Operator Calculus On Graphs Theory And Applications In Computer Science

Author : Staples George Stacey,Schott Rene
Publisher : World Scientific
Page : 428 pages
File Size : 43,7 Mb
Release : 2012-02-23
Category : Mathematics
ISBN : 9781908977571

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Operator Calculus On Graphs: Theory And Applications In Computer Science by Staples George Stacey,Schott Rene Pdf

This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science.Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with packages for performing symbolic computations.

Author : Leo J. Grady,Jonathan R. Polimeni
Publisher : Springer Science & Business Media
Page : 371 pages
File Size : 53,9 Mb
Release : 2010-07-23
Category : Computers
ISBN : 9781849962902

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Discrete Calculus by Leo J. Grady,Jonathan R. Polimeni Pdf

This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Many example applications from several fields of computational science are provided.

Author : Narsingh Deo
Publisher : Courier Dover Publications
Page : 496 pages
File Size : 42,6 Mb
Release : 2017-03-09
Category : Mathematics
ISBN : 9780486820811

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Graph Theory with Applications to Engineering and Computer Science by Narsingh Deo Pdf

Outstanding introductory treatment, geared toward advanced undergraduates and graduate students who require knowledge of graph theory. The first nine chapters constitute an excellent overview; the remaining chapters are more advanced and provide material for a variety of courses. 1974 edition.

Author : Martin Charles Golumbic,Irith Ben-Arroyo Hartman
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 45,5 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9780387250366

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Graph Theory, Combinatorics and Algorithms by Martin Charles Golumbic,Irith Ben-Arroyo Hartman Pdf

Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications focuses on discrete mathematics and combinatorial algorithms interacting with real world problems in computer science, operations research, applied mathematics and engineering. The book contains eleven chapters written by experts in their respective fields, and covers a wide spectrum of high-interest problems across these discipline domains. Among the contributing authors are Richard Karp of UC Berkeley and Robert Tarjan of Princeton; both are at the pinnacle of research scholarship in Graph Theory and Combinatorics. The chapters from the contributing authors focus on "real world" applications, all of which will be of considerable interest across the areas of Operations Research, Computer Science, Applied Mathematics, and Engineering. These problems include Internet congestion control, high-speed communication networks, multi-object auctions, resource allocation, software testing, data structures, etc. In sum, this is a book focused on major, contemporary problems, written by the top research scholars in the field, using cutting-edge mathematical and computational techniques.

Author : George Stacey Staples
Publisher : World Scientific
Page : 378 pages
File Size : 46,9 Mb
Release : 2019-09-24
Category : Mathematics
ISBN : 9789811202599

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Clifford Algebras And Zeons: Geometry To Combinatorics And Beyond by George Stacey Staples Pdf

Clifford algebras have many well-known applications in physics, engineering, and computer graphics. Zeon algebras are subalgebras of Clifford algebras whose combinatorial properties lend them to graph-theoretic applications such as enumerating minimal cost paths in dynamic networks. This book provides a foundational working knowledge of zeon algebras, their properties, and their potential applications in an increasingly technological world.As a graduate-level or advanced undergraduate-level mathematics textbook, it is suitable for self-study by researchers interested in new approaches to existing combinatorial problems and applications (wireless networks, Boolean satisfiability, coding theory, etc.).As the first textbook to explore algebraic and combinatorial properties of zeon algebras in depth, it is suitable for interdisciplinary study in analysis, algebra, and combinatorics. The material is complemented by the CliffMath software package for Mathematica, which is freely available through the book's webpage.

