902
ISBN #
Published
Pages
375
Grades
See What's Inside
Product Description
By Timothy Craine, Rheta Rubenstein
This PDF file presents the full text of Understanding Geometry for a Changing World, 71st Yearbook (2009) in a downloadable file that preserves the design and layout of the book while allowing users to search and print selected pages.
Please see Related Products below for individual chapter downloadsGeometry is currently enjoying a revival, partly as a result of the emergence of interactive geometry software. Articles in this yearbook examine expanding visions of geometry, the latest thinking about the development of students' geometric learning, and new perspectives on effective practices for teaching geometry in elementary through high school. The yearbook includes a CD with lessons, activity sheets, application files, video clips, and Web links.
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One of a series of books that support NCTM's Focus in High School Mathematics: Reasoning and Sense Making by providing additional guidance for making reasoning and sense making part of the mathematics experiences of all high school students every dayThis book is a collection of the best of NCTM's Addenda series, grades 5-8 and includes problems and examples that represent critical content for today's middle school curriculum. The problems focus on the four key practices:
• Roles of representation • Generalization • Problem solving • Connections in mathematics learning and teaching
This book has More4U, which includes additional resources online. Download activities, classroom materials, and blackline masters. Look inside book for access code
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Mathematical Curve Conjectures In this write-pair-share activity, a six-foot length of nylon rope is suspended at both ends to model a mathematical curve known as the hyperbolic cosine.
Partial Derivatives: Geometric Visualization This write-pair-share activity presents Calculus III students with a worksheet containing several exercises that require them to find partial derivatives of functions of two variables.
Riemann Sums and Area Approximations After covering the standard course material on area under a curve, Riemann sums and numerical integration, Calculus I students are given a write-pair-share activity that directs them to predict the best area approximation methods for each of several different functions.
U.S. Population Growth: What Does the Future Hold? Students are presented with a ConcepTest, a Question of the Day and a write-pair-share activity involving U.S. population growth. The results are quite revealing and show that while students may have learned how to perform the necessary calculations, their conceptual understanding concerning exponential growth may remain faulty.
Volumes of Solids of Revolution This write-pair-share activity presents Calculus II students with a worksheet containing several exercises that require them to find the volumes of solids of revolution using disk, washer and shell methods and to sketch three-dimensional representations of the resulting solids.
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Drug Calculations Online for Calculate with Confidence - 4th edition
Summary: Incorporating the ratio and proportion, formula, and dimensional analysis methods, this online course presents a step-by-step approach to the calculation and administration of drug dosages. This Drug Calculations Online course is designed to be used with the 4th edition of Gray: Calculate with Confidence.Once students have read topics in the text, the online course provides them an opportunity for application and practice.Animations, voice-overs, and interactive self-assessment activ...show moreities are used to provide an engaging and interactive course platform for students.This course includes practice problems to promote active learning and quizzes that instructors can use to evaluate students understanding of content presented in the course.A comprehensive test bank of approximately 300 questions is also provided for instructors to build quizzes and test. Includes three major drug calculation methods (ratio and proportion, formula (2 types) and dimensional analysis) to give students the option of choosing the method which works best for them. Each module is organized by topic sections that include an overview, objectives, a reading assignment for the topic being covered, example problems, practice problems, and one or more quizzes. Follows recommendations from the Joint Commission on Accreditation of Healthcare Organizations (JCAHO) and the Institute for Safe Medication Practices (ISMP) for use of acceptable abbreviations and dose designations. Many of the math practice problems include a tutorial for each of the three drug calculation methods. When one of the solution buttons is chosen, a step-by-step tutorial to solving the problem in the method chosen is initiated for the student to view. Animations are used throughout this course to demonstrate various concepts related to dosage calculation and drug administration. Some animations will require student participation such as using the mouse to move the plunger on a syringe. Interactive self-assessment activities related to various topic areas are incorporated throughout the course to allow the student to apply their knowledge in context.Voice-overs are used throughout the course to enhance the step-by-step