# Math 502: Combinatorics

This is the second of a two-semester introductory graduate-level course in combinatorics. The goal is to learn to apply the methods and ideas discussed in the first semester to more advanced topics, such as symmetric functions and combinatorial designs.

For the first half of the course, lectures were held at 8:00 AM in E 106.

For the second half of the course, lectures will be held at 10:00 AM MWF. All lectures and office hours will be held on Zoom.

**Zoom Meeting Room ID: 142-012-467**

There is a password and it has to do with an inside joke on combinatorial designs.

## Syllabus

For more details, see the Course Syllabus.

A revised syllabus for the second half of the semester due to the COVID-19 pandemic has been posted here: COVID-19 Syllabus.

## Resources

The primary textbooks for the course are *Enumerative Combinatorics*,
Vol. I and II, by Stanley, and *Designs, Graphs, Codes, and their Links*
by Cameron and Van Lint. For the last few weeks of the course, the book
*Matroid theory* by Oxley may also be useful, but is not a required
text.

For supplementary lecture notes relevant to many of the course topics, see Alexander Hulpke’s Notes.

Here is a link to Proctor’s elementary proof of the equivalence of the two definitions of Schur functions.

An excellent visualization of the 27 lines on a cubic surface (in this case, the `Clebsch surface’), which gives rise to the Schlafli graph discussed in class.

## Office hours

My office is Weber 125, but I won’t be there for the rest of the semester due to the coronavirus pandemic. Come find me on Zoom in the class meeting room listed above:

- Monday 9-10 am
- Thursday 1-2 pm
- By appointment (Email me at Maria [dot] Gillespie [at] colostate [dot] edu)
- Feel free to add me as a contact on Zoom (monksm [at] gmail [dot] com) and start a text chat with me. It’s probably the best substitute for dropping by my office when the door is open.

## Homework

Homework assignments will be posted here as the course progresses.

## Final project

See the syllabus for detailed instructions on the final project. To get started, copy the Overleaf template into a new document, delete the filler content, and fill in your own.

The final project is due on May 8. It must be strictly longer than 4 pages in length and strictly shorter than 16 pages in length.

## Exams

The final exam counts as the qualifier as well, and will therefore not be posted here. See the Course Syllabus for details.