An Introduction to Inequalities

Please read the disclaimer and description before downloading these notes.


This is a set of lecture notes for a short course on classical inequalities that I offered to graduate students at Bowling Green State University, Bowling Green, Ohio. The material was presented using a 'modified Moore method', wherein a third to as much as half of each class period was devoted to students presenting their solutions to (the included) problem sets.

The course is intended as a survey of elementary techniques in inequalities for novices and non-experts. Experts in the field seeking new, original, or research topics should look elsewhere. This is strictly for beginners!

Prerequisites for a thorough understanding of the course are essentially calculus (although a bit of advanced calculus would prove helpful in spots) and a first course in linear algebra (through eigenvalues).

There is enough material here for roughly 24 hour-and-a-half lectures; probably not quite enough for a full semester course. On the other hand, this would make excellent fodder for a problem-solving course or a student seminar. I should also point out that the choice of topics reflect my personal interests and I make no claims that they will suit everyone's tastes.

The notes are available here in pdf format. The file is roughly 1Mb and the printed version is 93 pages.


Neal L. Carothers