Foundations Of Combinatorics With Applications

Author : Edward A. Bender,S. Gill Williamson
Publisher : Courier Corporation
Page : 738 pages
File Size : 47,7 Mb
Release : 2013-01-18
Category : Mathematics
ISBN : 9780486151502

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Foundations of Combinatorics with Applications by Edward A. Bender,S. Gill Williamson Pdf

This introduction to combinatorics, the foundation of the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises.

Author : Edward A. Bender,Stanley Gill Williamson
Publisher : Addison Wesley Publishing Company
Page : 458 pages
File Size : 44,7 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015022034725

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Foundations of Applied Combinatorics by Edward A. Bender,Stanley Gill Williamson Pdf

This introduction to combinatorics is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises (some with solutions), notes, and references appear throughout the text. 75 figures. Appendixes.

Author : Gian-Carlo Rota
Publisher : Unknown
Page : 296 pages
File Size : 46,9 Mb
Release : 1978
Category : Combinatorial analysis
ISBN : UCAL:B5008667

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Studies in Foundations and Combinatorics by Gian-Carlo Rota Pdf

Author : Philippe Flajolet,Robert Sedgewick
Publisher : Cambridge University Press
Page : 825 pages
File Size : 51,9 Mb
Release : 2009-01-15
Category : Mathematics
ISBN : 9781139477161

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Analytic Combinatorics by Philippe Flajolet,Robert Sedgewick Pdf

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 : Kai-Uwe Schmidt,Arne Winterhof
Publisher : Walter de Gruyter GmbH & Co KG
Page : 506 pages
File Size : 45,7 Mb
Release : 2019-07-08
Category : Mathematics
ISBN : 9783110641967

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Combinatorics and Finite Fields by Kai-Uwe Schmidt,Arne Winterhof Pdf

The series is devoted to the publication of high-level monographs, surveys and proceedings which cover the whole spectrum of computational and applied mathematics. The books of this series are addressed to both specialists and advanced students. Interested authors may submit book proposals to the Managing Editor or to any member of the Editorial Board. Managing EditorUlrich Langer, Johannes Kepler University Linz, Austria Editorial BoardHansj rg Albrecher, University of Lausanne, SwitzerlandRonald H. W. Hoppe, University of Houston, USAKarl Kunisch, RICAM, Linz, Austria; University of Graz, AustriaHarald Niederreiter, RICAM, Linz, AustriaChristian Schmeiser, University of Vienna, Austria

Author : Ömer Eğecioğlu,Adriano M. Garsia
Publisher : Springer Nature
Page : 479 pages
File Size : 52,6 Mb
Release : 2021-05-13
Category : Mathematics
ISBN : 9783030712501

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Lessons in Enumerative Combinatorics by Ömer Eğecioğlu,Adriano M. Garsia Pdf

This textbook introduces enumerative combinatorics through the framework of formal languages and bijections. By starting with elementary operations on words and languages, the authors paint an insightful, unified picture for readers entering the field. Numerous concrete examples and illustrative metaphors motivate the theory throughout, while the overall approach illuminates the important connections between discrete mathematics and theoretical computer science. Beginning with the basics of formal languages, the first chapter quickly establishes a common setting for modeling and counting classical combinatorial objects and constructing bijective proofs. From here, topics are modular and offer substantial flexibility when designing a course. Chapters on generating functions and partitions build further fundamental tools for enumeration and include applications such as a combinatorial proof of the Lagrange inversion formula. Connections to linear algebra emerge in chapters studying Cayley trees, determinantal formulas, and the combinatorics that lie behind the classical Cayley–Hamilton theorem. The remaining chapters range across the Inclusion-Exclusion Principle, graph theory and coloring, exponential structures, matching and distinct representatives, with each topic opening many doors to further study. Generous exercise sets complement all chapters, and miscellaneous sections explore additional applications. Lessons in Enumerative Combinatorics captures the authors' distinctive style and flair for introducing newcomers to combinatorics. The conversational yet rigorous presentation suits students in mathematics and computer science at the graduate, or advanced undergraduate level. Knowledge of single-variable calculus and the basics of discrete mathematics is assumed; familiarity with linear algebra will enhance the study of certain chapters.

Author : Alan Tucker
Publisher : John Wiley & Sons
Page : 408 pages
File Size : 43,8 Mb
Release : 1980
Category : Mathematics
ISBN : STANFORD:36105031541597

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Applied Combinatorics by Alan Tucker Pdf

Author : L. S. Pontryagin
Publisher : Courier Corporation
Page : 112 pages
File Size : 52,5 Mb
Release : 2015-05-20
Category : Mathematics
ISBN : 9780486406855

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Foundations of Combinatorial Topology by L. S. Pontryagin Pdf

Concise, rigorous introduction to homology theory features applications to dimension theory and fixed-point theorems. Lucid coverage of the field includes examinations of complexes and their Betti groups, invariance of the Betti groups, and continuous mappings and fixed points. Proofs are presented in a complete and careful manner. A beneficial text for a graduate-level course, "this little book is an extremely valuable addition to the literature of algebraic topology." — The Mathematical Gazette.

Author : Yves Nievergelt
Publisher : Springer Science & Business Media
Page : 425 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201250

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Foundations of Logic and Mathematics by Yves Nievergelt Pdf

This modern introduction to the foundations of logic and mathematics not only takes theory into account, but also treats in some detail applications that have a substantial impact on everyday life (loans and mortgages, bar codes, public-key cryptography). A first college-level introduction to logic, proofs, sets, number theory, and graph theory, and an excellent self-study reference and resource for instructors.

