The Theory of Partitions

The Theory of Partitions
Author: George E. Andrews
Publisher: Cambridge University Press
Total Pages: 274
Release: 1998-07-28
Genre: Mathematics
ISBN: 9780521637664

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

Integer Partitions

Integer Partitions
Author: George E. Andrews
Publisher: Cambridge University Press
Total Pages: 156
Release: 2004-10-11
Genre: Mathematics
ISBN: 9780521600903

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

Partitions, q-Series, and Modular Forms

Partitions, q-Series, and Modular Forms
Author: Krishnaswami Alladi
Publisher: Springer Science & Business Media
Total Pages: 233
Release: 2011-11-01
Genre: Mathematics
ISBN: 1461400287

Partitions, q-Series, and Modular Forms contains a collection of research and survey papers that grew out of a Conference on Partitions, q-Series and Modular Forms at the University of Florida, Gainesville in March 2008. It will be of interest to researchers and graduate students that would like to learn of recent developments in the theory of q-series and modular and how it relates to number theory, combinatorics and special functions.

Number Theory

Number Theory
Author: George E. Andrews
Publisher: Courier Corporation
Total Pages: 292
Release: 2012-04-30
Genre: Mathematics
ISBN: 0486135101

Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.

Number Theory in the Spirit of Ramanujan

Number Theory in the Spirit of Ramanujan
Author: Bruce C. Berndt
Publisher: American Mathematical Soc.
Total Pages: 210
Release: 2006
Genre: Mathematics
ISBN: 0821841785

Ramanujan is recognized as one of the great number theorists of the twentieth century. Here now is the first book to provide an introduction to his work in number theory. Most of Ramanujan's work in number theory arose out of $q$-series and theta functions. This book provides an introduction to these two important subjects and to some of the topics in number theory that are inextricably intertwined with them, including the theory of partitions, sums of squares and triangular numbers, and the Ramanujan tau function. The majority of the results discussed here are originally due to Ramanujan or were rediscovered by him. Ramanujan did not leave us proofs of the thousands of theorems he recorded in his notebooks, and so it cannot be claimed that many of the proofs given in this book are those found by Ramanujan. However, they are all in the spirit of his mathematics. The subjects examined in this book have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematical research. Therefore, at the end of each of the seven chapters, Berndt discusses the results established in the chapter and places them in both historical and contemporary contexts. The book is suitable for advanced undergraduates and beginning graduate students interested in number theory.

Combinatorics and Complexity of Partition Functions

Combinatorics and Complexity of Partition Functions
Author: Alexander Barvinok
Publisher: Springer
Total Pages: 304
Release: 2017-03-13
Genre: Mathematics
ISBN: 3319518291

Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates.

Applied Discrete Structures

Applied Discrete Structures
Author: Ken Levasseur
Publisher: Lulu.com
Total Pages: 574
Release: 2012-02-25
Genre: Applied mathematics
ISBN: 1105559297

Applied Discrete Structures, is a two semester undergraduate text in discrete mathematics, focusing on the structural properties of mathematical objects. These include matrices, functions, graphs, trees, lattices and algebraic structures. The algebraic structures that are discussed are monoids, groups, rings, fields and vector spaces. Website: http: //discretemath.org Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http: //www.aimath.org/textbooks/. This version was created using Mathbook XML (https: //mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at UMass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at UMass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.

Introduction to the Theory of Sets

Introduction to the Theory of Sets
Author: Joseph Breuer
Publisher: Courier Corporation
Total Pages: 130
Release: 2012-08-09
Genre: Mathematics
ISBN: 0486154874

This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.