Proofs and Applications of the CSB (Cauchy-Schwarz-Bunyakowsky) and AM-GM (arithmetic mean-geometric mean) Inequalities

Speaker:  Raghavendra Tripathi

Date: 16th January 2018 (Tuesday)

Time: 09:15 pm – 10:15 pm

Venue: Lecture Hall I, Department of Mathematics

Abstract:

In this talk I will revisit two very basic gems of modern analysis, namely the CSB inequality and the AM-GM inequality. I will present an elegant proof of the AM-GM inequality which uses induction.
  As a consequence of these two simple inequalities I shall prove three seemingly unrelated results. (Two from analysis (the first result concerns the positions of roots of monic polynomial with real roots; the second concerns the bounds on tangential triangle and rectangle of monic polynomials which are positive in (-1,1)) and one from Graph Theory, namely a special case of Turan’s theorem).

Area: Analysis

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