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This course offers an introduction to the polynomial method as applied to solving problems in combinatorics in the last decade.
FREE
This course includes
Hours of videos
944 years, 4 months
Units & Quizzes
34
Unlimited Lifetime access
Access on mobile app
Certificate of Completion
The course also explores the connections between the polynomial method as used in these problems to the polynomial method in other fields, including computer science, number theory, and analysis
Course Currilcum
- Introduction Unlimited
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- The Berlekamp-Welch Algorithm Unlimited
- The Finite Field Nikodym and Kakeya Theorems Unlimited
- The Joints Problem Unlimited
- Why Polynomials? Unlimited
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- Introduction to Incidence Geometry Unlimited
- Crossing Numbers and the Szemeredi-Trotter Theorem Unlimited
- Crossing Numbers and Distance Problems Unlimited
- Crossing Numbers and Distinct Distances Unlimited
- Reguli; The Zarankiewicz Problem Unlimited
- The Elekes-Sharir Approach to the Distinct Distance Problem Unlimited
- Degree Reduction Unlimited
- Bezout Theorem Unlimited
- Special Points and Lines of Algebraic Surfaces Unlimited
- An Application to Incidence Geometry Unlimited
- Taking Stock Unlimited
- Detection Lemmas and Projection Theory Unlimited
- Local to Global Arguments Unlimited
- The Regulus Detection Lemma Unlimited
- Background on Connections Between Analysis and Combinatorics (Loomis-Whitney) Unlimited
- Hardy-Littlewood-Sobolev Inequality Unlimited
- Oscillating Integrals and Besicovitch’s Arrangement of Tubes Unlimited
- Besictovitch’s Construction Unlimited
- The Kakeya Problem Unlimited
- A Version of the Joints Theorem for Long Thin Tubes Unlimited
