Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
Prerequisites
- 18.211 Combinatorial Analysis
- 18.600 Probability and Random Variables
- Real Analysis—either 18.100A, 18.100B, or 18.100C
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.