Syllabus

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Prerequisites

or permission of instructor

Course Description

This course is a graduate-level introduction to the probabilistic method, a fundamental and powerful technique in combinatorics and theoretical computer science. The essence of the approach is to show that some combinatorial object exists and prove that a certain random construction works with positive probability. The course focuses on methodology as well as combinatorial applications.

Topics

  • Probabilistic method
  • Linearity of expectations
  • Alterations
  • Second moment method
  • Chernoff bound
  • Lovász local lemma
  • Correlation inequalities
  • Janson inequalities
  • Concentration of measure
  • Entropy method
  • The container method

Textbook

Alon, Noga and Joel H. Spencer. The Probabilistic Method. Wiley, 2016. ISBN: 9781119061953.

Grading

Grading is primarily based on homework grades (no exams). A modifier up to 5 percentage points may be applied (in either direction) in calculating the final grade, based on factors such as participation.

Course Info

Learning Resource Types

co_present Instructor Insights
notes Lecture Notes
assignment Problem Sets