Mathematics 310 - Theory of Partitions

The theory of partitions is a fundamental branch of combinatorics and number theory pertaining to enumerative properties and patterns of the integers. With its mathematical origins tracing back to the seventeenth century, partition theory has evolved through contributions made by many influential mathematicians including Euler, Legendre, Hardy, Ramanujan, Selberg and Dyson, and continues to be an active area of study today. Topics include partition identities and bijections, Ferrers diagrams and Durfee squares, partition generating functions and q-series, the pentagonal number theorem, q-binomial numbers (Gaussian polynomials), and partition congruences.

This course is expected to include both synchronous and asynchronous class sessions and activities, and opportunities for peer engagement.

Requisite: MATH 121 and 220, or other significant experience with proofs, or by consent of the instructor. Limited to 24 students. Spring semester. Professor Folsom.