explanation of medication administration procedures and the drug calculation methods demonstrated throughout the course. Quizzes are included within each module that instructors can use to evaluate students understanding of all the major topics covered in that particular module. A comprehensive test bank of approximately 300 questions, organized by module, will be provided for instructors to build quizzes and tests. Terminology is defined within the content for easy reference. Provides the latest drug administration techniques and devices and detailed explanation of the various forms of administering drugs, including oral, intravenous, intra-muscular, subcutaneous and other routes used in drug administration. This allows the student to become more knowledgeable about the specifics of each technique. Includes the most up-to-date, commonly used drugs so students have exposure to what is being used in the real world of clinical practice. Presents information on infusion pumps (enteral, single, multi-channel, PCA and insulin) to help students understand their increased use in drug administration. Drug Calculations Online to accompany Calculate with Confidence is a NEW drug calculations online course
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High School Pre-Calculus Tutor
9780878919109
ISBN:
0878919104
Publisher: Research & Education Assn
Summary: Algebra * Biology * Chemistry * Earth Science Geometry * Physics * Pre-Algebra * Pre-Calculus * Probability Trigonometry * Math Skills for SAT * Verbal Skills for SAT "With the Tutor Books, it's Easy to learn difficult subjects." The best help in preparing for homework and exams Includes every type of problem that may be assigned by your teacher or given on a test Guides you by working out problems in step-by-step de...tail Each "Tutor" helps you understand the subject fully, no matter which textbook you use.
Fogiel, M. is the author of High School Pre-Calculus Tutor, published under ISBN 9780878919109 and 0878919104. One hundred nine High School Pre-Calculus Tutor textbooks are available for sale on ValoreBooks.com, fifty six used from the cheapest price of $0.01, or buy new starting at $12.46.[read more]
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In the spatial or spatio-temporal context, specifying the correct covariance function is fundamental to obtain efficient predictions, and to understand the underlying physical process of interest. This book focuses on covariance and variogram functions, their role in prediction, and appropriate choice of these functions in applications. Both recent... more...
Among the group of physics honors students huddled in 1957 on a Colorado mountain watching Sputnik bisect the heavens, one young scientist was destined, three short years later, to become a key player in America's own top-secret spy satellite program. One of our era's most prolific mathematicians, Karl Gustafson was given just two weeks to... more...
This book concerns the origins of mathematical problem solving at the internationally active Osram and Telefunken Corporations during the golden years of broadcasting and electron tube research. The woman scientist Iris Runge, who received an interdisciplinary education at the University of Gottingen, was long employed as the sole mathematical authority... more...
The 16th-Century intellectual Robert Recorde is chiefly remembered for introducing the equals sign into algebra, yet the greater significance and broader scope of his work is often overlooked. This book presents an authoritative and in-depth analysis of the man, his achievements and his historical importance. This scholarly yet accessible work examines... more...
This book summarizes the results of various models under normal theory with a brief review of the literature. Statistical Inference for Models with Multivariate t-Distributed Errors : Includes a wide array of applications for the analysis of multivariate observations Emphasizes the development of linear statistical models with applications to... more...
Plot graphs, solve equations, and write code in a flash! If you work in a STEM field, chances are you'll be using MATLAB on a daily basis. MATLAB is a popular and powerful computational tool and this book provides everything you need to start manipulating and plotting your data. MATLAB has rapidly become the premier data tool, and MATLAB For Dummies... more...
Multiple factor analysis (MFA) enables users to analyze tables of individuals and variables in which the variables are structured into quantitative, qualitative, or mixed groups. Written by the co-developer of this methodology, Multiple Factor Analysis by Example Using R brings together the theoretical and methodological aspects of MFA. It also... more...
This book has been prepared to help psychiatrists expand their knowledge of statistical methods and fills the gaps in their applications as well as introduces data analysis software. The book emphasizes the classification of fundamental statistical methods in psychiatry research that are precise and simple. Professionals in the field of mental health... more...
Obtain the Best Estimate of a Strongly Scattering Object from Limited Scattered Field Data
Introduction to Imaging from Scattered Fields presents an overview of the challenging problem of determining information about an object from measurements of the field scattered from that object. It covers widely used approaches to recover information... more...
