combinatorics.in
← All courses

Open online course · Online · open to all

Advanced q-analysis I

Term
2025
Status
Archive
Format
Intensive online course. Attendees are expected to read the book independently alongside the lectures.
Lectures
Wednesdays 16:15 IST & Sundays 11:30 IST
Certificate
None is given for attending.
Registration
Closed — the form was due 20 April 2025.
A lattice path in a 3 × 5 box cuts out a partition inside the box — here (5, 3, 2). Summing q|λ| over all 56 paths gives the Gaussian binomial coefficient.

Course description

q-analysis is the study of identities arising from q-factorials — a generalisation of the usual factorial — and q-binomial coefficients, a subject consisting primarily of identities between certain kinds of series and products. A major source of inspiration comes from number theory and combinatorics, where both appear naturally via generating functions.

In this course we study integer partitions through the lens of q-analysis. Classical results due to Euler, Jacobi, Cauchy, Sylvester, Rogers, and Ramanujan form the bedrock, and we go on to more modern developments due to Bailey and Andrews.

Lectures

No lecture log was kept for this run of the course.