Introduction To Combinatorics

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Introductory Combinatorics

Author : Kenneth P. Bogart
Publisher : Harcourt Brace College Publishers
ISBN 13 :
Total Pages : 648 pages
Book Rating : 4.3/5 (91 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 Harcourt Brace College Publishers. This book was released on 1990 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory, Combinatorics, Third Edition is designed for introductory courses in combinatorics, or more generally, discrete mathematics. The author, Kenneth Bogart, has chosen core material of value to students in a wide variety of disciplines: mathematics, computer science, statistics, operations research, physical sciences, and behavioral sciences. The rapid growth in the breadth and depth of the field of combinatorics in the last several decades, first in graph theory and designs and more recently in enumeration and ordered sets, has led to a recognition of combinatorics as a field with which the aspiring mathematician should become familiar. This long-overdue new edition of a popular set presents a broad comprehensive survey of modern combinatorics which is important to the various scientific fields of study.

Introduction to Combinatorics

Author : Martin J. Erickson
Publisher : John Wiley & Sons
ISBN 13 : 1118030893
Total Pages : 210 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Introduction to Combinatorics by : Martin J. Erickson

Download or read book Introduction to Combinatorics written by Martin J. Erickson and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This gradual, systematic introduction to the main concepts of combinatorics is the ideal text for advanced undergraduate and early graduate courses in this subject. Each of the book's three sections--Existence, Enumeration, and Construction--begins with a simply stated first principle, which is then developed step by step until it leads to one of the three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Polya's graph enumeration formula, and Leech's 24-dimensional lattice. Along the way, Professor Martin J. Erickson introduces fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise new and innovative questions and observations. His carefully chosen end-of-chapter exercises demonstrate the applicability of combinatorial methods to a wide variety of problems, including many drawn from the William Lowell Putnam Mathematical Competition. Many important combinatorial methods are revisited several times in the course of the text--in exercises and examples as well as theorems and proofs. This repetition enables students to build confidence and reinforce their understanding of complex material. Mathematicians, statisticians, and computer scientists profit greatly from a solid foundation in combinatorics. Introduction to Combinatorics builds that foundation in an orderly, methodical, and highly accessible manner.

Introduction to Combinatorics

Author : Walter D. Wallis
Publisher : CRC Press
ISBN 13 : 1498777635
Total Pages : 424 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Introduction to Combinatorics by : Walter D. Wallis

Download or read book Introduction to Combinatorics written by Walter D. Wallis and published by CRC Press. This book was released on 2016-12-12 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: What Is Combinatorics Anyway? Broadly speaking, combinatorics is the branch of mathematics dealing with different ways of selecting objects from a set or arranging objects. It tries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural questions: does there exist a selection or arrangement of objects with a particular set of properties? The authors have presented a text for students at all levels of preparation. For some, this will be the first course where the students see several real proofs. Others will have a good background in linear algebra, will have completed the calculus stream, and will have started abstract algebra. The text starts by briefly discussing several examples of typical combinatorial problems to give the reader a better idea of what the subject covers. The next chapters explore enumerative ideas and also probability. It then moves on to enumerative functions and the relations between them, and generating functions and recurrences., Important families of functions, or numbers and then theorems are presented. Brief introductions to computer algebra and group theory come next. Structures of particular interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. The authors conclude with further discussion of the interaction between linear algebra and combinatorics. Features Two new chapters on probability and posets. Numerous new illustrations, exercises, and problems. More examples on current technology use A thorough focus on accuracy Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes, Flexible use of MapleTM and MathematicaTM

Notes on Introductory Combinatorics

Author : George Polya
Publisher : Springer Science & Business Media
ISBN 13 : 1475711018
Total Pages : 202 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Notes on Introductory Combinatorics by : George Polya

Download or read book Notes on Introductory Combinatorics written by George Polya and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the winter of 1978, Professor George P61ya and I jointly taught Stanford University's introductory combinatorics course. This was a great opportunity for me, as I had known of Professor P61ya since having read his classic book, How to Solve It, as a teenager. Working with P6lya, who ·was over ninety years old at the time, was every bit as rewarding as I had hoped it would be. His creativity, intelligence, warmth and generosity of spirit, and wonderful gift for teaching continue to be an inspiration to me. Combinatorics is one of the branches of mathematics that play a crucial role in computer sCience, since digital computers manipulate discrete, finite objects. Combinatorics impinges on computing in two ways. First, the properties of graphs and other combinatorial objects lead directly to algorithms for solving graph-theoretic problems, which have widespread application in non-numerical as well as in numerical computing. Second, combinatorial methods provide many analytical tools that can be used for determining the worst-case and expected performance of computer algorithms. A knowledge of combinatorics will serve the computer scientist well. Combinatorics can be classified into three types: enumerative, eXistential, and constructive. Enumerative combinatorics deals with the counting of combinatorial objects. Existential combinatorics studies the existence or nonexistence of combinatorial configurations.

