MT 445: Combinatorics

Fall 2018

The famous logician Frank Plumpton
Ramsey had three pigeons he dumped in-
to two holes and knew
that one contained two
without any further assumption.

The syllabus contains all the basic information about the course.

The class recaps contain a brief day-to-day summary and the reading assignments.

Exam Preparation

Midterm 1 Preparation Sheet

Midterm 2 Preparation Sheet

Final Preparation Sheet

Reading

The classic article by Gale and Shapley.

This article by Alon and Krivelich, which appears in the wonderful book The Princeton Companion to Mathematics, contains a nice overview of the field of extremal and probabilistic combinatorics. It touches on many of the topics that we cover during the course.

Some lecture notes pertaining to Mantel's and Turán's theorems, and some other lecture notes pertaining to the theorem of Kővari, Sós, and Turán and the complementary construction of Reiman.

An exposition about the card trick.

Problem Sets

PS1, PS1.tex
PS2, PS2.tex, figure
PS3, PS3.tex, figure, figure
PS4, PS4.tex, figure
PS5, PS5.tex, figure
PS6, PS6.tex
PS7, PS7.tex, figure
PS8, PS8.tex
PS9, PS9.tex
PS10, PS10.tex, figure
PS11, PS11.tex