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Author: J. H. van Lint Publisher: Cambridge University Press ISBN: 9780521006019 Category : Mathematics Languages : en Pages : 620
Book Description
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: J. H. van Lint Publisher: Cambridge University Press ISBN: 9780521006019 Category : Mathematics Languages : en Pages : 620
Book Description
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: John Harris Publisher: Springer Science & Business Media ISBN: 0387797114 Category : Mathematics Languages : en Pages : 392
Book Description
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.
Author: Sebastian M. Cioabă Publisher: Springer Nature ISBN: 9811909571 Category : Mathematics Languages : en Pages : 232
Book Description
This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book includes recent developments in the theory of signed adjacency matrices involving the proof of sensitivity conjecture and the theory of Ramanujan graphs. In addition, the book discusses topics such as Pick’s theorem on areas of lattice polygons and Graham–Pollak’s work on addressing of graphs. The concept of graph is fundamental in mathematics and engineering, as it conveniently encodes diverse relations and facilitates combinatorial analysis of many theoretical and practical problems. The text is ideal for a one-semester course at the advanced undergraduate level or beginning graduate level.
Author: Mark de Longueville Publisher: Springer Science & Business Media ISBN: 1441979093 Category : Mathematics Languages : en Pages : 246
Book Description
This undergraduate textbook in topological combinatorics covers such topics as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discrete geometry. Includes many figures and exercises.
Author: J. E. Graver Publisher: Springer Science & Business Media ISBN: 1461299144 Category : Mathematics Languages : en Pages : 363
Book Description
Combinatorics and graph theory have mushroomed in recent years. Many overlapping or equivalent results have been produced. Some of these are special cases of unformulated or unrecognized general theorems. The body of knowledge has now reached a stage where approaches toward unification are overdue. To paraphrase Professor Gian-Carlo Rota (Toronto, 1967), "Combinatorics needs fewer theorems and more theory. " In this book we are doing two things at the same time: A. We are presenting a unified treatment of much of combinatorics and graph theory. We have constructed a concise algebraically based, but otherwise self-contained theory, which at one time embraces the basic theorems that one normally wishes to prove while giving a common terminology and framework for the develop ment of further more specialized results. B. We are writing a textbook whereby a student of mathematics or a mathematician with another specialty can learn combinatorics and graph theory. We want this learning to be done in a much more unified way than has generally been possible from the existing literature. Our most difficult problem in the course of writing this book has been to keep A and B in balance. On the one hand, this book would be useless as a textbook if certain intuitively appealing, classical combinatorial results were either overlooked or were treated only at a level of abstraction rendering them beyond all recognition.
Author: Mikl¢s B¢na Publisher: World Scientific ISBN: 9812568859 Category : Mathematics Languages : en Pages : 492
Book Description
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.
Author: Miklós Bóna Publisher: World Scientific Publishing Company ISBN: 9813100729 Category : Mathematics Languages : en Pages : 568
Book Description
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
Author: J. H. van Lint Publisher: Cambridge University Press ISBN: 1139430637 Category : Mathematics Languages : en Pages : 439
Book Description
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: J. H. van Lint
Author: J. H. van Lint
Author: John Harris
Author: Sebastian M. Cioabă
Author: Mark de Longueville
Author: J. E. Graver
Author: Mikl¢s B¢na
Author: Miklós Bóna
Author: Simeon Ball
Author: Alan Tucker
Author: J. H. van Lint