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The Heart of Mathematics: An Invitation to Effective Thinking

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MAA Review

This is a very modest revision of the already-excellent second edition. It in an inquiry-based text and has what is probably a unique approach to a math appreciation course: rather than focusing on fun math or useful math, it tries to teach how mathematicians think and approach problems.

Although this third edition is 200 pages longer than its predecessor, much of the increase is due to reformatting, with about 80 pages of new material. Most of the book is completely unchanged. There is a new section in Chapter 5 on the Koenigsberg Bridge problem and Eulerian circuits, and Chapter 6 has been rearranged. The old Chapter 7, “Taming Uncertainty,” has been split into separate chapters on probability and on statistical analysis of data and statistical inference. Most of the book’s new material is in this new statistics chapter. This chapter adds a number of interesting real-world problems, such as “what exactly does 30% chance of rain mean?” and a look at the 1969 Vietnam draft lottery, where statistical data makes it clear that the draws were not randomized enough.

Bottom line: An improvement over an already-great text, but the improvements are fairly far along in the text and most courses will not get that far. Unfortunately, the existence of a new edition makes obsolete (in the eyes of booksellers) the previous perfectly-good edition.

Allen Stenger is a math hobbyist and retired software developer. He is webmaster and newsletter editor for the MAA Southwestern Section and is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis. He volunteers in his spare time at MathNerds.com, a math help site that fosters inquiry learning.

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