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Polynomial Methods in Combinatorics
About this Title
Larry Guth, Massachusetts Institute of Technology, Cambridge, MA
Publication: University Lecture Series
Publication Year:
2016; Volume 64
ISBNs: 978-1-4704-2890-7 (print); 978-1-4704-3214-0 (online)
DOI: https://doi.org/10.1090/ulect/064
MathSciNet review: MR3495952
MSC: Primary 05-01; Secondary 11B75, 13F20, 14N10, 52C10, 94B25
Table of Contents
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Front/Back Matter
Chapters
- Chapter 1. Introduction
- Chapter 2. Fundamental examples of the polynomial method
- Chapter 3. Why polynomials?
- Chapter 4. The polynomial method in error-correcting codes
- Chapter 5. On polynomials and linear algebra in combinatorics
- Chapter 6. The Bezout theorem
- Chapter 7. Incidence geometry
- Chapter 8. Incidence geometry in three dimensions
- Chapter 9. Partial symmetries
- Chapter 10. Polynomial partitioning
- Chapter 11. Combinatorial structure, algebraic structure, and geometric structure
- Chapter 12. An incidence bound for lines in three dimensions
- Chapter 13. Ruled surfaces and projection theory
- Chapter 14. The polynomial method in differential geometry
- Chapter 15. Harmonic analysis and the Kakeya problem
- Chapter 16. The polynomial method in number theory