Solomon Golombs Course On Undergraduate Combinatorics

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Solomon Golomb’s Course on Undergraduate Combinatorics

Author : Solomon W. Golomb
Publisher : Springer Nature
ISBN 13 : 3030722287
Total Pages : 458 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Solomon Golomb’s Course on Undergraduate Combinatorics by : Solomon W. Golomb

Download or read book Solomon Golomb’s Course on Undergraduate Combinatorics written by Solomon W. Golomb and published by Springer Nature. This book was released on 2021-10-15 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers an accessible introduction to combinatorics, infused with Solomon Golomb’s insights and illustrative examples. Core concepts in combinatorics are presented with an engaging narrative that suits undergraduate study at any level. Featuring early coverage of the Principle of Inclusion-Exclusion and a unified treatment of permutations later on, the structure emphasizes the cohesive development of ideas. Combined with the conversational style, this approach is especially well suited to independent study. Falling naturally into three parts, the book begins with a flexible Chapter Zero that can be used to cover essential background topics, or as a standalone problem-solving course. The following three chapters cover core topics in combinatorics, such as combinations, generating functions, and permutations. The final three chapters present additional topics, such as Fibonacci numbers, finite groups, and combinatorial structures. Numerous illuminating examples are included throughout, along with exercises of all levels. Three appendices include additional exercises, examples, and solutions to a selection of problems. Solomon Golomb’s Course on Undergraduate Combinatorics is ideal for introducing mathematics students to combinatorics at any stage in their program. There are no formal prerequisites, but readers will benefit from mathematical curiosity and a willingness to engage in the book’s many entertaining challenges.

Solomon Golomb's Course on Undergraduate Combinatorics

Author : Solomon W. Golomb
Publisher :
ISBN 13 : 9783030722296
Total Pages : 0 pages
Book Rating : 4.7/5 (222 download)

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Book Synopsis Solomon Golomb's Course on Undergraduate Combinatorics by : Solomon W. Golomb

Download or read book Solomon Golomb's Course on Undergraduate Combinatorics written by Solomon W. Golomb and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers an accessible introduction to combinatorics, infused with Solomon Golomb's insights and illustrative examples. Core concepts in combinatorics are presented with an engaging narrative that suits undergraduate study at any level. Featuring early coverage of the Principle of Inclusion-Exclusion and a unified treatment of permutations later on, the structure emphasizes the cohesive development of ideas. Combined with the conversational style, this approach is especially well suited to independent study. Falling naturally into three parts, the book begins with a flexible Chapter Zero that can be used to cover essential background topics, or as a standalone problem-solving course. The following three chapters cover core topics in combinatorics, such as combinations, generating functions, and permutations. The final three chapters present additional topics, such as Fibonacci numbers, finite groups, and combinatorial structures. Numerous illuminating examples are included throughout, along with exercises of all levels. Three appendices include additional exercises, examples, and solutions to a selection of problems. Solomon Golomb's Course on Undergraduate Combinatorics is ideal for introducing mathematics students to combinatorics at any stage in their program. There are no formal prerequisites, but readers will benefit from mathematical curiosity and a willingness to engage in the book's many entertaining challenges.

A First Course in Enumerative Combinatorics

Author : Carl G. Wagner
Publisher : American Mathematical Soc.
ISBN 13 : 1470459957
Total Pages : 272 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A First Course in Enumerative Combinatorics by : Carl G. Wagner

Download or read book A First Course in Enumerative Combinatorics written by Carl G. Wagner and published by American Mathematical Soc.. This book was released on 2020-10-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A First Course in Enumerative Combinatorics provides an introduction to the fundamentals of enumeration for advanced undergraduates and beginning graduate students in the mathematical sciences. The book offers a careful and comprehensive account of the standard tools of enumeration—recursion, generating functions, sieve and inversion formulas, enumeration under group actions—and their application to counting problems for the fundamental structures of discrete mathematics, including sets and multisets, words and permutations, partitions of sets and integers, and graphs and trees. The author's exposition has been strongly influenced by the work of Rota and Stanley, highlighting bijective proofs, partially ordered sets, and an emphasis on organizing the subject under various unifying themes, including the theory of incidence algebras. In addition, there are distinctive chapters on the combinatorics of finite vector spaces, a detailed account of formal power series, and combinatorial number theory. The reader is assumed to have a knowledge of basic linear algebra and some familiarity with power series. There are over 200 well-designed exercises ranging in difficulty from straightforward to challenging. There are also sixteen large-scale honors projects on special topics appearing throughout the text. The author is a distinguished combinatorialist and award-winning teacher, and he is currently Professor Emeritus of Mathematics and Adjunct Professor of Philosophy at the University of Tennessee. He has published widely in number theory, combinatorics, probability, decision theory, and formal epistemology. His Erdős number is 2.

