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University of California, Davis

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Kieval Lecture

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Fall, 1997

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*Cool Numbers, Hot Numbers, and How to Protect Yourself from the Abuse
of Numbers*

December 4, 1997 @ 8:00 P.M.
Science B 135
The Kieval Lecture will consider the abuse of numbers
by "experts" and the role of numbers in decisions. (The lecture will be
based on chapters in Professor Stein's recent book, *Strength in Numbers,*
(MAA- Review) (Amazon
Books Review) but will extend the discussion further.)

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Mathematics Department Colloquium

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* A Simple Question about Three Simple Polynomials*

December 4, 1997 @ 4:00 p.m. - Music 130
Tea @ 3:30 p.m. - outside Library 56
Abstract: Let a, b, and c be positive integers with greatest
common divisor equal to 1.

Consider the three Newton polynomials:
*x*^{a} + *y*^{a}, *x*^{b}
+ *y*^{b}, and *x*^{c} + *y*^{c}.
Is the field that they generate all of the symmetric rational functions?

Algebraic tools used to respond to this question involve
fields, rings, the dimension of a vector space, and the dimension of an
extension. Any undergraduate mathematics student would follow the drift
of this lecture and any who've had a semester of abstract algebra should
be able to follow the whole talk.

About Sherman Stein:

Sherman Stein recently retired from teaching at the University of California
at Davis. His pure research is in algebra, geometry, and combinatorics.
In his applied work he has written on the risk of drunk driving and the
limits of mathematics in decision making. He has also designed an ecologically
efficient lawn sprinkler. In addition to several high school and college
texts he recently wrote a book to give everyone a chance to enjoy mathematics,
"Strength in Numbers." (MAA-
Review) (Amazon
Books Review)