Course Meeting Times
Lectures: 2 sessions / week, 1.5 hours / session
Prerequisites
- 18.211 Combinatorial Analysis
- 18.600 Probability and Random Variables
- 18.100A Real Analysis, 18.100B Real Analysis, 18.100P Real Analysis, or 18.100Q Real Analysis
or permission of instructor
Course Description
This course is a graduate-level introduction to the probabilistic methods, 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
- Linearity of expectations
- Alterations
- Second moment
- Chernoff bound
- Lovász local lemma
- Correlation inequalities
- Janson inequalities
- Concentration of measure
- Entropy
- Containers
Textbook
Alon, Noga and Joel H. Spencer. The Probabilistic Method. Wiley, 2016. ISBN: 9781119061953. (The fourth edition is the latest, but earlier editions suffice.)
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.
Final letter grade cutoffs: Only non-starred problems are considered for the calculations of letter grades other than A and A+.
- A− : ≥ 85%
- B− : ≥ 70%
- C− : ≥ 50%
Grades of A and A+ are awarded at instructor’s discretion based on overall performance. Solving a significant number of starred problems is a requirement for grades of A and A+.
Note that for MIT students, ± grade modifiers do not count towards the GPA and do not appear on the external transcript.