Introduction to Combinatorics

Author : A. B. Slomson
Publisher : CRC Press
ISBN 13 : 9780412353703
Total Pages : 290 pages
Book Rating : 4.3/5 (537 download)

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Book Synopsis Introduction to Combinatorics by : A. B. Slomson

Download or read book Introduction to Combinatorics written by A. B. Slomson and published by CRC Press. This book was released on 1997-02-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The growth in digital devices, which require discrete formulation of problems, has revitalized the role of combinatorics, making it indispensable to computer science. Furthermore, the challenges of new technologies have led to its use in industrial processes, communications systems, electrical networks, organic chemical identification, coding theory, economics, and more. With a unique approach, Introduction to Combinatorics builds a foundation for problem-solving in any of these fields. Although combinatorics deals with finite collections of discrete objects, and as such differs from continuous mathematics, the two areas do interact. The author, therefore, does not hesitate to use methods drawn from continuous mathematics, and in fact shows readers the relevance of abstract, pure mathematics to real-world problems. The author has structured his chapters around concrete problems, and as he illustrates the solutions, the underlying theory emerges. His focus is on counting problems, beginning with the very straightforward and ending with the complicated problem of counting the number of different graphs with a given number of vertices. Its clear, accessible style and detailed solutions to many of the exercises, from routine to challenging, provided at the end of the book make Introduction to Combinatorics ideal for self-study as well as for structured coursework.

A Course in Combinatorics

Author : J. H. van Lint
Publisher : Cambridge University Press
ISBN 13 : 9780521006019
Total Pages : 620 pages
Book Rating : 4.0/5 (6 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 Cambridge University Press. This book was released on 2001-11-22 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.

How to Count

Author : R.B.J.T. Allenby
Publisher : CRC Press
ISBN 13 : 1420082612
Total Pages : 440 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis How to Count by : R.B.J.T. Allenby

Download or read book How to Count written by R.B.J.T. Allenby and published by CRC Press. This book was released on 2011-07-01 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizes a Problem Solving Approach A first course in combinatorics Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. Although the authors present most of the topics through concrete problems, they also emphasize the importance of proofs in mathematics. New to the Second Edition This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet’s pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises. Ideal for both classroom teaching and self-study, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and Pólya’s counting theorem.

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.

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.

Combinatorics

Author : Theodore G. Faticoni
Publisher : John Wiley & Sons
ISBN 13 : 1118407482
Total Pages : 328 pages
Book Rating : 4.1/5 (184 download)

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Book Synopsis Combinatorics by : Theodore G. Faticoni

Download or read book Combinatorics written by Theodore G. Faticoni and published by John Wiley & Sons. This book was released on 2014-08-21 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridges combinatorics and probability and uniquely includes detailed formulas and proofs to promote mathematical thinking Combinatorics: An Introduction introduces readers to counting combinatorics, offers examples that feature unique approaches and ideas, and presents case-by-case methods for solving problems. Detailing how combinatorial problems arise in many areas of pure mathematics, most notably in algebra, probability theory, topology, and geometry, this book provides discussion on logic and paradoxes; sets and set notations; power sets and their cardinality; Venn diagrams; the multiplication principal; and permutations, combinations, and problems combining the multiplication principal. Additional features of this enlightening introduction include: Worked examples, proofs, and exercises in every chapter Detailed explanations of formulas to promote fundamental understanding Promotion of mathematical thinking by examining presented ideas and seeing proofs before reaching conclusions Elementary applications that do not advance beyond the use of Venn diagrams, the inclusion/exclusion formula, the multiplication principal, permutations, and combinations Combinatorics: An Introduction is an excellent book for discrete and finite mathematics courses at the upper-undergraduate level. This book is also ideal for readers who wish to better understand the various applications of elementary combinatorics.

Combinatorics and Graph Theory

Author : John Harris
Publisher : Springer Science & Business Media
ISBN 13 : 0387797114
Total Pages : 392 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Combinatorics and Graph Theory by : John Harris

Download or read book Combinatorics and Graph Theory written by John Harris and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.

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.

Discrete Mathematics

Author : László Lovász
Publisher : Springer Science & Business Media
ISBN 13 : 0387217770
Total Pages : 298 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Discrete Mathematics by : László Lovász

Download or read book Discrete Mathematics written by László Lovász and published by Springer Science & Business Media. This book was released on 2006-05-10 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.

A Walk Through Combinatorics

Author : MiklÃ³s BÃ³na
Publisher : World Scientific Publishing Company
ISBN 13 : 9813100729
Total Pages : 568 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis A Walk Through Combinatorics by : MiklÃ³s BÃ³na

Download or read book A Walk Through Combinatorics written by MiklÃ³s BÃ³na and published by World Scientific Publishing Company. This book was released on 2011-05-09 with total page 568 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 two 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. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs (new to this edition), enumeration under group action (new to this edition), generating functions of labeled and unlabeled structures and algorithms and complexity. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide 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]. Sample Chapter(s) Chapter 1: Seven Is More Than Six. The Pigeon-Hole Principle (181 KB) Chapter 4: No Matter How You Slice It. The Binomial Theorem and Related Identities (228 KB) Chapter 15: Who Knows What It Looks Like,But It Exists. The Probabilistic Method (286 KB) Request Inspection Copy

Introduction to Enumerative and Analytic Combinatorics

Author : Miklos Bona
Publisher : CRC Press
ISBN 13 : 1482249103
Total Pages : 555 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Introduction to Enumerative and Analytic Combinatorics by : Miklos Bona

Download or read book Introduction to Enumerative and Analytic Combinatorics written by Miklos Bona and published by CRC Press. This book was released on 2015-09-18 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Enumerative and Analytic Combinatorics fills the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumerat

Applied Combinatorics

Author : Alan Tucker
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 408 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Applied Combinatorics by : Alan Tucker

Download or read book Applied Combinatorics written by Alan Tucker and published by John Wiley & Sons. This book was released on 1980 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.