Solomon Golomb S Course On Undergraduate Combinatorics

Author : Solomon W. Golomb,Andy Liu
Publisher : Springer Nature
Page : 458 pages
File Size : 43,6 Mb
Release : 2021-10-15
Category : Mathematics
ISBN : 9783030722289

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Solomon Golomb’s Course on Undergraduate Combinatorics by Solomon W. Golomb,Andy Liu Pdf

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.

Author : Solomon W. Golomb,Andy Liu
Publisher : Unknown
Page : 0 pages
File Size : 42,8 Mb
Release : 2021
Category : Electronic
ISBN : 3030722295

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Solomon Golomb's Course on Undergraduate Combinatorics by Solomon W. Golomb,Andy Liu Pdf

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.

Author : Carl G. Wagner
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 55,5 Mb
Release : 2020-10-29
Category : Education
ISBN : 9781470459956

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A First Course in Enumerative Combinatorics by Carl G. Wagner Pdf

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.

Author : Dennis Stanton,Dennis White
Publisher : Springer
Page : 186 pages
File Size : 41,7 Mb
Release : 1986-06-01
Category : Mathematics
ISBN : 9780387963471

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Constructive Combinatorics by Dennis Stanton,Dennis White Pdf

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.

Author : Fred S. Roberts,Barry Tesman
Publisher : Prentice Hall
Page : 856 pages
File Size : 48,9 Mb
Release : 2005
Category : Mathematics
ISBN : UCSC:32106017873479

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Applied Combinatorics by Fred S. Roberts,Barry Tesman Pdf

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.

Author : Carl Wagner
Publisher : Unknown
Page : 128 pages
File Size : 50,6 Mb
Release : 2020
Category : Combinatorial enumeration problems
ISBN : 1470462621

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A First Course in Enumerative Combinatorics by Carl Wagner Pdf

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

Author : J. H. van Lint,R. M. Wilson
Publisher : Cambridge University Press
Page : 616 pages
File Size : 43,6 Mb
Release : 2001-11-22
Category : Mathematics
ISBN : 0521803403

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A Course in Combinatorics by J. H. van Lint,R. M. Wilson Pdf

Combinatorics, a subject dealing with ways of arranging and distributing objects, 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 an essential tool in many scientific fields. In this second edition the authors have made the text as comprehensive as possible, dealing in a unified manner with such topics as 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. It is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level, and working mathematicians and scientists will also find it a valuable introduction and reference.

Author : Edward A. Bender,Stanley Gill Williamson
Publisher : Addison Wesley Publishing Company
Page : 458 pages
File Size : 43,8 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015022034725

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

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

Author : Lint
Publisher : Unknown
Page : 602 pages
File Size : 52,8 Mb
Release : 2001
Category : Combinatorial analysis
ISBN : 0521718171

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A Course In Combinatorics 2/Ed by Lint Pdf

Author : George Pólya,Robert E. Tarjan,Donald R. Woods
Publisher : Unknown
Page : 190 pages
File Size : 46,9 Mb
Release : 1983-01-01
Category : Analyse combinatoire
ISBN : 3764331232

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

Developed from the authorsa (TM) introductory combinatorics course, this book focuses on a branch of mathematics which plays a crucial role in computer science. Combinatorial methods provide many analytical tools used for determining the expected performance of computer algorithms. Elementary subjects such as combinations and permutations, and mathematical tools such as generating functions and PA3lyaa (TM)s Theory of Counting, are covered, as are analyses of specific problems such as Ramsey Theory, matchings, and Hamiltonian and Eulerian paths. This introduction will provide students with a solid foundation in the subject. ---- This is a delightful little paperback which presents a day-by-day transcription of a course taught jointly by PA3lya and Tarjan at Stanford University. Woods, the teaching assistant for the class, did a very good job of merging class notes into an interesting mini-textbook; he also included the exercises, homework, and tests assigned in the class (a very helpful addition for other instructors in the field). The notes are very well illustrated throughout and Woods and the BirkhAuser publishers produced a very pleasant text. One can count on PA3lya and Tarjan] for new insights and a fresh outlook. Both instructors taught by presenting a succession of examples rather than by presenting a body of theorya ] The book] is very well suited as supplementary material for any introductory class on combinatorics; as such, it is very highly recommended. Finally, for all of us who like the topic and delight in observing skilled professionals at work, this book is entertaining and, yes, instructive, reading. a Mathematical Reviews (Review of the original hardcover edition) The mathematical community welcomes this book as a final contribution to honour the teacher G. PA3lya. a Zentralblatt MATH (Review of the original hardcover edition)

Author : J. H. van Lint,Richard Michael Wilson
Publisher : Cambridge University Press
Page : 620 pages
File Size : 47,8 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.

Author : Victor Reiner
Publisher : American Mathematical Soc.
Page : 814 pages
File Size : 55,7 Mb
Release : 2017-05-17
Category : Combinatorial analysis
ISBN : 9781470416829

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Selected Works of Richard P. Stanley by Victor Reiner Pdf

Richard Stanley's work in combinatorics revolutionized and reshaped the subject. Many of his hallmark ideas and techniques imported from other areas of mathematics have become mainstays in the framework of modern combinatorics. In addition to collecting several of Stanley's most influential papers, this volume also includes his own short reminiscences on his early years, and on his celebrated proof of The Upper Bound Theorem.

Author : Béla Bajnok
Publisher : Springer Nature
Page : 443 pages
File Size : 47,7 Mb
Release : 2020-10-27
Category : Mathematics
ISBN : 9783030561741

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An Invitation to Abstract Mathematics by Béla Bajnok Pdf

This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics. Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise. This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts. From reviews of the first edition: Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. ... The book can be used as a text for traditional transition or structure courses ... but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA Reviews The style of writing is careful, but joyously enthusiastic.... The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background ... and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATH

Author : American Mathematical Society
Publisher : Unknown
Page : 628 pages
File Size : 44,9 Mb
Release : 1977
Category : Electronic journals
ISBN : UCAL:B3530686

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Notices of the American Mathematical Society by American Mathematical Society Pdf

Contains articles of significant interest to mathematicians, including reports on current mathematical research.

Author : Loren C. Larson
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461254980

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Problem-Solving Through Problems by Loren C. Larson Pdf

This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.