Additive Combinatorics

This book deals with additive combinatorics, a vibrant area of current mathematical research. Additive combinatorics – an offspring of combinatorial number theory and additive number theory – can be described as the study of combinatorial properties of sumsets in additive structures. It is a rather new field that is just now coming to its own; although some of its results have been known for centuries, many of its fundamental questions have only been settled recently or are still unsolved. For this and many other reasons, additive combinatorics provides an excellent area for research by students of any background: it has intriguing and promising questions for everyone.

Bela Bajnok is Professor of Mathematics at Gettysburg College and endowed Alumni Chair. He holds a PhD from Ohio State University. He has won several teaching awards, including the Creative Teaching Award at Gettysburg College and the Crawford Teaching Award from the Mathematical Association of America.
He is Director of the American Mathematics Competitions and I am on the Board of Pro Mathematica Arte (the organization that runs the Budapest Semesters in Mathematics).