Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Integer Partitions PDF full book. Access full book title Integer Partitions by George E. Andrews. Download full books in PDF and EPUB format.
Author: George E. Andrews Publisher: Cambridge University Press ISBN: 9780521841184 Category : Mathematics Languages : en Pages : 152
Book Description
The theory of integer partitions is a subject of enduring interest as well as a major research area. It has found numerous applications, including celebrated results such as the Rogers-Ramanujan identities. The aim of this introductory textbook is to provide an accessible and wide-ranging introduction to partitions, without requiring anything more than some familiarity with polynomials and infinite series. Many exercises are included, together with some solutions and helpful hints.
Author: Oscar Levin Publisher: Createspace Independent Publishing Platform ISBN: 9781724572639 Category : Languages : en Pages : 238
Book Description
Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.
Author: Toufik Mansour Publisher: CRC Press ISBN: 1439863334 Category : Computers Languages : en Pages : 617
Book Description
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.
Author: Bruce C. Berndt Publisher: American Mathematical Soc. ISBN: 0821841785 Category : Mathematics Languages : en Pages : 210
Book Description
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.
Author: Philippe Flajolet Publisher: Cambridge University Press ISBN: 1139477161 Category : Mathematics Languages : en Pages : 825
Book Description
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Author: Geoffrey B. Campbell Publisher: CRC Press ISBN: 1040026443 Category : Mathematics Languages : en Pages : 567
Book Description
Vector Partitions, Visible Points and Ramanujan Functions offers a novel theory of Vector Partitions, though very much grounded in the long-established work of others, that could be developed as an extension to the existing theory of Integer Partitions. The book is suitable for graduate students in physics, applied mathematics, number theory and computational mathematics. It takes the reader up to research level, presenting new results alongside known classical results from integer partitions and areas of vector and multipartite partition theory. It also sets forth new directions for research for the more advanced reader. Above all, the intention of the book is to bring new inspiration to others who study mathematics and related areas. It is hoped that some new ideas will be launched to add value and insight into many of the classical and new theories surrounding partitions. The book is an appreciation of the many gifted authors of research into partitions over the past century and before, in the hope that more may come of this for future generations. Features Provides a step-by-step guide through the known literature on Integer and Vector Partitions, and a focus on the not so well-known Visible Point Vector identities Serves as a reference for graduate students and researchers in physics, applied mathematics, number theory and computational mathematics Offers a variety of practical examples as well as sets of exercises suitable for students and researchers Geoffrey B. Campbell completed his PhD at Australian National University in 1998 under the esteemed physicist Professor Rodney Baxter. His affiliation with the Australian National University Mathematical Sciences Institute has continued for over 30 years. Within that time frame, Geoffrey also served eight years as an Honorary Research Fellow at LaTrobe University Mathematics and Statistics Department in Melbourne. Currently he writes ongoing articles for the Australian Mathematical Society Gazette. Within the international scope, Geoffrey currently serves as a PhD external committee member for a mathematics graduate student at Washington State University in America. Geoffrey has built a career within Australian Commonwealth and State government departments, including as an Advisor at the Department of Prime Minister and Cabinet; as Analyst Researcher for a Royal Commission. Geoffrey specializes in complex data, machine learning including data analytics. He is also a published poet in Australian anthologies and literary magazines.
Author: David R. Mazur Publisher: American Mathematical Soc. ISBN: 1470453002 Category : Education Languages : en Pages : 390
Book Description
Combinatorics is mathematics of enumeration, existence, construction, and optimization questions concerning finite sets. This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, generating functions, recurrence relations, Pólya theory, combinatorial designs, error correcting codes, partially ordered sets, and selected applications to graph theory including the enumeration of trees, the chromatic polynomial, and introductory Ramsey theory. The only prerequisites are single-variable calculus and familiarity with sets and basic proof techniques. The text emphasizes the brands of thinking that are characteristic of combinatorics: bijective and combinatorial proofs, recursive analysis, and counting problem classification. It is flexible enough to be used for undergraduate courses in combinatorics, second courses in discrete mathematics, introductory graduate courses in applied mathematics programs, as well as for independent study or reading courses. What makes this text a guided tour are the approximately 350 reading questions spread throughout its eight chapters. These questions provide checkpoints for learning and prepare the reader for the end-of-section exercises of which there are over 470. Most sections conclude with Travel Notes that add color to the material of the section via anecdotes, open problems, suggestions for further reading, and biographical information about mathematicians involved in the discoveries.
Author: George E. Andrews
Author: George E. Andrews
Author: George E. Andrews
Author: George E. Andrews
Author: Oscar Levin
Author: George E. Andrews
Author: Toufik Mansour
Author: Bruce C. Berndt
Author: Philippe Flajolet
Author: Geoffrey B. Campbell
Author: David R. Mazur