Introduction To Combinatorics

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Introduction to Combinatorics

Martin J. Erickson
Introduction to Combinatorics Book PDF

Author : Martin J. Erickson
Publisher : John Wiley & Sons
Page : 210 pages
File Size : 49,8 Mb
Release : 2011-10-24
Category : Mathematics
ISBN : 9781118030899

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Introduction to Combinatorics by Martin J. Erickson Pdf

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

Walter D. Wallis,John C. George
Introduction to Combinatorics Book PDF

Author : Walter D. Wallis,John C. George
Publisher : CRC Press
Page : 424 pages
File Size : 40,6 Mb
Release : 2016-12-12
Category : Mathematics
ISBN : 9781498777636

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Introduction to Combinatorics by Walter D. Wallis,John C. George Pdf

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

Introductory Combinatorics

Kenneth P. Bogart
Introductory Combinatorics Book PDF

Author : Kenneth P. Bogart
Publisher : Harcourt Brace College Publishers
Page : 648 pages
File Size : 43,8 Mb
Release : 1990
Category : Computers
ISBN : UOM:39015019632101

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Introductory Combinatorics by Kenneth P. Bogart Pdf

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

Gerald Berman,K. D. Fryer
Introduction to Combinatorics Book PDF

Author : Gerald Berman,K. D. Fryer
Publisher : Elsevier
Page : 315 pages
File Size : 41,6 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483273822

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Introduction to Combinatorics by Gerald Berman,K. D. Fryer Pdf

Introduction to Combinatorics focuses on the applications, processes, methodologies, and approaches involved in combinatorics or discrete mathematics. The book first offers information on introductory examples, permutations and combinations, and the inclusion-exclusion principle. Discussions focus on some applications of the inclusion-exclusion principle, derangements, calculus of sets, permutations, combinations, Stirling's formula, binomial theorem, regions of a plane, chromatic polynomials, and a random walk. The text then examines linear equations with unit coefficients, recurrence relations, and generating functions. Topics include derivatives and differential equations, solution of difference equations by means of generating functions, recurrence relations, summation method, difference methods, combinations with repetitions, solutions bounded below, and solutions bounded above and below. The publication takes a look at generating functions and difference equations, ramifications of the binomial theorem, finite structures, coloring problems, maps on a sphere, and geometry of the plane. The manuscript is a valuable reference for researchers interested in combinatorics.

Notes on Introductory Combinatorics

George Polya,Robert E. Tarjan,Donald R. Woods
Notes on Introductory Combinatorics Book PDF

Author : George Polya,Robert E. Tarjan,Donald R. Woods
Publisher : Springer Science & Business Media
Page : 202 pages
File Size : 46,5 Mb
Release : 2013-11-27
Category : Science
ISBN : 9781475711011

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Notes on Introductory Combinatorics by George Polya,Robert E. Tarjan,Donald R. Woods Pdf

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

A. B. Slomson
Introduction to Combinatorics Book PDF

Author : A. B. Slomson
Publisher : CRC Press
Page : 290 pages
File Size : 45,7 Mb
Release : 1997-02-01
Category : Mathematics
ISBN : 0412353709

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Introduction to Combinatorics by A. B. Slomson Pdf

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 Walk Through Combinatorics

Mikl¢s B¢na
A Walk Through Combinatorics Book PDF

Author : Mikl¢s B¢na
Publisher : World Scientific
Page : 492 pages
File Size : 40,8 Mb
Release : 2006
Category : Mathematics
ISBN : 9789812568854

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A Walk Through Combinatorics by Mikl¢s B¢na Pdf

This is a textbook for an introductory combinatorics course that can take up 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 edition, 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 for the talented and hard-working 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 and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, 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.

How to Count

R.B.J.T. Allenby,Alan Slomson
How to Count Book PDF

Author : R.B.J.T. Allenby,Alan Slomson
Publisher : CRC Press
Page : 440 pages
File Size : 55,8 Mb
Release : 2011-07-01
Category : Mathematics
ISBN : 9781420082616

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How to Count by R.B.J.T. Allenby,Alan Slomson Pdf

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.

Discrete Mathematics

László Lovász,József Pelikán,Katalin Vesztergombi
Discrete Mathematics Book PDF

Author : László Lovász,József Pelikán,Katalin Vesztergombi
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 52,5 Mb
Release : 2006-05-10
Category : Mathematics
ISBN : 9780387217772

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Discrete Mathematics by László Lovász,József Pelikán,Katalin Vesztergombi Pdf

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

Miklós Bóna
A Walk Through Combinatorics Book PDF

Author : Miklós Bóna
Publisher : World Scientific Publishing Company
Page : 568 pages
File Size : 49,9 Mb
Release : 2011-05-09
Category : Mathematics
ISBN : 9789813100725

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A Walk Through Combinatorics by Miklós Bóna Pdf

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

Combinatorics

Theodore G. Faticoni
Combinatorics Book PDF

Author : Theodore G. Faticoni
Publisher : John Wiley & Sons
Page : 328 pages
File Size : 40,6 Mb
Release : 2014-08-21
Category : Mathematics
ISBN : 9781118407486

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Combinatorics by Theodore G. Faticoni Pdf

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.

Introduction to Enumerative Combinatorics

Miklós Bóna
Introduction to Enumerative Combinatorics Book PDF

Author : Miklós Bóna
Publisher : McGraw-Hill Science/Engineering/Math
Page : 552 pages
File Size : 45,5 Mb
Release : 2007
Category : Mathematics
ISBN : UCSD:31822035236827

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Introduction to Enumerative Combinatorics by Miklós Bóna Pdf

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 Combinatorics with Applications

Edward A. Bender,S. Gill Williamson
Foundations of Combinatorics with Applications Book PDF

Author : Edward A. Bender,S. Gill Williamson
Publisher : Courier Corporation
Page : 738 pages
File Size : 48,6 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.

A Course in Combinatorics

J. H. van Lint,Richard Michael Wilson
A Course in Combinatorics Book PDF

Author : J. H. van Lint,Richard Michael Wilson
Publisher : Cambridge University Press
Page : 620 pages
File Size : 47,5 Mb
Release : 2001-11-22
Category : Mathematics
ISBN : 0521006015

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A Course in Combinatorics by J. H. van Lint,Richard Michael Wilson Pdf

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.

Combinatorics: The Art of Counting

Bruce E. Sagan
Combinatorics The Art of Counting Book PDF

Author : Bruce E. Sagan
Publisher : American Mathematical Soc.
Page : 304 pages
File Size : 45,8 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.