Lecture Notes | The Polynomial Method | Mathematics | MIT OpenCourseWare

Course Info

Instructor

Prof. Lawrence D Guth

Departments

Mathematics

As Taught In

Fall 2012

Level

Graduate

Topics

Mathematics
- Algebra and Number Theory
- Discrete Mathematics

Learning Resource Types

Problem Sets

Lecture Notes

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Lecture Notes

18.S997 Fall 2012 The Polynomial Method: The Regulus Detection Lemma

18.S997 Fall 2012 The Polynomial Method: A Version of the Joints Theorem for Long Thin Tubes

18.S997 Fall 2012 The Polynomial Method: An Application to Incidence Geometry

18.S997 Fall 2012 The Polynomial Method: Background on Connections Between Analysis and Combinatorics (Loomis-Whitney)

18.S997 Fall 2012 The Polynomial Method: Besictovitch's Construction

18.S997 Fall 2012 The Polynomial Method: Bezout Theorem

18.S997 Fall 2012 The Polynomial Method: Crossing Numbers and Distance Problems

18.S997 Fall 2012 The Polynomial Method: Crossing Numbers and Distinct Distances

18.S997 Fall 2012 The Polynomial Method: Crossing Numbers and the Szemeredi-Trotter Theorem

18.S997 Fall 2012 The Polynomial Method: Degree Reduction

18.S997 Fall 2012 The Polynomial Method: Detection Lemmas and Projection Theory

18.S997 Fall 2012 The Polynomial Method: Hardy-Littlewood-Sobolev Inequality

18.S997 Fall 2012 The Polynomial Method: Incidence Bounds in Three Dimensions

18.S997 Fall 2012 The Polynomial Method: Integer Polynomials That Vanish at Rational Points

18.S997 Fall 2012 The Polynomial Method: Introduction

18.S997 Fall 2012 The Polynomial Method: Introduction to Incidence Geometry

18.S997 Fall 2012 The Polynomial Method: Introduction to the Cellular Method

18.S997 Fall 2012 The Polynomial Method: Introduction to Thue's Theorem on Diophantine Approximation

18.S997 Fall 2012 The Polynomial Method: Local to Global Arguments

18.S997 Fall 2012 The Polynomial Method: Oscillating Integrals and Besicovitch's Arrangement of Tubes

18.S997 Fall 2012 The Polynomial Method: Polynomial Cell Decompositions

18.S997 Fall 2012 The Polynomial Method: Reguli; The Zarankiewicz Problem

18.S997 Fall 2012 The Polynomial Method: Special Points and Lines of Algebraic Surfaces

18.S997 Fall 2012 The Polynomial Method: Taking Stock

18.S997 Fall 2012 The Polynomial Method: The Berlekamp-Welch Algorithm

18.S997 Fall 2012 The Polynomial Method: The Elekes-Sharir Approach to the Distinct Distance Problem

18.S997 Fall 2012 The Polynomial Method: The Finite Field Nikodym and Kakeya Theorems

18.S997 Fall 2012 The Polynomial Method: The Joints Problem

18.S997 Fall 2012 The Polynomial Method: The Kakeya Problem

18.S997 Fall 2012 The Polynomial Method: Thue's Proof (Part II): Polynomials of Two Variables

18.S997 Fall 2012 The Polynomial Method: Thue's Proof (Part III)

18.S997 Fall 2012 The Polynomial Method: Using Cell Decompositions

18.S997 Fall 2012 The Polynomial Method: What's Special About Polynomials? (A Geometric Perspective)

18.S997 Fall 2012 The Polynomial Method: Why Polynomials? (Part 1)

Course Info

Instructor

Prof. Lawrence D Guth

Departments

Mathematics

As Taught In

Fall 2012

Level

Graduate

Topics

Mathematics
- Algebra and Number Theory
- Discrete Mathematics

Learning Resource Types

Problem Sets

Lecture Notes

Download Course

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