Combinatorics of Permutations

Author : Miklos Bona
Publisher : CRC Press
ISBN 13 : 1000563804
Total Pages : 528 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Combinatorics of Permutations by : Miklos Bona

Download or read book Combinatorics of Permutations written by Miklos Bona and published by CRC Press. This book was released on 2022-05-09 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: A CHOICE "Outstanding Academic Title," the first edition of this bestseller was lauded for its detailed yet engaging treatment of permutations. Providing more than enough material for a one-semester course, Combinatorics of Permutations, third edition continues to clearly show the usefulness of this subject for both students and researchers. The research in combinatorics of permutations has advanced rapidly since this book was published in a first edition. Now the third edition offers not only updated results, it remains the leading textbook for a course on the topic. Coverage is mostly enumerative, but there are algebraic, analytic, and topological parts as well, and applications. Since the publication of the second edition, there is tremendous progress in pattern avoidance (Chapters 4 and 5). There is also significant progress in the analytic combinatorics of permutations, which will be incorporated. •A completely new technique from extremal combinatorics disproved a long-standing conjecture, and this is presented in Chapter 4. •The area of universal permutations has undergone a lot of very recent progress, and that has been noticed outside the academic community as well. This also influenced the revision of Chapter 5. •New results in stack sorting are added to Chapter 8. •Chapter 9 applications to biology has been revised. The author’s other works include Introduction to Enumerative and Analytic Combinatorics, second edition (CHOICE "Outstanding Academic Title") and Handbook of Enumerative Combinatorics, published by CRC Press. The author also serves as Series Editor for CRC’s Discrete Mathematics and Its Applications.

Constructive Combinatorics

Author : Dennis Stanton
Publisher : Springer
ISBN 13 : 0387963472
Total Pages : 186 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Constructive Combinatorics by : Dennis Stanton

Download or read book Constructive Combinatorics written by Dennis Stanton and published by Springer. This book was released on 1986-06-01 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notes that eventually became this book were written between 1977 and 1985 for the course called Constructive Combinatorics at the University of Minnesota. This is a one-quarter (10 week) course for upper level undergraduate students. The class usually consists of mathematics and computer science majors, with an occasional engineering student. Several graduate students in computer science also attend. At Minnesota, Constructive Combinatorics is the third quarter of a three quarter sequence. The fIrst quarter, Enumerative Combinatorics, is at the level of the texts by Bogart [Bo], Brualdi [Br], Liu [Li] or Tucker [Tu] and is a prerequisite for this course. The second quarter, Graph Theory and Optimization, is not a prerequisite. We assume that the students are familiar with the techniques of enumeration: basic counting principles, generating functions and inclusion/exclusion. This course evolved from a course on combinatorial algorithms. That course contained a mixture of graph algorithms, optimization and listing algorithms. The computer assignments generally consisted of testing algorithms on examples. While we felt that such material was useful and not without mathematical content, we did not think that the course had a coherent mathematical focus. Furthermore, much of it was being taught, or could have been taught, elsewhere. Graph algorithms and optimization, for instance, were inserted into the graph theory course where they naturally belonged. The computer science department already taught some of the material: the simpler algorithms in a discrete mathematics course; effIciency of algorithms in a more advanced course.

