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Combinatorial Methods

2004 Mathematics
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Release : 2004
Genre : Mathematics
Kind : eBook
Book Rating : 629/5 ( reviews)

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Book Synopsis Combinatorial Methods by : Alexander Mikhalev

Download or read book Combinatorial Methods written by Alexander Mikhalev. This book was released on 2004. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20th Century. This book is divided into three fairly independent parts. Part I provides a brief exposition of several classical techniques in combinatorial group theory, namely, methods of Nielsen, Whitehead, and Tietze. Part II contains the main focus of the book. Here the authors show how the aforementioned techniques of combinatorial group theory found their way into affine algebraic geometry, a fascinating area of mathematics that studies polynomials and polynomial mappings. Part III illustrates how ideas from combinatorial group theory contributed to the theory of free algebras. The focus here is on Schreier varieties of algebras (a variety of algebras is said to be Schreier if any subalgebra of a free algebra of this variety is free in the same variety of algebras).

Polynomial Methods in Combinatorics

2016-06-10 Mathematics
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Release : 2016-06-10
Genre : Mathematics
Kind : eBook
Book Rating : 903/5 ( reviews)

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Book Synopsis Polynomial Methods in Combinatorics by : Larry Guth

Download or read book Polynomial Methods in Combinatorics written by Larry Guth. This book was released on 2016-06-10. Available in PDF, EPUB and Kindle. Book excerpt: 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 Erdős'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.

Combinatorial Methods in Density Estimation

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 254/5 ( reviews)

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Book Synopsis Combinatorial Methods in Density Estimation by : Luc Devroye

Download or read book Combinatorial Methods in Density Estimation written by Luc Devroye. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Density estimation has evolved enormously since the days of bar plots and histograms, but researchers and users are still struggling with the problem of the selection of the bin widths. This book is the first to explore a new paradigm for the data-based or automatic selection of the free parameters of density estimates in general so that the expected error is within a given constant multiple of the best possible error. The paradigm can be used in nearly all density estimates and for most model selection problems, both parametric and nonparametric.

Combinatorial Methods with Computer Applications

2016-04-19 Computers
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Release : 2016-04-19
Genre : Computers
Kind : eBook
Book Rating : 443/5 ( reviews)

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Book Synopsis Combinatorial Methods with Computer Applications by : Jonathan L. Gross

Download or read book Combinatorial Methods with Computer Applications written by Jonathan L. Gross. This book was released on 2016-04-19. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinat

Combinatorial Methods in Discrete Mathematics

1996-01-11 Mathematics
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Release : 1996-01-11
Genre : Mathematics
Kind : eBook
Book Rating : 138/5 ( reviews)

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Book Synopsis Combinatorial Methods in Discrete Mathematics by : Vladimir N. Sachkov

Download or read book Combinatorial Methods in Discrete Mathematics written by Vladimir N. Sachkov. This book was released on 1996-01-11. Available in PDF, EPUB and Kindle. Book excerpt: This is an attempt to present some complex problems of discrete mathematics in a simple and unified form using a unique, general combinatorial scheme. The author's aim is not always to present the most general results, but rather to focus attention on ones that illustrate the methods described. A distinctive aspect of the book is the large number of asymptotic formulae derived.This is an important book, describing many ideas not previously available in English; the author has taken the chance to update the text and references where appropriate.

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