Math 511: Introduction to Combinatorics
Spring 2009

To the schedule and homework page | supplementary notes and problems | student presentations | syllabus.

This course introduces many of the basic concepts, constructions, and examples of combinatorics. It is taught from the textbook of

The book will be on reserve in the Reserve Reading Room and will be available at the bookstore. It is a very wide-ranging introduction to much of combinatorics as a whole.


The course is not an introductory graduate course. The absolute minimum requirement is a good understanding of abstraction, facility with proofs, and a good modern algebra background (as from a graduate course), and the more graduate math you know, the better (that's the famous "mathematical maturity"). 511 is not normally open to first-year students, but there can be exceptions if I approve. If you aren't sure whether you might be interested or ready for this class, please see me.

This version of 511 is quite different from the usual one from Stanley, Enumerative Combinatorics, Vol. 1. The Stanley course will be offered next year (2010) by Laura Anderson. You can take both courses. There may be a technical obstacle to registering for two 511's (I'm not sure), but if so, you can do the second one as an independent study.


We meet on M, W, F 1:10 - 2:10 in LN-2205, and (usually) F 3:00 - 4:20 (depending on cookies) in LN-2205 (time and room changed on Fridays).

I've scheduled myself for all kinds of math trips this semester. Some will interfere with classes. Thus, we won't meet on the following days:

That's why we need make-up dates, hence the Friday class time.

Office hours

I will be happy to see graduate students at any time, as far as possible (that means, not early in the morning and not when I'm rushing to prepare a class). I'll be around most afternoons, but also I have regular office hours, when I promise to be around. They are M, W 2:20 - 3:30 and F 2:20 - 3:00.


There is a Combinatorics Seminar that meets 1:15-2:15 p.m. on Tuesdays. It is highly recommended that students interested in combinatorics attend the seminar, even if you don't understand much (at first).

How the Course Works

Course Outline

We will study a variety of chapters, to be decided later. The chapters are short but dense; you have to read slowly and closely.

Click here for the

class and homework schedule [Note the irregular schedule!] with readings and homework assignments,
supplementary material and extra problems (this is compulsory reading!), and
student presentations schedule.

Expected Student Work

I will expect you, the students, to study the material and to work on as many of the exercises as you can. (Most have solutions in the book, but of course you shouldn't look at them until you get seriously stuck.) I will frequently collect written work (see the homework assignments).

I will meet separately with each student frequently (every week or two) to discuss your progress and any questions you or I may have.

After the first couple of weeks I will also ask everyone to present some of the material from the book in class. This may be one theorem, a series of related results, an example, or any small part of the book.

There may be a take-home final.

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