Challenging Problems in Algebra

Challenging Problems in Algebra

by Alfred S. Posamentier, Charles T. Salkind
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Challenging Problems in Algebra by Alfred S. Posamentier, Charles T. Salkind

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.

Product Details

ISBN-13: 9780486691480
Publisher: Dover Publications
Publication date: 05/21/1996
Series: Dover Books on Mathematics Series
Pages: 288
Sales rank: 407,150
Product dimensions: 5.41(w) x 8.48(h) x 0.57(d)

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."

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Challenging Problems in Algebra 4 out of 5 based on 0 ratings. 1 reviews.
N_F_Taussig More than 1 year ago
The non-routine algebra problems in this text provide a stimulating intellectual workout. By non-routine, I mean that the problems require insight and, in some cases, ingenuity to solve. Rather than teaching you a skill and asking you to practice it, the authors assume that you have already developed those skills and ask you to apply them to unfamiliar and difficult problems. The problems draw upon topics taught in elementary, intermediate, and advanced algebra classes. Those topics include equations and inequalities; systems of linear equations; arithmetic, geometric, and harmonic means; relations and functions; maxima and minima; the relationship between algebra and geometry; sequences and series; combinatorics and probability; number theory; and Diophantine equations. Answers to all the problems in which a numerical answer or an algebraic expression is sought are given in an answer key, which gives you a chance to check your answer before reading the authors' solutions. However, not all those answers are correct. Solutions to all of the principal problems are given in a solution key, which is more reliable than the answer key. However, no solution is given to some of the problems that are variations on or extensions to the principal problems. While the authors label these variations and extensions "Challenges," they are generally no more challenging than the principal problems. The solution key is worth reading even if you have solved a problem correctly. The authors often solve not only the problem at hand but show you solve an entire class of related problems. Reading the solutions is also useful since the techniques developed there can sometimes be applied to subsequent problems in the text. Reading the appendices before commencing work on the problems is advisable since the relationships and techniques discussed in the appendices are useful in solving the problems. The appendices address terminating digits; the remainder and factor theorems; maximum product, minimum sum problems; arithmetic, geometric, and harmonic means; divisibility tests; the binomial theorem; some useful algebraic relationships; and how to write a proof by mathematical induction. Working through this text will enhance your problem-solving skills and extend your knowledge of algebra. The level of difficulty of the problems is similar to those in the American Mathematics Competition (AMC), which is not surprising since Charles T. Salkind was the editor of the American High School Mathematics Examination (AHSME), as the AMC was then known, from its inception in 1950 until his death in 1968. Unlike those problems, these problems are not multiple choice. While in many problems a numerical answer or an algebraic expression is sought, these problems also include proofs and investigations of algebraic relationships. While some editing errors detract from the quality of this text, the quality of the problems makes working through it worthwhile.