18.218 Probabilistic Method in Combinatorics, Spring 2019
Author(s)
Zhao, Yufei
Alternative Title
Probabilistic Method in Combinatorics
Date Issued
June 2019
Abstract
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.
Subjects
probabilistic method
Ramsey numbers
Lovász Local Lemma
hypergraph colorings
balancing vectors
sum-free sets
second Moment Method
Chernoff bound
Moser-Tardos algorithm
Janson’s inequalities
Harris-FKG inequality
Martingale convergence
Azuma’s inequality
entropy methods
occupancy method
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
This site (c) Massachusetts Institute of Technology 2023. Content within individual courses is (c) by the individual authors unless otherwise noted. The Massachusetts Institute of Technology is providing this Work (as defined below) under the terms of this Creative Commons public license ("CCPL" or "license") unless otherwise noted. The Work is protected by copyright and/or other applicable law. Any use of the work other than as authorized under this license is prohibited. By exercising any of the rights to the Work provided here, You (as defined below) accept and agree to be bound by the terms of this license. The Licensor, the Massachusetts Institute of Technology, grants You the rights contained here in consideration of Your acceptance of such terms and conditions.
Persistent DSpace Link
