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Books in Discrete mathematics combinatorics

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    • An Introduction to Discrete Mathematics

      • 1st Edition
      • Vidyadhar Kulkarni
      • English
      An Introduction to Discrete Mathematics offers an engaging and accessible introduction to discrete mathematics for beginning undergraduate students across a wide range of application areas, from mathematics to statistics, operations research, business, engineering, and the sciences. It provides solid foundation in precise proof writing methods, with early chapters introducing set theory and logic that are followed by deductive and inductive proof techniques, number theory, counting principles, permutations and combinations, probability of events, random variables, graphs, and weighted graphs.The book illustrates fundamental concepts in discrete mathematics with clear and precise definitions that are paired with examples and counter-examples as applied in combinatorics, discrete probability, and graph theory. Chapters include student exercises to enhance learning, and a solutions manual and example questions are available for instructors on a companion website.

    • Discrete Mathematics With Logic

      • 1st Edition
      • Martin Milanic + 2 more
      • English
      Discrete Mathematics provides key concepts and a solid, rigorous foundation in mathematical reasoning. Appropriate for undergraduate as well as a starting point for more advanced class, the resource offers a logical progression through key topics without assuming any background in algebra or computational skills and without duplicating what they will learn in higher level courses. The book is designed as an accessible introduction for students in mathematics or computer science as it explores questions that test the understanding of proof strategies, such as mathematical induction. For students interested to dive into this subject, the text offers a rigorous introduction to mathematical thought through useful examples and exercises.

    • Discrete Mathematics

      Essentials and Applications
      • 1st Edition
      • Ali Grami
      • English
      Discrete Mathematics: Essentials and Applications offers a comprehensive survey of the area, particularly concentrating on the basic principles and applications of Discrete Mathematics. This up-to-date text provides proofs of significance, keeping the focus on numerous relevant examples and many pertinent applications. Written in a simple and clear tone, the title features insightful descriptions and intuitive explanations of all complex concepts and ensures a thorough understanding of the subject matter.

    • Fixed Point Theory and Graph Theory

      Foundations and Integrative Approaches
      • 1st Edition
      • Monther Alfuraidan + 1 more
      • English
      Fixed Point Theory and Graph Theory provides an intersection between the theories of fixed point theorems that give the conditions under which maps (single or multivalued) have solutions and graph theory which uses mathematical structures to illustrate the relationship between ordered pairs of objects in terms of their vertices and directed edges. This edited reference work is perhaps the first to provide a link between the two theories, describing not only their foundational aspects, but also the most recent advances and the fascinating intersection of the domains. The authors provide solution methods for fixed points in different settings, with two chapters devoted to the solutions method for critically important non-linear problems in engineering, namely, variational inequalities, fixed point, split feasibility, and hierarchical variational inequality problems. The last two chapters are devoted to integrating fixed point theory in spaces with the graph and the use of retractions in the fixed point theory for ordered sets.

    • The Julius Petersen Graph Theory Centennial

      • 1st Edition
      • L.D. Andersen + 7 more
      • English
      Julius Petersen's paper, Die Theorie der regulären graphs in Acta Mathematica, volume 15 (1891), stands at the beginning of graph theory as we know it today.The Danish group of graph theorists decided in 1985 to mark the 150th birthday of Petersen in 1989, as well as the centennial of his paper.It was felt that the occasion called for a presentation of Petersen's famous paper in its historical context and, in a wider sense, of Petersen's life and work as a whole. However, the readily available information about Julius Petersen amounted to very little (not even a full bibliography existed) and virtually nothing was known about the circumstances that led him to write his famous paper.The study of Petersen's life and work has resulted in several papers, in particular a biography, a bibliography, an annotated edition of the letters surrounding Petersen's paper of 1891, an analysis of Petersen's paper and an annotated edition of parts of Petersen's correspondence with Sylow on Galois theory. The first four of these papers, together with a survey of matching theory, form the first part of this book. In addition to these five special papers, there are papers submitted in the celebration of the Petersen centennial.