Author : Junming Xu
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 47,8 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781441986986

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Theory and Application of Graphs by Junming Xu Pdf

In the spectrum of mathematics, graph theory which studies a mathe matical structure on a set of elements with a binary relation, as a recognized discipline, is a relative newcomer. In recent three decades the exciting and rapidly growing area of the subject abounds with new mathematical devel opments and significant applications to real-world problems. More and more colleges and universities have made it a required course for the senior or the beginning postgraduate students who are majoring in mathematics, computer science, electronics, scientific management and others. This book provides an introduction to graph theory for these students. The richness of theory and the wideness of applications make it impossi ble to include all topics in graph theory in a textbook for one semester. All materials presented in this book, however, I believe, are the most classical, fundamental, interesting and important. The method we deal with the mate rials is to particularly lay stress on digraphs, regarding undirected graphs as their special cases. My own experience from teaching out of the subject more than ten years at University of Science and Technology of China (USTC) shows that this treatment makes hardly the course di:fficult, but much more accords with the essence and the development trend of the subject.

Author : Toufik Mansour,Matthias Schork
Publisher : CRC Press
Page : 506 pages
File Size : 54,8 Mb
Release : 2015-09-18
Category : Mathematics
ISBN : 9781466579897

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Commutation Relations, Normal Ordering, and Stirling Numbers by Toufik Mansour,Matthias Schork Pdf

Commutation Relations, Normal Ordering, and Stirling Numbers provides an introduction to the combinatorial aspects of normal ordering in the Weyl algebra and some of its close relatives. The Weyl algebra is the algebra generated by two letters U and V subject to the commutation relation UV - VU = I. It is a classical result that normal ordering pow

Author : Jorgen Bang-Jensen,Gregory Z. Gutin
Publisher : Springer Science & Business Media
Page : 769 pages
File Size : 40,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781447138860

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Digraphs by Jorgen Bang-Jensen,Gregory Z. Gutin Pdf

The study of directed graphs (digraphs) has developed enormously over recent decades, yet the results are rather scattered across the journal literature. This is the first book to present a unified and comprehensive survey of the subject. In addition to covering the theoretical aspects, the authors discuss a large number of applications and their generalizations to topics such as the traveling salesman problem, project scheduling, genetics, network connectivity, and sparse matrices. Numerous exercises are included. For all graduate students, researchers and professionals interested in graph theory and its applications, this book will be essential reading.

Author : Y. Alavi,G. Chartrand,L. Lesniak,D.R. Lick,C.E. Wall
Publisher : Unknown
Page : 128 pages
File Size : 55,9 Mb
Release : 1985
Category : Electronic
ISBN : OCLC:234219758

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Graph Theory with Applications to Algorithms and by Y. Alavi,G. Chartrand,L. Lesniak,D.R. Lick,C.E. Wall Pdf

Author : Dieter Jungnickel
Publisher : Springer Science & Business Media
Page : 655 pages
File Size : 45,6 Mb
Release : 2007-09-26
Category : Mathematics
ISBN : 9783540727804

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Graphs, Networks and Algorithms by Dieter Jungnickel Pdf

Revised throughout Includes new chapters on the network simplex algorithm and a section on the five color theorem Recent developments are discussed

Author : Gregory Budzban,Harry Randolph Hughes,Henri Schurz
Publisher : American Mathematical Soc.
Page : 236 pages
File Size : 51,9 Mb
Release : 2016-06-29
Category : Combinatorial geometry
ISBN : 9781470419455

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Probability on Algebraic and Geometric Structures by Gregory Budzban,Harry Randolph Hughes,Henri Schurz Pdf

This volume contains the proceedings of the International Research Conference “Probability on Algebraic and Geometric Structures”, held from June 5–7, 2014, at Southern Illinois University, Carbondale, IL, celebrating the careers of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea. These proceedings include survey papers and new research on a variety of topics such as probability measures and the behavior of stochastic processes on groups, semigroups, and Clifford algebras; algebraic methods for analyzing Markov chains and products of random matrices; stochastic integrals and stochastic ordinary, partial, and functional differential equations.

Author : Goulnara Arzhantseva
Publisher : EPFL Press
Page : 312 pages
File Size : 46,6 Mb
Release : 2009-03-16
Category : Mathematics
ISBN : 1439804001

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Limits of Graphs in Group Theory and Computer Science by Goulnara Arzhantseva Pdf

A collection of research articles and survey papers, this text highlights current methods and open problems in the geometric, combinatorial, and computational aspects of group theory. New interactions with broad areas of theoretical computer science are also considered. Pub 3/09.

