18.218 Probabilistic Method in Combinatorics, Spring 2019

Author(s)
Zhao, Yufei
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Alternative title
Probabilistic Method in Combinatorics
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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.
Date issued
2019-06
URI
https://hdl.handle.net/1721.1/151192
Department
Massachusetts Institute of Technology. Department of Mathematics
Other identifiers
18.218-Spring2019
Other identifiers
18.218
IMSCP-MD5-0282d72460e569d6f4bd54e8bbdcfeab
Keywords
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
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