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9780470432051When it comes to learning linear algebra, engineers trust Anton. The tenth edition presents the key concepts and topics along with engaging and contemporary applications. The chapters have been reorganized to bring up some of the more abstract topics and make the material more accessible. More theoretical exercises at all levels of difficulty are integrated throughout the pages, including true/false questions that address conceptual ideas. New marginal notes provide a fuller explanation when new methods and complex logical steps are included in proofs. Small-scale applications also show how concepts are applied to help engineers develop their mathematical reasoning.
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Mathematica/C Online Resources
This page contains links to online educational resources designed for
use with the Mathematica/C version of Introduction to Scientific
Programming by Joseph L. Zachary.
Diskette
The diskette that is included with the textbook includes a Mathematica
notebook for each chapter that contains Mathematica code, the custom
Mathematica library that is exploited in the book, and the complete
implementation of every C program that appears in the book. The
Mathematica material is formatted for both Mathematica 2.2 and
Mathematica 3.0.
Browse
the contents of the diskette and retrieve individual components.
Upgraded Mathematica Libraries
We have upgraded the Mathematica libraries contained on the diskette
to support some of the Mathematica notebooks described in the next
section. If you use those notebooks, you will need to obtain new
versions of the libraries. You can
Tutorial Material
A suite of laboratory materials is being developed to accompany the
text, including HTML-based tutorials enhanced with Java applets and
Mathematica notebooks. The tutorials can be used with any
Java-capable Web browser; the notebooks are available for use with
both Mathematica 2.2 and 3.0.
Check this page frequently. During the latter part of 1997 and the
early part of 1998, new laboratory materials will appear regularly.
The entries that appear below without links indicate places where work
on laboratory materials is in progress.
Computational Science
Applet that animates the orbits of Earth and Mars.
Population Density: Computational Properties of Numbers
Notebook that gives a brief introduction to the use of
Mathematica notebooks.
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The family in this book is moving to a new neighborhood. They have a lot of work to do! They need to unload the moving truck, unpack boxes, and put everything away. The kids make new friends and discover all the fun they can have with the empty boxes. While building forts from the empty packing boxes, the kids discover many new shapes and their dimensions.... more...
egghead's Guide to Geometry will help students improve their understanding of the fundamental concepts of geometry. With the help of Peterson's new character, egghead, students can strengthen their math skills with narrative cartoons and graphics. Along the way there are plenty of study tips and exercises, making this the perfect guide for students... more...
The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characterizes both euclidean and hyperbolic geometry with respect to natural properties of (general) translations and general distances of X. Also for these spaces X, it studies... more...
This book mainly deals with the Bochner–Riesz means of multiple Fourier integral and series on Euclidean spaces. It aims to give a systematical introduction to the fundamental theories of the Bochner–Riesz means and important achievements attained in the last 50 years. For the Bochner–Riesz means of multiple Fourier integral, it... more...
The first edition of Connections was chosen by the National Association of Publishers (USA) as the best book in "Mathematics, Chemistry, and Astronomy — Professional and Reference" in 1991. It has been a comprehensive reference in design science, bringing together in a single volume material from the areas of proportion in architecture... more...
Meyer's Geometry and Its Applications, Second Edition , combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text... more...
Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logicalSay goodbye to dry presentations, grueling formulas, and abstract theory that would put Einstein to sleep--now there's an easier way to master chemistry, biology, trigonometry, and geometry. McGraw-Hill's Demystified Series teaches complex subjects in a unique, easy-to-absorb manner and is designed for users without formal training, unlimited time,... more...
You, Too, Can Understand Geometry - Just Ask Dr. Math ! Have you started studying geometry in math class? Do you get totally lost trying to find the perimeter of a rectangle or the circumference of a circle? Don't worry. Grasping the basics of geometry doesn't have to be as scary as it sounds. Dr. Math-the popular online math resource-is here to help!... more...