A Path to Combinatorics for Undergraduates

Author : Titu Andreescu
Publisher : Springer Science & Business Media
ISBN 13 : 9780817642884
Total Pages : 252 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis A Path to Combinatorics for Undergraduates by : Titu Andreescu

Download or read book A Path to Combinatorics for Undergraduates written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2003-11-11 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions. Topics encompass permutations and combinations, binomial coefficients and their applications, bijections, inclusions and exclusions, and generating functions. Each chapter features fully-worked problems, including many from Olympiads and other competitions, as well as a number of problems original to the authors; at the end of each chapter are further exercises to reinforce understanding, encourage creativity, and build a repertory of problem-solving techniques. The authors' previous text, "102 Combinatorial Problems," makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book's unusual problems and examples will interest seasoned mathematicians as well. "A Path to Combinatorics for Undergraduates" is a lively introduction not only to combinatorics, but to mathematical ingenuity, rigor, and the joy of solving puzzles.

Counting: The Art of Enumerative Combinatorics

Author : George E. Martin
Publisher : Springer Science & Business Media
ISBN 13 : 9780387952253
Total Pages : 272 pages
Book Rating : 4.9/5 (522 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 2001-06-21 with total page 272 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.

Introduction to Enumerative Combinatorics

Author : Miklós Bóna
Publisher : McGraw-Hill Science/Engineering/Math
ISBN 13 :
Total Pages : 552 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Introduction to Enumerative Combinatorics by : Miklós Bóna

Download or read book Introduction to Enumerative Combinatorics written by Miklós Bóna and published by McGraw-Hill Science/Engineering/Math. This book was released on 2007 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by one of the leading authors and researchers in the field, this comprehensive modern text offers a strong focus on enumeration, a vitally important area in introductory combinatorics crucial for further study in the field. Miklós Bóna's text fills the gap between introductory textbooks in discrete mathematics and advanced graduate textbooks in enumerative combinatorics, and is one of the very first intermediate-level books to focus on enumerative combinatorics. The text can be used for an advanced undergraduate course by thoroughly covering the chapters in Part I on basic enumeration and by selecting a few special topics, or for an introductory graduate course by concentrating on the main areas of enumeration discussed in Part II. The special topics of Part III make the book suitable for a reading course. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

Foundations of Applied Combinatorics

Author : Edward A. Bender
Publisher : Addison Wesley Publishing Company
ISBN 13 :
Total Pages : 458 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Foundations of Applied Combinatorics by : Edward A. Bender

Download or read book Foundations of Applied Combinatorics written by Edward A. Bender and published by Addison Wesley Publishing Company. This book was released on 1991 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Applied Combinatorics

Author : Fred S. Roberts
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 856 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis Applied Combinatorics by : Fred S. Roberts

Download or read book Applied Combinatorics written by Fred S. Roberts and published by Prentice Hall. This book was released on 2005 with total page 856 pages. Available in PDF, EPUB and Kindle. Book excerpt: For courses in undergraduate Combinatorics. Many new detailed applications are covered, including material on list colourings, expanding discussion of scheduling legislative committees, material on DNA sequence alignment, and material on cryptography. *NEW Section dealing with stable marriages and their many modern applications, including the assignment of interns to hospitals, dynamic labour markets, and strategic behaviour. *A mix of difficulty in topics with careful annotation that makes it possible to use this book in a variety of courses. *Treatment of applications as major topics of their own rather than as isolated examples. *Use of real applications from the current literature and the extensive modern literature citations. *Problem-solving through a variety of exercises that test routine ideas, introduce new concepts and applications, or attempt to challenge the reader to use the combinatorial techniques developed.

A Path to Combinatorics for Undergraduates

Author : Titu Andreescu
Publisher :
ISBN 13 : 9780817681555
Total Pages : 254 pages
Book Rating : 4.6/5 (815 download)

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Book Synopsis A Path to Combinatorics for Undergraduates by : Titu Andreescu

Download or read book A Path to Combinatorics for Undergraduates written by Titu Andreescu and published by . This book was released on 2014-09-01 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Course in Combinatorics

Author : J. H. Van Lint
Publisher :
ISBN 13 : 9780511672897
Total Pages : 0 pages
Book Rating : 4.6/5 (728 download)

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Book Synopsis A Course in Combinatorics by : J. H. Van Lint

Download or read book A Course in Combinatorics written by J. H. Van Lint and published by . This book was released on 2001 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second edition of a popular text which covers the whole field of combinatorics.

