Combinatorial Mathematics (MATH580/CS571)

Official Course Description

Fundamental results on core topics of combinatorial mathematics: classical enumeration, basic graph theory, extremal problems on finite sets, probabilistic methods, design theory, discrete optimization.

Unofficial Description (Student Feedback)

This course is divided into two parts. The first part is on enumerative combinatorics, which is a more advanced version of Math 413. The second part is on graph theory, which is a more advanced version of Math 412. The official textbook for this textbook is Combinatorial Mathematics by Douglas B West.

Official Prerequisites

MATH412 MATH413

Notes on Enrolling

As this is a graduate course, undergraduate students will need permission from the undergraduate director to enroll. A previous combinatorics course or experience with other graduate courses is generally expected.

Degree Requirements Fulfilled

This course satisfies a core requirement or an elective requirement* for the following programs:

Computer Science, BS (Algorithms and Models of Computation Focus Area)

General Advice

While this class is technically self-contained, it is notoriously difficult without a previous background in combinatorics. Historically, students struggle more with the second half of this course, so it is strongly recommended that one has taken MATH412 or learned / self-studied graph theory beforehand. Both the exercises in West’s textbook and the past 580 comprehensive exams serve as excellent practice for the exams in this course.

General Postrequisites

Taking Math 580 opens up the Math 58X sequence, that is Math 581, 582, 583, 584, 585, and 586, all of which go more into depth into specific concepts and techniques taught in 580.

Resources

MATH 580 Textbook

Recent Professors

Abhishek Methuku, Jozsef Balogh