Polynomial Methods in Combinatorics (University Lecture Series) (University Lecture, 64) - Softcover

Larry Guth

Softcover

ISBN 10: 1470428903 ISBN 13: 9781470428907

Publisher: American Mathematical Society, 2016

Synopsis

This book explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics. One of the first results in this story is a short elegant solution of the Kakeya problem for finite fields, which was considered a deep and difficult problem in combinatorial geometry. The author also discusses in detail various problems in incidence geometry associated to Paul Erdos's famous distinct distances problem in the plane from the 1940s. The proof techniques are also connected to error-correcting codes, Fourier analysis, number theory, and differential geometry. Although the mathematics discussed in the book is deep and far-reaching, it should be accessible to first- and second-year graduate students and advanced undergraduates. The book contains approximately 100 exercises that further the reader's understanding of the main themes of the book.

About this title

About the Author

Larry Guth, Massachusetts Institute of Technology, Cambridge, MA, USA.

Review

One of the strengths that combinatorial problems have is that they are understandable to non-experts in the field...One of the strengths that polynomials have is that they are well understood by mathematicians in general. Larry Guth manages to exploit both of those strengths in this book and provide an accessible and enlightening drive through a selection of combinatorial problems for which polynomials have been used to great effect. --Simeon Ball, Jahresbericht der Deutschen Mathematiker-Vereinigung

In the 273 page long book, a huge number of concepts are presented, and many results concerning them are formulated and proved. The book is a perfect presentation of the theme. --Béla Uhrin, Mathematical Reviews

It is extremely challenging to present a current (and still very active) research area in a manner that a good mathematics undergraduate would be able to grasp after a reasonable effort, but the author is quite successful in this task, and this would be a book of value to both undergraduates and graduates. --Terence Tao, University of California, Los Angeles, author of An Epsilon of Room I, II and Hilbert's Fifth Problem and Related Topics

Edition details

• Publisher: American Mathematical Society
• Publication date: 2016
• ISBN 10: 1470428903
• ISBN 13: 9781470428907
• Binding: Paperback
• Language: English
• Number of pages: 273