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The Junior Colloquium kicks off next week with a talk by Professor David Dobbs (see title and abstract below). The Junior Colloquium is a series of mathematics talks aimed at undergraduates, but graduate students and faculty are welcome to (and often do) attend. Generally the expected background is not high (e.g. basic calculus); if more (or less) background is needed then this will be stated in the abstract. So if you want to learn about some interesting mathematics and applications in a relaxed and often entertaining setting, join math majors and others at the JC this semester. All talks will be held in HBB 102 at 3:35 on the following Thursdays, so mark your calendars. Free pizza in Aconda 113 precedes each talk by 20 minutes or so. September 16 Professor David Dobbs, UT October 14 Professor David Anderson, UT October 28 Dr. Sara Del Valle, Los Alamos National Lab November 4 Dr. Paul Thurston, Tower Research Capital November 11 Professor Joan Lind, UT There will also be a special, widely advertised talk by Professor Hugh Bray of Duke University on December 13. More information, including location, will be sent later. Thanks to Fernando Schwartz for arranging the talk. Next week's talk: THE PROBABILITY OF A STATISTICAL ODDITY IN BASEBALL Professor David E. Dobbs, UT ABSTRACT We begin by comparing the batting performances of four baseball players. Tables include each player’s batting averages for the first half of the season, the second half of the season, and the entire season. It is noticed that Player A has “lost paradoxically” to Player D in the following sense: Player A had a higher batting average than Player D in both halves of the season, but Player D had a higher batting average than Player A for the entire season. The main part of the talk determines the probability that such a “paradoxical loss” could befall Player A. The analysis makes certain realistic assumptions. A theorem is proved involving a branch of a rectangular hyperbola, and we also make use of the SOLVER feature of a graphing calculator. The discussion depends only on Precalculus and Calculus II (the latter is needed only because some definite integrals arise in the calculations) and thus provides an introduction to the calculation of probability for continuous (as opposed to discrete) uniform probability density functions. We determine the probability that Player A could lose paradoxically to a player with a lower first-half batting average, as well as the probability that Player A could lose (not necessarily paradoxically) to such a player. We close with some comments about more realistic models, some philosophic musing about paradoxes, and a theorem that reinforces one’s intuition about fractions. Conrad Plaut Professor, Director of UT Math Honors Math Department Aconda Ct. 104 1534 Cumberland Ave. University of Tennessee Knoxville, TN 37996-0612 Office: Aconda Ct. 401A Phone: 865-974-4319 http://web.utk.edu/~cplaut