Math 421: Combinatorics


Welcome to Combinatorics, which you can describe to your friends as Advanced Counting. In the math world, we say something more like “the study of the properties and structures of discrete, finite objects.”   


Text: Introductory Combinatorics, by Richard Brualdi (5th edition).


Topics: Time permitting, we will cover most of chapters 1-8, with possible forays into chapters 9 and 11.


Class Philosophy: One learns math by doing it, not by watching other people do it. With white-board tables, we’ll all be able to do lots of math. You will be required to participate actively during class, and work very hard outside of it.  For most class meetings, you’ll have a reading assignment.  In class, we’ll discuss the readings, working through any difficulties you have.  From time to time, we’ll also have a set of problems to do.  Generally, you’ll be responsible for presenting those problems in class. 


Office Hours: 








As you probably know, I’m around a lot at other times as well.  If you’d like to meet, just drop by – or drop me an email. 


My Contact Info:

Phone: x4433   Email:  Office: 175 Schaefer Hall


Grades: Your grade for the semester will be determined as follows:






Midterm Quiz


Open Problem Project


Class Participation




Homework will be assigned frequently; sometimes I will collect it and grade it. The date for the Midterm will be announced later in the semester. The final will be a take home exam.


Open Problem Project:  In groups of at most three, you will select an open problem (upon consultation and approval by me), and will document your progress on the problem during the semester.   Your final product will be twofold: an oral presentation and a paper of at least five pages.  Your paper will describe the history of the problem (who posed it and why), the background needed to understand the problem (including all necessary definitions, related theorems, and some examples), and a description of the approaches you took. Potential sources for problems include our discussions in class, books on combinatorics, and many websites, including:

The Open Problem Garden (look at combinatorics, graph theory, even theoretical comp. sci.)

Doug West’s page of open problems in graph theory and combinatorics


The Geometry Junkyard:  

The Open Problem Project

The list of pages linking to open problems



Deadlines:         October 15: Problem selected by you and approved by Dave. 

November 12: One page progress report due.

December 3:  Written report due.

December 8,10:  Oral presentations of problem, results, and progress.