Combinatorics The Art Of Counting

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Combinatorics: The Art of Counting

Author : Bruce E. Sagan
Publisher : American Mathematical Soc.
ISBN 13 : 1470460327
Total Pages : 304 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Combinatorics: The Art of Counting by : Bruce E. Sagan

Download or read book Combinatorics: The Art of Counting written by Bruce E. Sagan and published by American Mathematical Soc.. This book was released on 2020-10-16 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Counting: The Art of Enumerative Combinatorics

Author : George E. Martin
Publisher : Springer Science & Business Media
ISBN 13 : 1475748787
Total Pages : 263 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Counting: The Art of Enumerative Combinatorics by : George E. Martin

Download or read book Counting: The Art of Enumerative Combinatorics written by George E. Martin and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to discrete mathematics. At the end of the book the reader should be able to answer counting questions such as: How many ways are there to stack n poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip? The book can be used as a textbook for a semester course at the sophomore level. The first five chapters can also serve as a basis for a graduate course for in-service teachers.

Combinatorial Reasoning

Author : Duane DeTemple
Publisher : John Wiley & Sons
ISBN 13 : 1118652134
Total Pages : 488 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Combinatorial Reasoning by : Duane DeTemple

Download or read book Combinatorial Reasoning written by Duane DeTemple and published by John Wiley & Sons. This book was released on 2014-04-08 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by two well-known scholars in the field,Combinatorial Reasoning: An Introduction to the Art ofCounting presents a clear and comprehensive introduction to theconcepts and methodology of beginning combinatorics. Focusing onmodern techniques and applications, the book develops a variety ofeffective approaches to solving counting problems. Balancing abstract ideas with specific topical coverage, thebook utilizes real world examples with problems ranging from basiccalculations that are designed to develop fundamental concepts tomore challenging exercises that allow for a deeper exploration ofcomplex combinatorial situations. Simple cases are treated firstbefore moving on to general and more advanced cases. Additionalfeatures of the book include: • Approximately 700 carefully structured problems designedfor readers at multiple levels, many with hints and/or shortanswers • Numerous examples that illustrate problem solving usingboth combinatorial reasoning and sophisticated algorithmicmethods • A novel approach to the study of recurrence sequences,which simplifies many proofs and calculations • Concrete examples and diagrams interspersed throughout tofurther aid comprehension of abstract concepts • A chapter-by-chapter review to clarify the most crucialconcepts covered Combinatorial Reasoning: An Introduction to the Art ofCounting is an excellent textbook for upper-undergraduate andbeginning graduate-level courses on introductory combinatorics anddiscrete mathematics.

Proofs that Really Count

Author : Arthur T. Benjamin
Publisher : American Mathematical Society
ISBN 13 : 1470472597
Total Pages : 210 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Proofs that Really Count by : Arthur T. Benjamin

Download or read book Proofs that Really Count written by Arthur T. Benjamin and published by American Mathematical Society. This book was released on 2022-09-21 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.

Combinatorics

Author : Bruce Eli Sagan
Publisher :
ISBN 13 : 9781470462802
Total Pages : 327 pages
Book Rating : 4.4/5 (628 download)

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Book Synopsis Combinatorics by : Bruce Eli Sagan

Download or read book Combinatorics written by Bruce Eli Sagan and published by . This book was released on 2020 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 abstra

Applied Combinatorial Mathematics

Author : George Pólya
Publisher :
ISBN 13 :
Total Pages : 644 pages
Book Rating : 4.0/5 ( download)

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Book Synopsis Applied Combinatorial Mathematics by : George Pólya

Download or read book Applied Combinatorial Mathematics written by George Pólya and published by . This book was released on 1981 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Counting and Probability

Author : David Patrick
Publisher :
ISBN 13 : 9781934124109
Total Pages : 0 pages
Book Rating : 4.1/5 (241 download)

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Book Synopsis Introduction to Counting and Probability by : David Patrick

Download or read book Introduction to Counting and Probability written by David Patrick and published by . This book was released on 2007-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Understand Mathematics, Understand Computing

Author : Arnold L. Rosenberg
Publisher : Springer Nature
ISBN 13 : 3030583767
Total Pages : 550 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Understand Mathematics, Understand Computing by : Arnold L. Rosenberg

Download or read book Understand Mathematics, Understand Computing written by Arnold L. Rosenberg and published by Springer Nature. This book was released on 2020-12-05 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the authors aim to endow the reader with an operational, conceptual, and methodological understanding of the discrete mathematics that can be used to study, understand, and perform computing. They want the reader to understand the elements of computing, rather than just know them. The basic topics are presented in a way that encourages readers to develop their personal way of thinking about mathematics. Many topics are developed at several levels, in a single voice, with sample applications from within the world of computing. Extensive historical and cultural asides emphasize the human side of mathematics and mathematicians. By means of lessons and exercises on “doing” mathematics, the book prepares interested readers to develop new concepts and invent new techniques and technologies that will enhance all aspects of computing. The book will be of value to students, scientists, and engineers engaged in the design and use of computing systems, and to scholars and practitioners beyond these technical fields who want to learn and apply novel computational ideas.

