q-analysis is the study of identities arising from q-factorials (a generalization of the usual notion of factorials) and q-binomial coefficients (a generalization of the usual notion of binomial coefficients), a subject consisting primarily of identities between certain kinds of series and products. A major source of inspiration for the topic comes from problems in number theory and combinatorics, where q-factorials and q-binomial coefficients appear quite naturally via generating functions. In this course, we will study integer partitions through the lens of q-analysis, and classical results due to Euler, Jacobi, Cauchy, Sylvester, Rogers, and Ramanujan in the area will form the bedrock of this course. We will also discuss more modern developments due to Bailey and Andrews.
We aim to complete Chapters 5 to 9 of An Introduction to q-analysis by Warren P. Johnson, American Mathematical Society, 2020.
This is an intensive online course. Attendees are expected to read the book material independently, along with the lectures.
No certificate will be given for attending the course.
If you wish to register for this course then please fill this form by 20 April 2025.
Lecture schedule: Wednesdays 1615 IST & Sundays 1130 IST.