Partitions

Catalog description

This course provides an overview of theory of partitions. This course focuses on the partition function p(n) and its number theoretic behavior and combinatorial structure, along with related problems. To achieve the main goal, generating function theory, basic hypergeometric series, q-series, and some related combinatorial theory are discussed. Building on these relevant theories, students will be able to understand and prove the arithmetic properties of p(n) and related identities including the Rogers-Ramanujan identities. Students will also be able to recognize and apply the same methods to similar functions and identities.