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.

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