The Unity of Combinatorics

Author : Ezra Brown
Publisher : American Mathematical Soc.
ISBN 13 : 1470465094
Total Pages : 353 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Unity of Combinatorics by : Ezra Brown

Download or read book The Unity of Combinatorics written by Ezra Brown and published by American Mathematical Soc.. This book was released on 2021-04-05 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics, or the art and science of counting, is a vibrant and active area of pure mathematical research with many applications. The Unity of Combinatorics succeeds in showing that the many facets of combinatorics are not merely isolated instances of clever tricks but that they have numerous connections and threads weaving them together to form a beautifully patterned tapestry of ideas. Topics include combinatorial designs, combinatorial games, matroids, difference sets, Fibonacci numbers, finite geometries, Pascal's triangle, Penrose tilings, error-correcting codes, and many others. Anyone with an interest in mathematics, professional or recreational, will be sure to find this book both enlightening and enjoyable. Few mathematicians have been as active in this area as Richard Guy, now in his eighth decade of mathematical productivity. Guy is the author of over 300 papers and twelve books in geometry, number theory, graph theory, and combinatorics. In addition to being a life-long number-theorist and combinatorialist, Guy's co-author, Ezra Brown, is a multi-award-winning expository writer. Together, Guy and Brown have produced a book that, in the spirit of the founding words of the Carus book series, is accessible “not only to mathematicians but to scientific workers and others with a modest mathematical background.”

Combinatorics

Author : Pavle Mladenović
Publisher : Springer
ISBN 13 : 3030008312
Total Pages : 365 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Combinatorics by : Pavle Mladenović

Download or read book Combinatorics written by Pavle Mladenović and published by Springer. This book was released on 2019-03-13 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a theoretical background for several topics in combinatorial mathematics, such as enumerative combinatorics (including partitions and Burnside's lemma), magic and Latin squares, graph theory, extremal combinatorics, mathematical games and elementary probability. A number of examples are given with explanations while the book also provides more than 300 exercises of different levels of difficulty that are arranged at the end of each chapter, and more than 130 additional challenging problems, including problems from mathematical olympiads. Solutions or hints to all exercises and problems are included. The book can be used by secondary school students preparing for mathematical competitions, by their instructors, and by undergraduate students. The book may also be useful for graduate students and for researchers that apply combinatorial methods in different areas.

Foundations of Combinatorics with Applications

Author : Edward A. Bender
Publisher : Courier Corporation
ISBN 13 : 0486151506
Total Pages : 738 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Foundations of Combinatorics with Applications by : Edward A. Bender

Download or read book Foundations of Combinatorics with Applications written by Edward A. Bender and published by Courier Corporation. This book was released on 2013-01-18 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Enumerative Combinatorics

Author : Miklos Bona
Publisher : CRC Press
ISBN 13 : 1482220865
Total Pages : 1073 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Handbook of Enumerative Combinatorics by : Miklos Bona

Download or read book Handbook of Enumerative Combinatorics written by Miklos Bona and published by CRC Press. This book was released on 2015-03-24 with total page 1073 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today's most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods.This important new work is edited by Miklos Bona of the University of Florida where he

Analytic Combinatorics

Author : Philippe Flajolet
Publisher : Cambridge University Press
ISBN 13 : 1139477161
Total Pages : 825 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Analytic Combinatorics by : Philippe Flajolet

Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Enumerative Combinatorics: Volume 1

Author : Richard P. Stanley
Publisher : Cambridge University Press
ISBN 13 : 1107015421
Total Pages : 641 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Enumerative Combinatorics: Volume 1 by : Richard P. Stanley

Download or read book Enumerative Combinatorics: Volume 1 written by Richard P. Stanley and published by Cambridge University Press. This book was released on 2012 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets.

Combinatorics

Author : Robin J. Wilson
Publisher : Oxford University Press
ISBN 13 : 0198723490
Total Pages : 177 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Combinatorics by : Robin J. Wilson

Download or read book Combinatorics written by Robin J. Wilson and published by Oxford University Press. This book was released on 2016 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal) Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Notes on Counting: An Introduction to Enumerative Combinatorics

Author : Peter J. Cameron
Publisher : Cambridge University Press
ISBN 13 : 1108417361
Total Pages : 235 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Notes on Counting: An Introduction to Enumerative Combinatorics by : Peter J. Cameron

Download or read book Notes on Counting: An Introduction to Enumerative Combinatorics written by Peter J. Cameron and published by Cambridge University Press. This book was released on 2017-06-29 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to enumerative combinatorics, vital to many areas of mathematics. It is suitable as a class text or for individual study.

Lessons in Enumerative Combinatorics

Author : Ömer Eğecioğlu
Publisher : Springer Nature
ISBN 13 : 3030712508
Total Pages : 479 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Lessons in Enumerative Combinatorics by : Ömer Eğecioğlu

Download or read book Lessons in Enumerative Combinatorics written by Ömer Eğecioğlu and published by Springer Nature. This book was released on 2021-05-13 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.