Affiliation: University of Wisconsin
Title Of Talk: Some inequalities for symmetric polynomials
Abstract: There will be two topics in this talk. The first will deal with a problem when teaching calculus. After introducing Rolle's theorem and giving some reasons why it is true, it is used to prove the mean value theorem. Then Rolle's theorem is basically ignored since the mean value theorem is used instead. When I taught calculus this is what I did, since the only other direct uses of Rolle's theorem I knew involved problems which would take too long to motivate for students just starting calculus. I now know a problem which can be solved with Rolle's theorem and little else which is easy to motivate. Part of the surprise comes from when the inequalities which arise in this problem were first proven.
The second type of inequality which will be discussed seems to have first arisen in 1820 by Lehmus, but most of the references to this inequality are to an inequality found by Schur which Hardy, Littlewood and Polya included as a problem in their book "Inequalities". Some related results will be given.
Last update made Thu Feb 11 08:27:48 PST 2016.