## The Theory of Partitions

Author: George E. Andrews
Publisher: Cambridge University Press
ISBN: 9780521637664
Format: PDF, Mobi

Discusses mathematics related to partitions of numbers into sums of positive integers.

## Introduction to the Modern Theory of Dynamical Systems

Author: Anatole Katok
Publisher: Cambridge University Press
ISBN: 9780521575577
Format: PDF, ePub, Mobi

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

Author: George E. Andrews
Publisher: Cambridge University Press
ISBN: 9780521789882
Format: PDF

An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.

## Integer Partitions

Author: George E. Andrews
Publisher: Cambridge University Press
ISBN: 9780521600903
Format: PDF

Provides a wide ranging introduction to partitions, accessible to any reader familiar with polynomials and infinite series.

## Prime Numbers and the Riemann Hypothesis

Author: Barry Mazur
Publisher: Cambridge University Press
ISBN: 1107101921
Format: PDF

This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.

## Eigenspaces of Graphs

Author: Dragoš M. Cvetković
Publisher: Cambridge University Press
ISBN: 9780521573528
Format: PDF, Docs

This book describes the spectral theory of finite graphs.

## The Symmetric Group

Author: Bruce Sagan
Publisher: Springer Science & Business Media
ISBN: 1475768044
Format: PDF, Docs

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

## Combinatorics of Set Partitions

Author: Toufik Mansour
Publisher: CRC Press
ISBN: 1439863334
Format: PDF, ePub, Mobi

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

Author: William Fulton
Publisher: Cambridge University Press
ISBN: 9780521567244
Format: PDF, ePub

Describes combinatorics involving Young tableaux and their uses in representation theory and algebraic geometry.

## Q series with Applications to Combinatorics Number Theory and Physics

Author: Bruce C. Berndt
Publisher: American Mathematical Soc.
ISBN: 0821827464
Format: PDF, Kindle

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.