Algebraic Methods in Combinatorics, Spring 2019


Grid on a cubic

When:

Mondays, Wednesdays 3:30

Where:

Wean Hall 8201 [map]

What:

The course is about algebraic aspects of (Hungarian-style) combinatorics. This is an application-driven course. Throughout the course, our aim is to prove inequalities about concrete combinatorial objects. We will see how techniques from linear algebra and a little bit of algebraic geometry to achieve this goal.

This is an advanced graduate course. To benefit from this course, you must have basic familiarity with combinatorics be extremely comfortable with linear algebra. You also need to have the hard-to-define ``mathematical maturity'', which includes broad familiarity with the common undergraduate mathematical background, skill in abstraction reasoning, and general interest in pretty mathematics. In particular, you need to be acquainted with finite fields, groups and with rudiments of real analysis. However, I will not assume familiarity with concepts not usually taught to mathematics undergraduate students. In particular, this course requires no prior knowledge of algebraic geometry.

Algebraic techniques I expect to cover in the course include:

Resources:

There are two books devoted to applications of linear algebra to combinatorics.

More resources will be added to this page as the course progresses.

More fun:

I am often in my office; feel free to drop by with short questions or just to chat math. If you have a longer question, or just want to make sure of a meeting time, please talk to me in class or send me an e-mail to make an appointment.

Course activities:

By the end of each Sunday, you must send me by e-mail a question about the material covered that week. If you have no questions, it can be a pro forma question (with an answer), or a problem you made up. This is worth 10% of the grade.

There will be no in-class tests. There will be several homeworks. For PhD students, the homeworks will completely determine the grade. For undergraduate and master students, at the end of the semester there will be a 30-minute oral test on a randomly chosen topic covered in the class. The test will count for 50% of the grade.

Students are expected to fully participate in the class. Discussions during the lectures are encouraged.

Lectures:


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