Polynomial Methods in Combinatorics (University Lecture Series)

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9781470428907: Polynomial Methods in Combinatorics (University Lecture Series)

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.

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About the Author:

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

Review:

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

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 Erd s 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

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Larry Guth
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Descripción American Mathematical Society, United States, 2016. Paperback. Estado de conservación: New. Language: English . Brand New Book. 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. Nº de ref. de la librería AAW9781470428907

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Larry Guth
Editorial: American Mathematical Society, United States (2016)
ISBN 10: 1470428903 ISBN 13: 9781470428907
Nuevos Paperback Cantidad: 1
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The Book Depository
(London, Reino Unido)
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Descripción American Mathematical Society, United States, 2016. Paperback. Estado de conservación: New. Language: English . Brand New Book. 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. Nº de ref. de la librería AAW9781470428907

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Descripción American Mathematical Society. Estado de conservación: Brand New. Ships from USA. FREE domestic shipping. Nº de ref. de la librería 1470428903

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Descripción Estado de conservación: New. pp. 273. Nº de ref. de la librería 371216257

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Descripción Amer Mathematical Society, 2016. Paperback. Estado de conservación: Brand New. 273 pages. 10.25x7.00x0.75 inches. In Stock. Nº de ref. de la librería 1470428903

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Larry Guth
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ISBN 10: 1470428903 ISBN 13: 9781470428907
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Descripción American Mathematical Society, 2016. Paperback. Estado de conservación: New. Nº de ref. de la librería P111470428903

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