Author : Jonathan L. Gross,Jay Yellen,Mark Anderson
Publisher : CRC Press
Page : 577 pages
File Size : 51,6 Mb
Release : 2018-11-05
Category : Computers
ISBN : 9780429757099

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Graph Theory and Its Applications by Jonathan L. Gross,Jay Yellen,Mark Anderson Pdf

Graph Theory and Its Applications, Third Edition is the latest edition of the international, bestselling textbook for undergraduate courses in graph theory, yet it is expansive enough to be used for graduate courses as well. The textbook takes a comprehensive, accessible approach to graph theory, integrating careful exposition of classical developments with emerging methods, models, and practical needs. The authors’ unparalleled treatment is an ideal text for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology. Features of the Third Edition Expanded coverage on several topics (e.g., applications of graph coloring and tree-decompositions) Provides better coverage of algorithms and algebraic and topological graph theory than any other text Incorporates several levels of carefully designed exercises that promote student retention and develop and sharpen problem-solving skills Includes supplementary exercises to develop problem-solving skills, solutions and hints, and a detailed appendix, which reviews the textbook’s topics About the Authors Jonathan L. Gross is a professor of computer science at Columbia University. His research interests include topology and graph theory. Jay Yellen is a professor of mathematics at Rollins College. His current areas of research include graph theory, combinatorics, and algorithms. Mark Anderson is also a mathematics professor at Rollins College. His research interest in graph theory centers on the topological or algebraic side.

Author : Vitaly Ivanovich Voloshin
Publisher : Unknown
Page : 0 pages
File Size : 41,9 Mb
Release : 2009
Category : Graph theory
ISBN : 1606923749

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Introduction to Graph Theory by Vitaly Ivanovich Voloshin Pdf

Graph Theory is an important area of contemporary mathematics with many applications in computer science, genetics, chemistry, engineering, industry, business and in social sciences. It is a young science invented and developing for solving challenging problems of 'computerised' society for which traditional areas of mathematics such as algebra or calculus are powerless. This book is for math and computer science majors, for students and representatives of many other disciplines (like bioinformatics, for example) taking the courses in graph theory, discrete mathematics, data structures, algorithms.It is also for anyone who wants to understand the basics of graph theory, or just is curious. No previous knowledge in graph theory or any other significant mathematics is required. The very basic facts from set theory, proof techniques and algorithms are sufficient to understand it; but even those are explained in the text. The book discusses the key concepts of graph theory with emphasis on trees, bipartite graphs, cycles, chordal graphs, planar graphs and graph colouring.The reader is conducted from the simplest examples, definitions and concepts, step by step, towards an understanding of a few most fundamental facts in the field.

Author : Jonathan L. Gross
Publisher : CRC Press
Page : 664 pages
File Size : 42,9 Mb
Release : 2007-11-16
Category : Mathematics
ISBN : 9781584887430

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Combinatorial Methods with Computer Applications by Jonathan L. Gross Pdf

Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinatorial methods course or in a combined graph theory and combinatorics course. After an introduction to combinatorics, the book explores six systematic approaches within a comprehensive framework: sequences, solving recurrences, evaluating summation expressions, binomial coefficients, partitions and permutations, and integer methods. The author then focuses on graph theory, covering topics such as trees, isomorphism, automorphism, planarity, coloring, and network flows. The final chapters discuss automorphism groups in algebraic counting methods and describe combinatorial designs, including Latin squares, block designs, projective planes, and affine planes. In addition, the appendix supplies background material on relations, functions, algebraic systems, finite fields, and vector spaces. Paving the way for students to understand and perform combinatorial calculations, this accessible text presents the discrete methods necessary for applications to algorithmic analysis, performance evaluation, and statistics as well as for the solution of combinatorial problems in engineering and the social sciences.