Math 454: Combinatorial Theory

Important Links:

Course Syllabus
Canvas Login

See the post-semester student survey results here.

Class: MTWTh from 12:20-2:20PM EDT via Zoom

All information will be posted on our Canvas site.

Course Description:

Combinatorics is a broad subject that mainly deals with the counting, construction, and optimization of discrete objects (as opposed to continuous objects - think of the natural numbers, versus the real numbers). Such problems are near the intersection of mathematics and computer science; many can be solved using algorithms, but many cannot! We will study different types of combinatorial problems and the techniques used to answer these problems, which form the foundations of today's research in discrete mathematics.

This class is not lecture-based but discovery-based. Why, you might ask? Because when people discover ideas for themselves, they tend to retain those ideas longer and to understand them more deeply than if someone else revealed the ideas. Much of class time will be spent in developing and exploring key concepts by working on problems in groups. But at the same time, it's easy to miss part of a relevant idea when you're thinking about it on your own, so we will always follow up on what we discover with class check-ins, informal presentations of ideas and solutions, and assigned reading. Practice problems will be assigned after every class, to be discussed at the beginning of the next class. Longer problem sets will be assigned on a weekly basis.

The prerequisites are Calc II and Linear Algebra. Intro to Proofs (Math 300) is not required, but we will see many proofs and practice writing proofs both in homework and during class.

Course Outline:

(updated after the course concluded)