MATH-337 Number theory I.c - Combinatorial number theory

Combinatorics is the study of discrete structures, and number theory the study of arithmetic. At the interface of these domains we encounter the fascinating field of combinatorial number theory (sometimes also called arithmetic combinatorics), which concentrates on the study of arithmetic structures. Two of the key areas that we will focus on during this course are Ramsey theory, encompassing Schur's Theorem, van der Waerden's Theorem, and the Erdos-Szekeres Theorem, and additive combinatorics, featuring Hindman's Theorem and Roth's Theorem. This course will help foster both your combinatorial and analytic intuition in mathematics and will allow you to visualize the natural numbers in new and complex ways. We will also discover connections to subjects that you have seen before, such as number theory, analysis, group theory and set theory.