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The Theory of Partitions

The Theory of Partitions Author George E. Andrews
ISBN-10 052163766X
Release 1998-07-28
Pages 255
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Discusses mathematics related to partitions of numbers into sums of positive integers.

Introduction to the Modern Theory of Dynamical Systems

Introduction to the Modern Theory of Dynamical Systems Author Anatole Katok
ISBN-10 0521575575
Release 1997
Pages 802
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This book provides a self-contained comprehensive exposition of the theory of dynamical systems. The book begins with a discussion of several elementary but crucial examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate and up.

Special Functions

Special Functions Author George E. Andrews
ISBN-10 0521789885
Release 1999
Pages 664
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An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.

Integer Partitions

Integer Partitions Author George E. Andrews
ISBN-10 0521600901
Release 2004-10-11
Pages 141
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Provides a wide ranging introduction to partitions, accessible to any reader familiar with polynomials and infinite series.

The Symmetric Group

The Symmetric Group Author Bruce Sagan
ISBN-10 9781475768046
Release 2013-03-09
Pages 240
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This book brings together many of the important results in this field. From the reviews: ""A classic gets even better....The edition has new material including the Novelli-Pak-Stoyanovskii bijective proof of the hook formula, Stanley’s proof of the sum of squares formula using differential posets, Fomin’s bijective proof of the sum of squares formula, group acting on posets and their use in proving unimodality, and chromatic symmetric functions." --ZENTRALBLATT MATH

Eigenspaces of Graphs

Eigenspaces of Graphs Author Dragoš M. Cvetković
ISBN-10 0521573521
Release 1997-01-09
Pages 258
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This book describes the spectral theory of finite graphs.

Prime Numbers and the Riemann Hypothesis

Prime Numbers and the Riemann Hypothesis Author Barry Mazur
ISBN-10 9781107101920
Release 2016-04-11
Pages 150
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This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.

Combinatorics of Set Partitions

Combinatorics of Set Partitions Author Toufik Mansour
ISBN-10 9781439863336
Release 2012-07-27
Pages 516
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Focusing on a very active area of mathematical research in the last decade, Combinatorics of Set Partitions presents methods used in the combinatorics of pattern avoidance and pattern enumeration in set partitions. Designed for students and researchers in discrete mathematics, the book is a one-stop reference on the results and research activities of set partitions from 1500 A.D. to today. Each chapter gives historical perspectives and contrasts different approaches, including generating functions, kernel method, block decomposition method, generating tree, and Wilf equivalences. Methods and definitions are illustrated with worked examples and MapleTM code. End-of-chapter problems often draw on data from published papers and the author’s extensive research in this field. The text also explores research directions that extend the results discussed. C++ programs and output tables are listed in the appendices and available for download on the author’s web page.

Young Tableaux

Young Tableaux Author William Fulton
ISBN-10 0521567246
Release 1997
Pages 260
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Describes combinatorics involving Young tableaux and their uses in representation theory and algebraic geometry.

Q series with Applications to Combinatorics Number Theory and Physics

Q series with Applications to Combinatorics  Number Theory  and Physics Author Bruce C. Berndt
ISBN-10 9780821827468
Release 2001
Pages 277
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The subject of $q$-series can be said to begin with Euler and his pentagonal number theorem. In fact, $q$-series are sometimes called Eulerian series. Contributions were made by Gauss, Jacobi, and Cauchy, but the first attempt at a systematic development, especially from the point of view of studying series with the products in the summands, was made by E. Heine in 1847. In the latter part of the nineteenth and in the early part of the twentieth centuries, two English mathematicians, L. J. Rogers and F. H. Jackson, made fundamental contributions. In 1940, G. H. Hardy described what we now call Ramanujan's famous $_1\psi_1$ summation theorem as ``a remarkable formula with many parameters.'' This is now one of the fundamental theorems of the subject. Despite humble beginnings, the subject of $q$-series has flourished in the past three decades, particularly with its applications to combinatorics, number theory, and physics. During the year 2000, the University of Illinois embraced The Millennial Year in Number Theory. One of the events that year was the conference $q$-Series with Applications to Combinatorics, Number Theory, and Physics. This event gathered mathematicians from the world over to lecture and discuss their research. This volume presents nineteen of the papers presented at the conference. The excellent lectures that are included chart pathways into the future and survey the numerous applications of $q$-series to combinatorics, number theory, and physics.

Matroid Applications

Matroid Applications Author Neil White
ISBN-10 0521381657
Release 1992-03-05
Pages 363
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This volume, the third in a sequence that began with The Theory of Matroids and Combinatorial Geometries, concentrates on the applications of matroid theory to a variety of topics from engineering (rigidity and scene analysis), combinatorics (graphs, lattices, codes and designs), topology and operations research (the greedy algorithm).

Sperner Theory

Sperner Theory Author Konrad Engel
ISBN-10 0521452066
Release 1997-01-28
Pages 417
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Emphasises the powerful methods arising from the fusion of combinatorial techniques with programming, linear algebra, and probability theory.

Canonical Ramsey Theory on Polish Spaces

Canonical Ramsey Theory on Polish Spaces Author Vladimir Kanovei
ISBN-10 9781107434332
Release 2013-09-12
Pages 265
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This book lays the foundations for an exciting new area of research in descriptive set theory. It develops a robust connection between two active topics: forcing and analytic equivalence relations. This in turn allows the authors to develop a generalization of classical Ramsey theory. Given an analytic equivalence relation on a Polish space, can one find a large subset of the space on which it has a simple form? The book provides many positive and negative general answers to this question. The proofs feature proper forcing and Gandy–Harrington forcing, as well as partition arguments. The results include strong canonization theorems for many classes of equivalence relations and sigma-ideals, as well as ergodicity results in cases where canonization theorems are impossible to achieve. Ideal for graduate students and researchers in set theory, the book provides a useful springboard for further research.

Mathematical Theory of Entropy

Mathematical Theory of Entropy Author Nathaniel F. G. Martin
ISBN-10 0521177383
Release 2011-06-02
Pages 286
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This excellent 1981 treatment of the mathematical theory of entropy gives an accessible exposition its application to other fields.

Applied Finite Group Actions

Applied Finite Group Actions Author Adalbert Kerber
ISBN-10 3540659412
Release 1999-08-18
Pages 454
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Written by one of the top experts in the fields of combinatorics and representation theory, this book distinguishes itself from the existing literature by its applications-oriented point of view. The second edition is extended, placing more emphasis on applications to the constructive theory of finite structures. Recent progress in this field, in particular in design and coding theory, is described.

Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields

Nonlinear Oscillations  Dynamical Systems  and Bifurcations of Vector Fields Author John Guckenheimer
ISBN-10 9781461211402
Release 2013-11-21
Pages 462
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An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

Integrable Systems

Integrable Systems Author N.J. Hitchin
ISBN-10 9780199676774
Release 2013-03-14
Pages 136
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Designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors, this book has its origins in a lecture series given by the internationally renowned authors. Written in an accessible, informal style, it fills a gap in the existing literature.