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PowerPoint Math Lessons for Arithmetic, Beginning, Intermediate and College Algebra
1. Lessons are listed by topic.
2. Detailed Examples with explanation of each step as it appears.
3. Practice Problems given during lesson to enhance
comprehension.
Workbooks are available for the above courses. Homework problems with answers are included.
Performing all homework problems will help you gain proficiency on the various topics.
Videos on How-to use various useful features of your
calculator.
Videos on How to use various educational websites
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College Algebra: Concepts and Contexts, 1st Edition
Student Solutions Manual for Stewart/Redlin/Watson/Panman's College Algebra: Concepts and Contexts
Study Guide for Stewart/Redlin/Watson/Panman's College Algebra: Concepts and Contexts
Summary
This book bridges the gap between traditional and reform approaches to algebra encouraging users to see mathematics in context. It presents fewer topics in greater depth, prioritizing data analysis as a foundation for mathematical modeling, and emphasizing the verbal, numerical, graphical and symbolic representations of mathematical concepts as well as connecting mathematics to real life situations drawn from the users' majors.
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Download
Chapter 5: CK-12 Algebra Explorations Concepts, Grade 3
Introduction
In these concepts, you will be introduced to eight key concepts of algebra and will practice your problem solving skills. There are eight concepts, and each one focuses on a key algebraic thinking strategy. You will focus on describing, identifying your job, planning, solving, and checking your thinking.
Chapter Outline
Chapter Summary
Summary
In these concepts we used proportional reasoning when we solved comparison problems, interpreted pictographs, and determined better buys. We thought about equality and inequality and wrote equations when we interpreted and reasoned about pictures of pan balances. We saw variables as unknowns when we solved for the weights of blocks on scales and for the unknowns in circles and arrows diagrams. We also saw variables as varying quantities when we completed tables for functions. In all of the concepts, we practiced interpreting representations of mathematical relationships when we looked at pan balances, circle and arrow grid diagrams, tables of values, weight scales, weigh equations, better-buy signs, and pictographs.
Image Attributions
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Description
Proportional reasoning, variables, using equations to solve problems, and making and interpreting tables for functions
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Summary: These popular and proven workbooks help students build confidence before attempting end-of-chapter problems. They provide short exercises that focus on developing a particular skill, mostly requiring students to draw or interpret sketches and graphsAddison-Wesley, 08/11/2007, Paperback, Good condition.
$1.99 +$3.99 s/h
VeryGood
Wonder Book Frederick, MD
Addison-Wesley, 08/11/2007, Paperback, Very Good condition. 2nd ed
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״The Flash mathlets are divided into two sections.The For Students and Instructors section contains Flash applets which may...
see more
״The Flash mathlets are divided into two sections.The For Students and Instructors section contains Flash applets which may be useful to instructors for classroom demonstrations, as well as to students for independent work and exploration. The For Developers section presents applets together with varied templates and the complete, object-oriented, easily-customizable source code that can be used by instructors for creating their own customized versions of the applets.״
A collection of mathlets for Precalculus, Single Variable Calculus, Multivariable Calculus and Vector Analysis, Parametric...
see more
A collection of mathlets for Precalculus, Single Variable Calculus, Multivariable Calculus and Vector Analysis, Parametric Curves and Surfaces, Derivatives, Integrals and Integration Theorems, and Topology and Geometry.
This site "provides an eclectic mix of sound, science, and Incan history in order to raise students' interest in Euclidean...
see more
This site "provides an eclectic mix of sound, science, and Incan history in order to raise students' interest in Euclidean geometry. Visitors will find geometry problems, proofs, quizzes, puzzles, quotations, visual displays, 'scientific speculation', and more."
The geometric definition of a parabola is the set of all points whose distance from a fixed point, the focus, is equal to its...
see more
The geometric definition of a parabola is the set of all points whose distance from a fixed point, the focus, is equal to its distance from a fixed line, the directrix. On this web page, you will explore the geometric definition of a parabola and see how the focus and directrix effect the parabola's shape. You'll also see how parabolas can model different real world situations, including water fountains, projectiles, and the cables supporting the Verrazano Narrows Bridge.
