Spring 2026
Bhargav Narayanan
Course Description:
This is the second part of a two-semester course surveying basic topics in combinatorics. Topics for the full semester will include:
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 and hypergraphs, combinatorial discrepancy, Ramsey theory, correlation inequalities
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 2024
Jeffry Kahn
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 and hypergraphs, combinatorial discrepancy, Ramsey theory, correlation inequalities
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 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