An Invitation To Combinatorics PDF Download
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Author | : Shahriar Shahriari |
Publisher | : Cambridge University Press |
Total Pages | : 631 |
Release | : 2021-07-22 |
Genre | : MATHEMATICS |
ISBN | : 1108476546 |
Download An Invitation to Combinatorics Book in PDF, ePub and Kindle
A conversational introduction to combinatorics for upper undergraduates, emphasizing problem solving and active student participation.
Author | : Stephen Melczer |
Publisher | : Springer |
Total Pages | : 418 |
Release | : 2021-12-24 |
Genre | : Mathematics |
ISBN | : 9783030670825 |
Download An Invitation to Analytic Combinatorics Book in PDF, ePub and Kindle
This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains. After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theory can help refine some of these computability questions. Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text.
Author | : Matthias Beck |
Publisher | : American Mathematical Soc. |
Total Pages | : 308 |
Release | : 2018-12-12 |
Genre | : Combinatorial analysis |
ISBN | : 147042200X |
Download Combinatorial Reciprocity Theorems: An Invitation to Enumerative Geometric Combinatorics Book in PDF, ePub and Kindle
Combinatorial reciprocity is a very interesting phenomenon, which can be described as follows: A polynomial, whose values at positive integers count combinatorial objects of some sort, may give the number of combinatorial objects of a different sort when evaluated at negative integers (and suitably normalized). Such combinatorial reciprocity theorems occur in connections with graphs, partially ordered sets, polyhedra, and more. Using the combinatorial reciprocity theorems as a leitmotif, this book unfolds central ideas and techniques in enumerative and geometric combinatorics. Written in a friendly writing style, this is an accessible graduate textbook with almost 300 exercises, numerous illustrations, and pointers to the research literature. Topics include concise introductions to partially ordered sets, polyhedral geometry, and rational generating functions, followed by highly original chapters on subdivisions, geometric realizations of partially ordered sets, and hyperplane arrangements.
Author | : Jiří Matoušek |
Publisher | : Oxford University Press |
Total Pages | : 462 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 0198570430 |
Download Invitation to Discrete Mathematics Book in PDF, ePub and Kindle
A clear and self-contained introduction to discrete mathematics for undergraduates and early graduates.
Author | : Daniel A. Marcus |
Publisher | : American Mathematical Soc. |
Total Pages | : 148 |
Release | : 1998-12-31 |
Genre | : Mathematics |
ISBN | : 0883857103 |
Download Combinatorics Book in PDF, ePub and Kindle
The format of this book is unique in that it combines features of a traditional text with those of a problem book. The material is presented through a series of problems, about 250 in all, with connecting text; this is supplemented by 250 additional problems suitable for homework assignment. The problems are structured in order to introduce concepts in a logical order and in a thought-provoking way. The first four sections of the book deal with basic combinatorial entities; the last four cover special counting methods. Many applications to probability are included along the way. Students from a wide range of backgrounds--mathematics, computer science, or engineering--will appreciate this appealing introduction.
Author | : Mateusz Michałek |
Publisher | : American Mathematical Society |
Total Pages | : 226 |
Release | : 2021-03-05 |
Genre | : Mathematics |
ISBN | : 1470453673 |
Download Invitation to Nonlinear Algebra Book in PDF, ePub and Kindle
Nonlinear algebra provides modern mathematical tools to address challenges arising in the sciences and engineering. It is useful everywhere, where polynomials appear: in particular, data and computational sciences, statistics, physics, optimization. The book offers an invitation to this broad and fast-developing area. It is not an extensive encyclopedia of known results, but rather a first introduction to the subject, allowing the reader to enter into more advanced topics. It was designed as the next step after linear algebra and well before abstract algebraic geometry. The book presents both classical topics—like the Nullstellensatz and primary decomposition—and more modern ones—like tropical geometry and semidefinite programming. The focus lies on interactions and applications. Each of the thirteen chapters introduces fundamental concepts. The book may be used for a one-semester course, and the over 200 exercises will help the readers to deepen their understanding of the subject.
