Summer 2022 – The Theory of Integer Partitions

This is the main website for the Johannes Kepler University, Institute of Algebra, Special Topics course on Theory of Partitions.

If you are interested to audit the course please feel free to show up to one of our lectures.

The lectures will be held on Monday 10:15 – 11:45 at Science Park 5 room 103.

Due to my affiliation at University of Bath, I need to be in UK occasionally. We will make other appointments and meet at a different time for these dates.

We rescheduled some lectures: We will have our last three lectures on:
-June 13 (at the normal location),
-June 15th (the location – most likely SP2 Seminar Room and the time will be announced) and
-June 20th (at the normal location)

Office Hours:
There are no set office hours. If you have a question or need help with something, send me an email and we can make an appointment.

Homework / Grading:

I will be assigning homework that I will not collect throughout the semester. You can work on these problems in groups. You can also get hints from me.

At the end of the semester, the students can choose to take an exam for a grade. In that exam, I will be asking a random sample of these homework problems.

Lecture Notes

I am typing my own notes. If you find typos, unclear statements, wrong proofs, bad definitions, the meaning of life, etc. please let me know.

The lecture notes and homework problems are HERE

  1. The first two lectures happened in person, but the lecture notes have everything.
    (Then a participant tested positive so we made the positive change and started having hybrid lectures.)
  2. March 21th lecture:
  3. March 28th lecture:
  4. April 4th lecture:
  5. April 25th lecture:
  6. April 29th lecture:
  7. May 2nd lecture:
  8. May 6th lecture:
  9. May 16th lecture:
  10. May 23rd lecture:
  11. June 13th lecture:
  12. June 15th lecture:
  13. June 20th lecture:
    Thank you for an amazing semester. It was an huge fun and an honor to teach you.

Here are my notes on the Second Workshop on Theory of Partitions that happened in the Nesin Mathematics Village. You can watch extracurricular partition theory related talks from some experts and me on this website: Second Workshop on Integer Partitions (These videos also have some solutions to some homework problems but it is better that you try to solve them yourself, instead of finding and watching the solutions from 25~ish hours of partition theory related lecture footage).

Other resources

  • G. E. Andrews The Theory of Partitions. Encyclopedia of Mathematics, Vol 2, Addison-Wesley, 197
  • T. Apostol Introduction to Analytic Number Theory. Springer, UTM
  • G. Gasper and M. Rahman – Basic Hypergeometric Series