This website allows the user to explore the definitions and graphs of the circular functions sine and cosine. The sketches...
see more
This website allows the user to explore the definitions and graphs of the circular functions sine and cosine. The sketches on this page will give the user a deeper understanding into the correlation between the unit circle and the sine and cosine waves.
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Product Description
Singapore Math's Discovering Mathematics series focuses on teaching students integrated pre-algebra, algebra, geometry, trigonometry, and advanced math topics effectively. Various approaches are used to present topics, including an intuitive or an experimental approach for some. Teacher involvement is required to teach this program. Discovering Mathematics 1A is designed for Grades 7-8. 218 full-color pages, softcover.
Features include:
Worked examples followed by a similar Try It! question for students to ensure they understand the concepts.
Each chapter is followed by a review exercise, an Extend Your Learning Curve activity, and questions requiring sentence or paragraph answers for reflecting on learning experiences.
The answer key at the back of the book provides answers to the Try It! and the problems in the exercises for the Basic Practice, Further Practice, and Maths@Work questions. It does not include answers to the class activities, Brainworks questions, or the Extend Your Learning Curve activities; those answers are found in the sold-separately Teacher's Guide.
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Wednesday, May 24, 2006
Which math courses?
Since the time allocation is limited, I can take only some math courses and the problem is that I am not sure which courses are most important for a successful economist and which course I should take first. Can you possibly suggest for me a list of math courses that a typical economics student should take step by step
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1441925228
9781441925220
40 Puzzles and Problems in Probability and Mathematical Statistics:This book is based on the view that cognitive skills are best acquired by solving challenging, non-standard probability problems. Many of the puzzles and problems presented here are either new within a problem solving context or are variations of classical problems which follow directly from elementary concepts.
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Overview
REA's Math Workbook for Numbers and Operations is perfect for any high school student studying for the New Jersey HSPA!
This math workbook will help high school math students at all learning levels understand basic mathematics. Students will develop the skills, confidence, and knowledge they need to succeed on the New Jersey HSPA!
REA's Numbers & Operations Math Workbook includes:
Over 20 review lessons with many step-by-step examples
Each lesson builds on the students' past progress
Drills reinforce essential skills
Skill scorecard measures progress and success
"Math Flash" feature provides tips and strategies
Quizzes measure subject mastery
Answer key with detailed explanations
The Numbers & Operations Math Workbook will help students master the basics of mathematics—and help them face their next math test—with confidence!
Related Subjects
Meet the Author
Read an Excerpt
About This Book
This book will help high school math students at all learning levels understand basic mathematics. Students will develop the skills, confidence, and knowledge they need to succeed on high school math exams with emphasis on passing high school graduation exams.
More than 20 easy-to-follow lessons break down the material into the basics. In-depth, step-by-step examples and solutions reinforce student learning, while the "Math Flash" feature provides useful tips and strategies, including advice on common mistakes to avoid.
Students can take drills and quizzes to test themselves on the subject matter, then review any areas in which they need improvement or additional reinforcement. The book concludes with a final exam, designed to comprehensively test what students have learned.
The Ready, Set, Go! Numbers & Operations Workbook will help students master the basics of mathematics—and help them face their next math test—with confidence
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...The scientific information is conveyed in one of three different formats:
Data Representation (38%). This format presents graphic and tabular material similar to that found in science journals and texts. The questions associated with this format measure skills such as graph reading, interpretatAt the core of rational expressions is factorization. I simplify the learning of these concepts by showing how easy they can be if students factor the polynomials and look for opportunities to cancel terms before multiplying or dividing. Often times, this requires addressing student weaknesses in factorization.
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9027725616
9789027725615
Clifford Algebra to Geometric Calculus:Matrix algebra has been called "the arithmetic of higher mathematics" Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebm' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quatemions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.
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books.google.com - Problem-Solving Strategies is a unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. The discussion of problem solving strategies is extensive. It is written for trainers and participants of contests of all levels... Strategies
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