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 firsthalf 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 379960612
Office: Aconda Ct. 401A
Phone: 8659744319
http://web.utk.edu/~cplaut
