A Gentle Introduction to Inequalities: A Casebook from the Fullerton Mathematical Circle

Authors

Adam Glesser, California State University, FullertonFollow
Matt Rathbun, California State University, FullertonFollow
Bogdan Suceavă, California State University, FullertonFollow

Abstract

Run for nearly a decade, the Fullerton Mathematical Circle at California State University, Fullerton prepares middle and high school students for mathematical research by exposing them to difficult problems whose solutions require only age-appropriate techniques and background. This work highlights one of the avenues of study, namely inequalities. We cover Engel's lemma, the Cauchy--Schwartz inequality, and the AM-GM inequality, as well as providing a wealth of problems where these results can be applied. Full solutions or hints, several written by Math Circle students, are given for all of the problems, as well as some commentary on how or when to assist students, and details about the pedagogical value of certain problems.

Description of Program

The Fullerton Mathematical Circle is run by the Department of Mathematics at California State University, Fullerton. It started in 2011 and has served hundreds of elementary, middle, and high school students over that time. Participants have ended presenting their work at regional conferences, as well as publishing their work in research journals.

https://www.fullerton.edu/math/resources/mathcircle.php

For more information, contact Bogdan Suceava at bsuceava@fullerton.edu.

Recommended Citation

Glesser, Adam; Rathbun, Matt; and Suceavă, Bogdan (2021) "A Gentle Introduction to Inequalities: A Casebook from the Fullerton Mathematical Circle," Journal of Math Circles: Vol. 2: Iss. 1, Article 1.
Available at: https://digitalcommons.cwu.edu/mathcirclesjournal/vol2/iss1/1