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Polynomial Methods in Combinatorics
Larry Guth
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Description for Polynomial Methods in Combinatorics
Paperback. Series: University Lecture Series. Num Pages: 273 pages, illustrations. BIC Classification: PBD; PBM; PBP; PBV. Category: (G) General (US: Trade). Dimension: 180 x 356 x 16. Weight in Grams: 506.
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.
Product Details
Publisher
American Mathematical Society
Format
Paperback
Publication date
2016
Series
University Lecture Series
Condition
New
Number of Pages
273
Place of Publication
Providence, United States
ISBN
9781470428907
SKU
V9781470428907
Shipping Time
Usually ships in 7 to 11 working days
Ref
99-1
About Larry Guth
Larry Guth, Massachusetts Institute of Technology, Cambridge, MA, USA.
Reviews for Polynomial Methods in Combinatorics
Some of the greatest advances in geometric combinatorics and harmonic analysis in recent years have been accomplished using the polynomial method. Larry Guth gives a readable and timely exposition of this important topic, which is destined to influence a variety of critical developments in combinatorics, harmonic analysis and other areas for many years to come. -Alex Iosevich, University of Rochester, author of The Erdos Distance Problem and A View from the Top. 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 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. -Bela Uhrin, Mathematical Reviews