Spring 2024
Swee Hong Chan
Course Description:
This is the second part of a two-semester course surveying basic topics in combinatorics. Topics for the full semester should include the topics below.
Enumeration: (basics, generating functions, recurrence relations, inclusion-exclusion, asymptotics)
Matching theory, polyhedral and fractional issues
Partially ordered sets and lattices, Mobius functions
Theory of finite sets: isoperimetry, intersecting families, and related topics
Correlation inequalities
Ramsey theory
Probabilistic methods
Algebraic and Fourier methods
Entropy Method
Text:
van Lint-Wilson (optional; there is no real text, and we will appeal to appropriate references)
Prerequisites:
There are no formal prerequisites, but the course assumes a level of mathematical maturity consistent with having taken serious undergraduate courses in linear algebra and/or real analysis. (Basic linear algebra will be helpful, real analysis less so; it will be good to have seen at least a little combinatorics and probability.) Taking 583 without having been in 582 is possible: check with me if in doubt.
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Spring 2023
Jeffry Kahn
Course Description:
This is the second part of a two-semester course surveying basic topics in combinatorics. Topics for the full year should include (at least) the topics below.
Enumeration: (basics, generating functions, recurrence relations, inclusion-exclusion, asymptotics)
Matching theory, polyhedral and fractional issues
Partially ordered sets and lattices, Mobius functions
Theory of finite sets: isoperimetry, intersecting families, and related topics
Combinatorial discrepancy
Correlation inequalities
Ramsey theory
Probabilistic methods
Algebraic and Fourier methods
Entropy Methods
Text:
van Lint-Wilson (optional; there is no real text, and we will appeal to appropriate references)
Prerequisites:
There are no formal prerequisites, but the course assumes a level of mathematical maturity consistent with having taken serious undergraduate courses in linear algebra and/or real analysis. (Basic linear algebra will be helpful, real analysis less so; it will be good to have seen at least a little combinatorics.) Taking 583 without having been in 582 is possible: check with me if in doubt.
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Spring 2022
Bhargav Narayanan
Course Description:
This is the second part of a two-semester course surveying basic topics in combinatorics. Topics for the full year (582 and 583) should include most of the following, along side selected recent developments.
Enumeration: basics, generating functions, recurrence relations, inclusion-exclusion, asymptotics
Matching theory, polyhedral and fractional issues
Partially ordered sets and lattices, Mobius functions
Theory of finite sets: isoperimetry, intersecting families, and related topics
Combinatorial discrepancy
Correlation inequalities
Ramsey theory
Probabilistic methods
Algebraic and Fourier methods
Entropy Methods
Text:
van Lint-Wilson/Bollobas is nice but optional. There is really no text; various relevant books will be on reserve.
Prerequisites:
There are no formal prerequisites, but the course assumes a level of mathematical maturity consistent with having had good courses in linear algebra (such as 640:350) and real analysis (such as 640:411) at the undergraduate level. It will help to have seen at least a little prior combinatorics, and (very) rudimentary probability will also occasionally be useful. See me if in doubt.
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Spring 2021 - Jeffry Kahn
Course Description:
This is the second part of a two-semester course surveying basic topics in combinatorics. Topics for the full year should (at least) incude most of the topics below. Enumeration (basics, generating functions, recurrence relations, inclusion-exclusion, asymptotics) - Matching theory, polyhedral and fractional issues - Partially ordered sets and lattices, Mobius functions - Theory of finite sets, hypergraphs, combinatorial discrepancy, Ramsey theory, correlation inequalities - Probabilistic methods - Algebraic and Fourier methods - Entropy methods
Text:
van Lint-Wilson (nice but optional); various relevant books will be on reserve.
Prerequisites:
There are no formal prerequisites, but the course assumes a level of mathematical maturity consistent with having taken serious undergraduate courses in linear algebra and/or real analysis. (Basic linear algebra will be helpful, real analysis less so; it will be good to have seen at least a little combinatorics.) Taking 583 without having been in 582 is possible: check with me if in doubt.
Schedule of Sections:
Previous Semesters:
- Spring 2021 Prof. Kahn
- Spring 2020 Prof. Narayanan
- Spring 2018 Prof. Beck