    • A Collection of Contributions in Honour of Jack van Lint

      • 1st Edition
      • P.J. Cameron + 1 more
      • English
      This collection of contributions is offered to Jack van Lint on the occasion of his sixtieth birthday and appears simultaneously in the series Topics in Discrete Mathematics and as a special double volume of Discrete Mathematics (Volumes 106/107). It is hoped that the papers selected, all written by experts in their own fields, represent the many interesting areas that together constitute the discipline of Discrete Mathematics. It is in this sphere that van Lint has become the acknowledged master and this expansive volume serves to demonstrate the enormous significance he has had on the development of Discrete Mathematics during the last 30 years.

    • Interconnection Networks

      • 1st Edition
      • Volume 5
      • J.-C. Bermond
      • English
      Most of the articles in this book deal with static or point-to-pointInterc... Networks. In particular, new constructions are proposed basedon different tools from discrete mathematics. Many new records have beenestablished in the table of the maximum number of vertices of graphs withmaximum degree &Dgr; and diameter D. Properties of thesenetworks (and of more classical ones) are analyzed in many of the otherpapers. About 40% of the articles deal with fault tolerance orvulnerability properties using either combinatorial tools or probabilisticones.

    • Designs and Graphs

      • 1st Edition
      • Volume 4
      • C.J. Colbourn + 2 more
      • English
      In 1988, the news of Egmont Köhler's untimely death at the age of 55reached his friends and colleagues. It was widely felt that a lastingmemorial tribute should be organized. The result is the present volume,containing forty-two articles, mostly in combinatorial design theory andgraph theory, and all in memory of Egmont Köhler. Designs and graphswere his areas of particular interest; he will long be remembered for hisresearch on cyclic designs, Skolem sequences, t-designs and theOberwolfach problem. Professors Lenz and Ringel give a detailedappreciation of Köhler's research in the first article of thisvolume.There is, however, one aspect of Egmont Köhler's biographythat merits special attention. Before taking up the study of mathematics atthe age of 31, he had completed training as a musician (studying bothcomposition and violoncello at the Musikhochschule in Berlin), and workedas a cellist in a symphony orchestra for some years. This accounts for hisinterest in the combinatorial aspects of music. His work and lectures inthis direction had begun to attract the interest of many musicians, and hehad commenced work on a book on mathematical aspects of musical theory. Itis tragic indeed that his early death prevented the completion of his work;the surviving paper on the classification and complexity of chordsindicates the loss that his death meant to the area, as he was almostuniquely qualified to bring mathematics and music together, being aprofessional in both fields.

    • Directions in Infinite Graph Theory and Combinatorics

      With an introduction by C.St.J.A. Nash-Williams
      • 1st Edition
      • Volume 3
      • R. Diestel
      • English
      This book has arisen from a colloquium held at St. John's College, Cambridge, in July 1989, which brought together most of today's leading experts in the field of infinite graph theory and combinatorics. This was the first such meeting ever held, and its aim was to assess the state of the art in the discipline, to consider its links with other parts of mathematics, and to discuss possible directions for future development. This volume reflects the Cambridge meeting in both level and scope. It contains research papers as well as expository surveys of particular areas. Together they offer a comprehensive portrait of infinite graph theory and combinatorics, which should be particularly attractive to anyone new to the discipline.

    • The Joy of Finite Mathematics

      The Language and Art of Math
      • 1st Edition
      • Chris P. Tsokos + 1 more
      • English
      The Joy of Finite Mathematics: The Language and Art of Math teaches students basic finite mathematics through a foundational understanding of the underlying symbolic language and its many dialects, including logic, set theory, combinatorics (counting), probability, statistics, geometry, algebra, and finance. Through detailed explanations of the concepts, step-by-step procedures, and clearly defined formulae, readers learn to apply math to subjects ranging from reason (logic) to finance (personal budget), making this interactive and engaging book appropriate for non-science, undergraduate students in the liberal arts, social sciences, finance, economics, and other humanities areas. The authors utilize important historical facts, pose interesting and relevant questions, and reference real-world events to challenge, inspire, and motivate students to learn the subject of mathematical thinking and its relevance. The book is based on the authors’ experience teaching Liberal Arts Math and other courses to students of various backgrounds and majors, and is also appropriate for preparing students for Florida’s CLAST exam or similar core requirements.