Author : Bruce E. Sagan
Publisher : American Mathematical Soc.
Page : 304 pages
File Size : 48,5 Mb
Release : 2020-10-16
Category : Education
ISBN : 9781470460327

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Combinatorics: The Art of Counting by Bruce E. Sagan Pdf

This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.

Author : Jonathan L. Gross
Publisher : CRC Press
Page : 664 pages
File Size : 55,5 Mb
Release : 2007-11-16
Category : Mathematics
ISBN : 9781584887430

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Combinatorial Methods with Computer Applications by Jonathan L. Gross Pdf

Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinatorial methods course or in a combined graph theory and combinatorics course. After an introduction to combinatorics, the book explores six systematic approaches within a comprehensive framework: sequences, solving recurrences, evaluating summation expressions, binomial coefficients, partitions and permutations, and integer methods. The author then focuses on graph theory, covering topics such as trees, isomorphism, automorphism, planarity, coloring, and network flows. The final chapters discuss automorphism groups in algebraic counting methods and describe combinatorial designs, including Latin squares, block designs, projective planes, and affine planes. In addition, the appendix supplies background material on relations, functions, algebraic systems, finite fields, and vector spaces. Paving the way for students to understand and perform combinatorial calculations, this accessible text presents the discrete methods necessary for applications to algorithmic analysis, performance evaluation, and statistics as well as for the solution of combinatorial problems in engineering and the social sciences.

Author : Stanley Gill Williamson
Publisher : Courier Corporation
Page : 548 pages
File Size : 50,6 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 0486420760

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Combinatorics for Computer Science by Stanley Gill Williamson Pdf

Useful guide covers two major subdivisions of combinatorics — enumeration and graph theory — with emphasis on conceptual needs of computer science. Each part is divided into a "basic concepts" chapter emphasizing intuitive needs of the subject, followed by four "topics" chapters that explore these ideas in depth. Invaluable practical resource for graduate students, advanced undergraduates, and professionals with an interest in algorithm design and other aspects of computer science and combinatorics. References for Linear Order & for Graphs, Trees, and Recursions. 219 figures.

Author : Herbert S. Wilf
Publisher : SIAM
Page : 49 pages
File Size : 50,8 Mb
Release : 1989-01-01
Category : Mathematics
ISBN : 9780898712315

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Combinatorial Algorithms by Herbert S. Wilf Pdf

Covers key recent advances in combinatorial algorithms.

Author : R. Balakrishnan,Sriraman Sridharan
Publisher : CRC Press
Page : 361 pages
File Size : 46,6 Mb
Release : 2018-10-26
Category : Mathematics
ISBN : 9781351019125

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Foundations of Discrete Mathematics with Algorithms and Programming by R. Balakrishnan,Sriraman Sridharan Pdf

Discrete Mathematics has permeated the whole of mathematics so much so it has now come to be taught even at the high school level. This book presents the basics of Discrete Mathematics and its applications to day-to-day problems in several areas. This book is intended for undergraduate students of Computer Science, Mathematics and Engineering. A number of examples have been given to enhance the understanding of concepts. The programming languages used are Pascal and C.

Author : K. D. Joshi
Publisher : New Age International
Page : 768 pages
File Size : 51,6 Mb
Release : 1989
Category : Mathematics
ISBN : 8122401201

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Foundations of Discrete Mathematics by K. D. Joshi Pdf

This Book Is Meant To Be More Than Just A Text In Discrete Mathematics. It Is A Forerunner Of Another Book Applied Discrete Structures By The Same Author. The Ultimate Goal Of The Two Books Are To Make A Strong Case For The Inclusion Of Discrete Mathematics In The Undergraduate Curricula Of Mathematics By Creating A Sequence Of Courses In Discrete Mathematics Parallel To The Traditional Sequence Of Calculus-Based Courses.The Present Book Covers The Foundations Of Discrete Mathematics In Seven Chapters. It Lays A Heavy Emphasis On Motivation And Attempts Clarity Without Sacrificing Rigour. A List Of Typical Problems Is Given In The First Chapter. These Problems Are Used Throughout The Book To Motivate Various Concepts. A Review Of Logic Is Included To Gear The Reader Into A Proper Frame Of Mind. The Basic Counting Techniques Are Covered In Chapters 2 And 7. Those In Chapter 2 Are Elementary. But They Are Intentionally Covered In A Formal Manner So As To Acquaint The Reader With The Traditional Definition-Theorem-Proof Pattern Of Mathematics. Chapters 3 Introduces Abstraction And Shows How The Focal Point Of Todays Mathematics Is Not Numbers But Sets Carrying Suitable Structures. Chapter 4 Deals With Boolean Algebras And Their Applications. Chapters 5 And 6 Deal With More Traditional Topics In Algebra, Viz., Groups, Rings, Fields, Vector Spaces And Matrices.The Presentation Is Elementary And Presupposes No Mathematical Maturity On The Part Of The Reader. Instead, Comments Are Inserted Liberally To Increase His Maturity. Each Chapter Has Four Sections. Each Section Is Followed By Exercises (Of Various Degrees Of Difficulty) And By Notes And Guide To Literature. Answers To The Exercises Are Provided At The End Of The Book.