Author | : Steven J. Rosenberg |
Publisher | : CRC Press |
Total Pages | : 397 |
Release | : 2021-12-22 |
Genre | : Mathematics |
ISBN | : 1000516334 |
Download An Invitation to Abstract Algebra Book in PDF, ePub and Kindle
Studying abstract algebra can be an adventure of awe-inspiring discovery. The subject need not be watered down nor should it be presented as if all students will become mathematics instructors. This is a beautiful, profound, and useful field which is part of the shared language of many areas both within and outside of mathematics. To begin this journey of discovery, some experience with mathematical reasoning is beneficial. This text takes a fairly rigorous approach to its subject, and expects the reader to understand and create proofs as well as examples throughout. The book follows a single arc, starting from humble beginnings with arithmetic and high-school algebra, gradually introducing abstract structures and concepts, and culminating with Niels Henrik Abel and Evariste Galois’ achievement in understanding how we can—and cannot—represent the roots of polynomials. The mathematically experienced reader may recognize a bias toward commutative algebra and fondness for number theory. The presentation includes the following features: Exercises are designed to support and extend the material in the chapter, as well as prepare for the succeeding chapters. The text can be used for a one, two, or three-term course. Each new topic is motivated with a question. A collection of projects appears in Chapter 23. Abstract algebra is indeed a deep subject; it can transform not only the way one thinks about mathematics, but the way that one thinks—period. This book is offered as a manual to a new way of thinking. The author’s aim is to instill the desire to understand the material, to encourage more discovery, and to develop an appreciation of the subject for its own sake.
Author | : Ian Anderson |
Publisher | : Courier Corporation |
Total Pages | : 276 |
Release | : 2002-01-01 |
Genre | : Mathematics |
ISBN | : 9780486422572 |
Download Combinatorics of Finite Sets Book in PDF, ePub and Kindle
Among other subjects explored are the Clements-Lindström extension of the Kruskal-Katona theorem to multisets and the Greene-Kleitmen result concerning k-saturated chain partitions of general partially ordered sets. Includes exercises and solutions.
Author | : Andrew V. Sills |
Publisher | : CRC Press |
Total Pages | : 257 |
Release | : 2017-10-16 |
Genre | : Mathematics |
ISBN | : 1351647962 |
Download An Invitation to the Rogers-Ramanujan Identities Book in PDF, ePub and Kindle
The Rogers--Ramanujan identities are a pair of infinite series—infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator algebra theory, physics (especially statistical mechanics), and computer science (especially algorithmic proof theory). Presented in a coherant and clear way, this will be the first book entirely devoted to the Rogers—Ramanujan identities and will include related historical material that is unavailable elsewhere.
Author | : Robin Wilson |
Publisher | : OUP Oxford |
Total Pages | : 392 |
Release | : 2013-06-27 |
Genre | : Mathematics |
ISBN | : 0191630624 |
Download Combinatorics: Ancient & Modern Book in PDF, ePub and Kindle
Who first presented Pascal's triangle? (It was not Pascal.) Who first presented Hamiltonian graphs? (It was not Hamilton.) Who first presented Steiner triple systems? (It was not Steiner.) The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: 1) it constitutes the first book-length survey of the history of combinatorics; and 2) it assembles, for the first time in a single source, researches on the history of combinatorics that would otherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction by Donald E. Knuth to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings on permutations to late-Renaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler's contributions to such wide-ranging topics as partitions, polyhedra, and latin squares to the 20th century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections by the distinguished combinatorialist, Peter J. Cameron. This book is not expected to be read from cover to cover, although it can be. Rather, it aims to serve as a valuable resource to a variety of audiences. Combinatorialists with little or no knowledge about the development of their subject will find the historical treatment stimulating. A historian of mathematics will view its assorted surveys as an encouragement for further research in combinatorics. The more general reader will discover an introduction to a fascinating and too little known subject that continues to stimulate and inspire the work of scholars today.