L. E. SADOVSKII and A. L. SADOVSKII. Providence, RI: American Mathematical Society, 1993. ISBN 0-8218-9500-1. ix + 152 pp. $20.00 (P).
This short paperback book is a translation (from Russian) of a collection of materials illustrating applications of mathematical ideas to sports. The authors intend it to be "for high school and college students" (p. ix). The level is certainly beyond most American high school students, but there are a number of interesting applications that might appeal to a good undergraduate student looking for an independent project topic. Mathematical application areas include probability and Markov chains (applied to tennis and basketball), voter theory (judging figure skaters and gymnasts), statistics (looking at progressions of world records), linear programming (to determine the lineup for a basketball team, stock players on soccer clubs, and plan a healthy athletic diet), game theory (for making substitutions in soccer, exerting a final spurt in speed skating, waxing skis, choosing to pass in weightlifting, and matching lines in ice hockey), tournament organization (Olympic format, round robins, and Latin squares) a nd rating systems (Elo's method for chess and tennis player rankings). Unfortunately, over half of the references are in Russian, so students may have some initial difficulty in following up on a particular topic.
Readers will notice that many of the examples are somewhat dated. Although the publication date is 1993, this fourth printing was issued in 2000. The original Russian manuscript was written several years earlier and, other than a few marginal notes by the editor, was not updated. One dated example is the excellent discussion in Chapter 2 of a model for examining the...
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