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Author: Sharad S. Sane
Publisher: Hindustan Book Agency
ISBN: 9789380250489
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This is a basic text on combinatorics that deals with all the three aspects of the discipline: tricks, techniques and theory, and attempts to blend them. The book has several distinctive features. Probability and random variables with their interconnections to permutations are discussed. The theme of parity has been specially included and it covers applications ranging from solving the Nim game to the quadratic reciprocity law. Chapters related to geometry include triangulations and Sperner's theorem, classification of regular polytopes, tilings and an introduction to the Eulcidean Ramsey theory. Material on group actions covers Sylow theory, automorphism groups and a classification of finite subgroups of orthogonal groups. All chapters have a large number of exercises with varying degrees of difficulty, ranging from material suitable for Mathematical Olympiads to research.
Author: Sharad S. Sane
Publisher: Hindustan Book Agency
ISBN: 9789380250489
Category : Mathematics
Languages : en
Pages : 0
Get Book Here
Book Description
This is a basic text on combinatorics that deals with all the three aspects of the discipline: tricks, techniques and theory, and attempts to blend them. The book has several distinctive features. Probability and random variables with their interconnections to permutations are discussed. The theme of parity has been specially included and it covers applications ranging from solving the Nim game to the quadratic reciprocity law. Chapters related to geometry include triangulations and Sperner's theorem, classification of regular polytopes, tilings and an introduction to the Eulcidean Ramsey theory. Material on group actions covers Sylow theory, automorphism groups and a classification of finite subgroups of orthogonal groups. All chapters have a large number of exercises with varying degrees of difficulty, ranging from material suitable for Mathematical Olympiads to research.
Author: Alexander Mikhalev
Publisher: Springer Science & Business Media
ISBN: 9780387405629
Category : Mathematics
Languages : en
Pages : 336
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Book Description
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).
Author: Chuan-Chong Chen
Publisher: World Scientific
ISBN: 9789810211394
Category : Mathematics
Languages : en
Pages : 314
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Book Description
A textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included.
Author: Daniel I. A. Cohen
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 318
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Book Description
Author: Sharad S. Sane
Publisher: Springer
ISBN: 938627955X
Category : Mathematics
Languages : en
Pages : 477
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Book Description
This is a basic text on combinatorics that deals with all the three aspects of the discipline: tricks, techniques and theory, and attempts to blend them. The book has several distinctive features. Probability and random variables with their interconnections to permutations are discussed. The theme of parity has been specially included and it covers applications ranging from solving the Nim game to the quadratic reciprocity law. Chapters related to geometry include triangulations and Sperner's theorem, classification of regular polytopes, tilings and an introduction to the Eulcidean Ramsey theory. Material on group actions covers Sylow theory, automorphism groups and a classification of finite subgroups of orthogonal groups. All chapters have a large number of exercises with varying degrees of difficulty, ranging from material suitable for Mathematical Olympiads to research.
Author: Peter Jephson Cameron
Publisher: Cambridge University Press
ISBN: 9780521457613
Category : Mathematics
Languages : en
Pages : 372
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Book Description
Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra. This textbook stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof. The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics.
Author: D. Richard Kuhn
Publisher: CRC Press
ISBN: 1466552301
Category : Computers
Languages : en
Pages : 333
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Book Description
Combinatorial testing of software analyzes interactions among variables using a very small number of tests. This advanced approach has demonstrated success in providing strong, low-cost testing in real-world situations. Introduction to Combinatorial Testing presents a complete self-contained tutorial on advanced combinatorial testing methods for re
Author: Luc Devroye
Publisher: Springer Science & Business Media
ISBN: 1461301254
Category : Mathematics
Languages : en
Pages : 219
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Book Description
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.
Author: Radislav A. Potyrailo
Publisher: Springer Science & Business Media
ISBN: 0387737138
Category : Science
Languages : en
Pages : 495
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Book Description
Chemical sensors are in high demand for applications as varied as water pollution detection, medical diagnostics, and battlefield air analysis. Designing the next generation of sensors requires an interdisciplinary approach. The book provides a critical analysis of new opportunities in sensor materials research that have been opened up with the use of combinatorial and high-throughput technologies, with emphasis on experimental techniques. For a view of component selection with a more computational perspective, readers may refer to the complementary volume of Integrated Analytical Systems edited by M. Ryan et al., entitled “Computational Methods for Sensor Material Selection”.
Author: Larry Guth
Publisher: American Mathematical Soc.
ISBN: 1470428903
Category : Mathematics
Languages : en
Pages : 287
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Book Description
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.
