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Challenging Problems in Algebra (Dover Books on Mathematics)

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Challenging Problems in Algebra (Dover Books on Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

Designed for high-school students and teachers with an interest in mathematical problem-solving, this stimulating collection includes more than 300 problems that are "off the beaten path" — i.e., problems that give a new twist to familiar topics that introduce unfamiliar topics. With few exceptions, their solution requires little more than some knowledge of elementary algebra, though a dash of ingenuity may help.
Readers will find here thought-provoking posers involving equations and inequalities. Diophantine equations, number theory, quadratic equations, logarithms, combinations and probability, and much more. The problems range from fairly easy to difficult, and many have extensions or variations the author calls "challenges."
By studying these nonroutine problems, students will not only stimulate and develop problem-solving skills, they will acquire valuable underpinnings for more advanced work in mathematics.

Synopsis:

Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, and more. Detailed solutions, as well as brief answers, for all problems are provided.

Synopsis:

Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, more. Detailed solutions.

About the Author

Al Posamentier is currently Dean of the School of Education and Professor of Mathematics Education at Mercy College, New York. He is Professor Emeritus of Mathematics Education at The City College of the City University of New York, and former Dean of the School of Education, where he was for 40 years. He is the author and co-author of more than 55 mathematics books for teachers, secondary and elementary school students, and the general readership. Dr. Posamentier is also a frequent commentator in newspapers and journals on topics relating to education.

Alfred S. Posamentier: Math's Champion

Dr. Alfred S. Posamentier, Professor Emeritus of Mathematics Education at New York's City College and, from 1999 to 2009, the Dean of City College's School of Education, has long been a tireless advocate for the importance of mathematics in education. He is the author or co-author of more than 40 mathematics books for teachers, students, and general readers including The Fascinating Fibonacci Numbers (Prometheus, 2007) and Mathematical Amazements and Surprises: Fascinating Figures and Noteworthy Numbers (Prometheus, 2009).

His incisive views on aspects of mathematics education may often be encountered in the Letters columns and on the op-ed pages of The New York Times and other newspapers and periodicals. For Dover he provided, with co-author Charles T. Salkind, something very educational and also fun, two long-lived books of problems: Challenging Problems in Geometry and Challenging Problems in Algebra, both on the Dover list since 1996.

Why solve problems? Here's an excerpt from a letter Dr. Posamentier sent to The New York Times following an article about Martin Gardner's career in 2009:

"Teachers shouldn't think that textbook exercises provide problem-solving experiences — that's just drill. Genuine problem solving is what Mr. Gardner has been espousing. Genuine problem solving provides a stronger command of mathematics and exhibits its power and beauty. Something sorely lacking in our society."

Table of Contents

Introduction

Preparing to Solve a Problem

SECTION I First Year Algebra

1. Posers: Innocent and Sophisticated

2. Arithmetic: Mean and Otherwise

3. Relations: Familiar and Surprising

4. Bases: Binary and Beyond

5. "Equations, Inequations, and Pitfalls"

6. Correspondence: Functionally Speaking

7. Equations and Inequations: Traveling in Groups

8. Miscellaneous: Curiosity Cases

SECTION II Second Year Algebra

9. Diophantine Equations: The Whole Answer

10. Functions: A Correspondence Course

11. "Inequalities, More or Less"

12. Number Theory: Divide and Conquer

13. Maxima and Minima: Ups and Downs

14. Quadratic Equations: Fair and Square

15. Systems of Equations: Strictly Simultaneous

16. Algebra and Geometry: Often the Twain Shall Meet

17. Sequences and Series: Progression Procession

18. Logarithms: A Power Play

19. Combinations and Probability: Choices and Chances

20. An Algebraic Potpourri

Answers

Appendices

Product Details

ISBN:
9780486691480
With:
Salkind, Charles T.
Author:
Salkind, Charles T.
Author:
Ind
Author:
Posamentier, Alfred S.
Author:
Charles T. Salk
Author:
Mathematics
Publisher:
Dover Publications
Location:
New York :
Subject:
Mathematics
Subject:
Algebra
Subject:
Problems, exercises, etc.
Subject:
Algebra - General
Subject:
Algebra - Elementary
Subject:
Prog. learning
Subject:
Algebra -- Problems, exercises, etc.
Subject:
General Mathematics
Subject:
Algebra - Intermediate
Subject:
Mathematics-Algebra Other
Edition Number:
2
Edition Description:
Trade Paper
Series:
Dover books on mathematics
Series Volume:
132
Publication Date:
19960531
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
288
Dimensions:
8.5 x 5.38 in 0.67 lb

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Related Subjects


Reference » Science Reference » General
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Science and Mathematics » Mathematics » Calculus » Precalculus
Science and Mathematics » Mathematics » General

Challenging Problems in Algebra (Dover Books on Mathematics) New Trade Paper
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Product details 288 pages Dover Publications - English 9780486691480 Reviews:
"Synopsis" by ,
Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, and more. Detailed solutions, as well as brief answers, for all problems are provided.
"Synopsis" by , Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, more. Detailed solutions.

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