Spring 2023
Bhargav Narayanan
Subtitle:
Recent Developments
Course Description:
This course will address some of the exciting recent developments in the field of discrete mathematics. Amongst other things, we will cover the recent resolutions of Kahn-Kalai/Talagrand conjectures on thresholds, spectral methods and the resolution of the sensitivity conjecture, the development of hypergraph containers, and some recent developments in the theory of discrete random matrices.
Text:
None
Prerequisites:
Some familiarity with undergraduate algebra (linear and abstract), as well as general mathematical maturity
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Fall 2021 - Jeffry Kahn
Subtitle:
Extremal Combinatorics
Course Description:
The name "extremal combinatorics" covers many of the most significant discrete developments of recent (and less recent) years, and many of the most interesting open problems. We'll sample some of these, trying to emphasize the wide range of ideas, methods and extra-combinatorial machinery that come into play.
Text:
None
Prerequisites:
Apart from basic combinatorics, I'll try to make the course "self-contained," meaning some maturity will help but we'll fill in background as needed. Check with me if in doubt.
Schedule of Sections:
Previous Semesters:
- Fall 2020 Prof. Kopparty
- Spring 2020 Prof. Kahn
- Fall 2019 Prof. Kopparty
- Spring 2019 Prof. Narayanan
- Spring 2018 Prof. Saraf
- Fall 2017 Prof. Kahn
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Please note: the instructor and course information changes from semester to semester for this course number. Specifics for each semester below.
Spring 2019
Bhargav Narayanan Peruvemba
Subtitle:
Topics in Combinatorics
Course Description:
This is a topics course in discrete mathematics. Instead of pursuing a single overarching theme, we shall look at a few different problems whose solutions illustrate important techniques in the field. The focus will be on introducing tools from algebra, analysis and probability, and showing how these can be brought to bear on combinatorial problems.
Text:
No textbook covers the requisite material. We will borrow from a mixture of research papers, surveys and lecture notes.
Prerequisites:
The course will be more or less self-contained, but will assume familiarity with undergraduate algebra and probability.*
Spring 2018
Shubhangi Saraf
Subtitle:
Algebraic gems in discrete mathematics and theoretical computer science
Course Description:
In the last few decades, algebraic methods have proven to be extremely powerful in several areas of discrete mathematics and theoretical computer science. Many of these important advances in the field have relied on very simple properties of polynomials. In this course we will see many interesting and often surprising applications of linear algebra and polynomials to combinatorics, discrete geometry, complexity theory and algorithm design. We will develop all the algebraic tools that we need along the way.
Text:
none
Prerequisites:
Basic combinatorics/discrete math, basic linear algebra, mathematical maturity
Fall 2017
Jeffry Kahn
Subtitle:
Extremal Combinatorics
Course Description:
The term "Extremal Combinatorics" covers many of the most significant discrete developments of recent (and less recent) years, and many of the most interesting open problems. We'll sample some of these, trying to emphasize the wide range of ideas, methods and extra-combinatorial machinery that come into play.
Text:
None; relevant books will be on reserve.
Prerequisites:
There are no formal prerequisites but it will help to have at least seen the combinatorics sequence, 642.582-3. I'll try to fill in background as we go along. Check with me if in doubt.
