Author : George E. Andrews
Publisher : Cambridge University Press
Page : 274 pages
File Size : 43,68 MB
Release : 1998-07-28
Category : Mathematics
ISBN : 9780521637664
Discusses mathematics related to partitions of numbers into sums of positive integers.
Author : George E. Andrews
Publisher : Cambridge University Press
Page : 156 pages
File Size : 22,23 MB
Release : 2004-10-11
Category : Mathematics
ISBN : 9780521600903
Provides a wide ranging introduction to partitions, accessible to any reader familiar with polynomials and infinite series.
Author : Krishnaswami Alladi
Publisher : Springer Science & Business Media
Page : 233 pages
File Size : 25,11 MB
Release : 2011-11-01
Category : 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.
Author : George E. Andrews
Publisher : Courier Corporation
Page : 292 pages
File Size : 49,88 MB
Release : 2012-04-30
Category : 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.
Author : Bruce C. Berndt
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 27,20 MB
Release : 2006
Category : 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.
Author : Ken Levasseur
Publisher : Lulu.com
Page : 574 pages
File Size : 49,82 MB
Release : 2012-02-25
Category : Computers
ISBN : 1105559297
''In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach and move them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked. The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics. To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs. Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete. The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words. An Instructor's Guide is available to any instructor who uses the text. It includes: Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; Suggested coverage times; Detailed solutions to most even-numbered exercises; Sample quizzes, exams, and final exams. This textbook has been used in classes at Casper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).''--
Author : Leyuan Shi
Publisher : Springer
Page : 260 pages
File Size : 48,51 MB
Release : 2008-11-14
Category : Mathematics
ISBN : 9780387719085
Thesubjectofthisbookisthenested partitions method(NP),arelativelynew optimization method that has been found to be very e?ective solving discrete optimization problems. Such discrete problems are common in many practical applications and the NP method is thus useful in diverse application areas. It can be applied to both operational and planning problems and has been demonstrated to e?ectively solve complex problems in both manufacturing and service industries. To illustrate its broad applicability and e?ectiveness, in this book we will show how the NP method has been successful in solving complex problems in planning and scheduling, logistics and transportation, supply chain design, data mining, and health care. All of these diverse app- cationshaveonecharacteristicincommon:theyallleadtocomplexlarge-scale discreteoptimizationproblemsthatareintractableusingtraditionaloptimi- tion methods. 1.1 Large-Scale Optimization IndevelopingtheNPmethodwewillconsideroptimization problemsthatcan be stated mathematically in the following generic form: minf(x), (1.1) x?X where the solution space or feasible region X is either a discrete or bounded ? set of feasible solutions. We denote a solution to this problem x and the ? ? objective function value f = f (x ).
Author : Alexander Barvinok
Publisher : Springer
Page : 304 pages
File Size : 18,87 MB
Release : 2017-03-13
Category : 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.
Author : Toufik Mansour
Publisher : CRC Press
Page : 617 pages
File Size : 26,22 MB
Release : 2012-07-27
Category : Computers
ISBN : 1439863334
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 : Harry Walter
Publisher : Elsevier
Page : 731 pages
File Size : 13,89 MB
Release : 2012-12-02
Category : Science
ISBN : 0323142915
Partitioning in Aqueous Two-Phase Systems: Theory, Methods, Uses, and Applications to Biotechnology is a collection of papers that discusses the applications of aqueous two-phase systems to problems of separation and extraction of macromolecules, organelles, and cells. Papers focus on the theoretical basis and the practical details of the procedures used. Some of the papers describe in one or a few steps how two components can be separated by the investigator manipulating their partitions so that one component is in one phase and the other component is in the other phase or at the interface. Investigators can also avail of developed batch extractions for plant organelles, cell membranes, nucleic acids, and proteins. The book cites as an example the partitioning of right-side-out and inside-out vesicles (obtained from fragments of thylakoid membranes) to the top and bottom phases, respectively, of a Dx-PEG system. Other papers describe the use of the countercurrent distribution when single extraction steps are not sufficient to produce a separation in materials that do not differ greatly in their partitioning behavior. The collection can prove valuable for bio-chemists, cellular biologists, micro-biologists, and developmental biologists.
