Average Reviews:
(More customer reviews)Like Larson's book, "Problem Solving Through Problems", this is a textbook aimed at preparing students for mathematics contests such as the annual Putnam Competition. It will probably also be of interest to high school students preparing for some of the higher level contests such as the AIME, USAMO, and the international olympiad. The text consists of a large collection of problems, along with many solutions. There's little here on heuristics for problem solving. Instead, the book focuses on bits of mathematical theory that often come up in solving such problems but may not often come up in the undergraduate curriculum ( things like Jensen's inequality, the pigeonhole principle, etc.) Larson's "Problem Solving Through Problems" is similar in style and content. For more on problem solving heuristics, see Polya's "Mathematical Discovery" or "Thinking Mathematically" by Mason, Burton, and Stacey.
Click Here to see more reviews about: Principles of Mathematical Problem Solving
This book presents the principles and specific problem-solving methods that can be used to solve a variety of mathematical problems. The book provides clear examples of various problem-solving methods accompanied by numerous exercises and their solutions. Principles of Mathematical Problem Solving introduces and explains specific problem-solving methods (with examples), and gives a set of exercises and complete solutions for each method. The idea is that by studying the principles and applying them to the exercises, the reader will gain problem-solving ability as well as general mathematical insight. Eventually, the reader should be able to produce results that have "the whole air of intuition." Organized according to specific techniques in separate chapters, techniques include induction and the pigeonhole principle, among others. Arranged in order of increasing difficulty, the book presents a wide variety of problem sets designed to illustrate significant mathematical ideas. Each chapter also includes a moderate amount of the "theory" behind each problem-solving principle it presents. An essential resource for every student of mathematics and every professional who needs to solve mathematical problems.
Click here for more information about Principles of Mathematical Problem Solving
