Topics in Combinatorics: Analysis of Boolean Functions | Mathematics | MIT OpenCourseWare

Course Info

Instructor

Prof. Dor Minzer

Departments

Mathematics

As Taught In

Spring 2021

Level

Graduate

Topics

Mathematics
- Probability and Statistics

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Lecture Notes

Lecture 1: Course Overview and the Basic Set-up

Lecture 2: The BLR Lineairty Test and Random Restrictions

Lecture 3: PAC Learning and Learning Sparse Functions

Lecture 4: Influences of Boolean Functions

Lecture 5: Hypercontractive Inequality

Lecture 6: The FKN Theorem and the KKL Theorem

Lecture 7: Talagrand’s Version of the KKL Theorem, the Friedgut Junta Theorem, and Isoperimetric Inequalities

Lectures 8–10: Noise Stability and Arrow’s Impossibility Theorem

Lectures 11–12: Erdos-Ko-Rado Type Theorem, the p-biased Cube, and Properties of Quasi-random Families

Lectures 13–14: Invariance Principle, the Berry-Essen Theorem, and Hypercontractivity in Gaussian Space

Lecture 15: Introduction to Complexity Theory, Approximation Problems, and the PCP Theorem

Lecture 16: The Goemans-Williamson Algorithm and A Hardness Result for Max-Cut

Lecture 17: Preliminaries, the Reduction, and Analysis of the Reduction

Course Info

Instructor

Prof. Dor Minzer

Departments

Mathematics

As Taught In

Spring 2021

Level

Graduate

Topics

Mathematics
- Probability and Statistics

Learning Resource Types

Lecture Notes

Problem Sets

Projects

Download Course

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