18.226 | Fall 2022 | Graduate

Probabilistic Methods in Combinatorics

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 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.

Course Info

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As Taught In
Fall 2022
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Online Textbook
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Lecture Videos
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