Introductory Combinatorics

Author : Richard A. Brualdi
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Introductory Combinatorics by : Richard A. Brualdi

Download or read book Introductory Combinatorics written by Richard A. Brualdi and published by Prentice Hall. This book was released on 1977 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory Combinatorics emphasizes combinatorial ideas, including the pigeon-hole principle, counting techniques, permutations and combinations, Polya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, and combinatortial structures (matchings, designs, graphs). Written to be entertaining and readable, this book's lively style reflects the author's joy for teaching the subject. It presents an excellent treatment of Polya's Counting Theorem that doesn't assume the student is familiar with group theory. It also includes problems that offer good practice of the principles it presents. The third edition of Introductory Combinatorics has been updated to include new material on partially ordered sets, Dilworth's Theorem, partitions of integers and generating functions. In addition, the chapters on graph theory have been completely revised. A valuable book for any reader interested in learning more about combinatorics.

A Walk Through Combinatorics

Author : Miklós Bóna
Publisher : World Scientific Publishing Company
ISBN 13 : 9789813148840
Total Pages : 593 pages
Book Rating : 4.1/5 (488 download)

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Book Synopsis A Walk Through Combinatorics by : Miklós Bóna

Download or read book A Walk Through Combinatorics written by Miklós Bóna and published by World Scientific Publishing Company. This book was released on 2016-09-15 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first three editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs. New to this edition are the Quick Check exercises at the end of each section. In all, the new edition contains about 240 new exercises. Extra examples were added to some sections where readers asked for them. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs, enumeration under group action, generating functions of labeled and unlabeled structures and algorithms and complexity. The book encourages students to learn more combinatorics, provides them with a not only useful but also enjoyable and engaging reading. The Solution Manual is available upon request for all instructors who adopt this book as a course text. Please send your request to [email protected]. The previous edition of this textbook has been adopted at various schools including UCLA, MIT, University of Michigan, and Swarthmore College. It was also translated into Korean.

A First Course in Enumerative Combinatorics

Author : Carl Wagner
Publisher :
ISBN 13 : 9781470462628
Total Pages : pages
Book Rating : 4.4/5 (626 download)

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Book Synopsis A First Course in Enumerative Combinatorics by : Carl Wagner

Download or read book A First Course in Enumerative Combinatorics written by Carl Wagner and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A First Course in Enumerative Combinatorics provides an introduction to the fundamentals of enumeration for advanced undergraduates and beginning graduate students in the mathematical sciences. The book offers a careful and comprehensive account of the standard tools of enumeration--recursion, generating functions, sieve and inversion formulas, enumeration under group actions--and their application to counting problems for the fundamental structures of discrete mathematics, including sets and multisets, words and permutations, partitions of sets and integers, and graphs and trees. The author's

Introductory Combinatorics

Author : Kenneth P. Bogart
Publisher : Pitman Publishing
ISBN 13 :
Total Pages : 400 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Introductory Combinatorics by : Kenneth P. Bogart

Download or read book Introductory Combinatorics written by Kenneth P. Bogart and published by Pitman Publishing. This book was released on 1983 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the core material of value to students in a wide variety of fields, this book presents a broad comprehensive survey of modern combinatorics at an introductory level. The author begins with an introduction of concepts fundamental to all branches of combinatorics in the context of combinatorial enumeration. Chapter 2 is devoted to enumeration problems that involve counting the number of equivalence classes of an equivalence relation. Chapter 3 discusses somewhat less direct methods of enumeration, the principle of inclusion and exclusion and generating functions. The remainder of the book is devoted to a study of combinatorial structures.

Polyominoes

Author : Solomon W. Golomb
Publisher : Princeton University Press
ISBN 13 : 0691215057
Total Pages : 204 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Polyominoes by : Solomon W. Golomb

Download or read book Polyominoes written by Solomon W. Golomb and published by Princeton University Press. This book was released on 2020-06-30 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inspiring popular video games like Tetris while contributing to the study of combinatorial geometry and tiling theory, polyominoes have continued to spark interest ever since their inventor, Solomon Golomb, introduced them to puzzle enthusiasts several decades ago. In this fully revised and expanded edition of his landmark book, the author takes a new generation of readers on a mathematical journey into the world of the deceptively simple polyomino. Golomb incorporates important, recent developments, and poses problems, inviting the reader to play with and develop an understanding of the extraordinary properties of polyominoes.