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Posted June 28, 2010
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An intellectually stimulating set of non-routine algebra problems.
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.Was this review helpful? Yes NoThank you for your feedback. Report this reviewThank you, this review has been flagged.
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.