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Books in Discrete mathematics combinatorics

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • Latin Squares and their Applications

    • 2nd Edition
    • A. Donald Keedwell + 1 more
    • English
    Latin Squares and Their Applications, Second edition offers a long-awaited update and reissue of this seminal account of the subject. The revision retains foundational, original material from the frequently-cited 1974 volume but is completely updated throughout. As with the earlier version, the author hopes to take the reader ‘from the beginnings of the subject to the frontiers of research’. By omitting a few topics which are no longer of current interest, the book expands upon active and emerging areas. Also, the present state of knowledge regarding the 73 then-unsolved problems given at the end of the first edition is discussed and commented upon. In addition, a number of new unsolved problems are proposed. Using an engaging narrative style, this book provides thorough coverage of most parts of the subject, one of the oldest of all discrete mathematical structures and still one of the most relevant. However, in consequence of the huge expansion of the subject in the past 40 years, some topics have had to be omitted in order to keep the book of a reasonable length. Latin squares, or sets of mutually orthogonal latin squares (MOLS), encode the incidence structure of finite geometries; they prescribe the order in which to apply the different treatments in designing an experiment in order to permit effective statistical analysis of the results; they produce optimal density error-correcting codes; they encapsulate the structure of finite groups and of more general algebraic objects known as quasigroups. As regards more recreational aspects of the subject, latin squares provide the most effective and efficient designs for many kinds of games tournaments and they are the templates for Sudoku puzzles. Also, they provide a number of ways of constructing magic squares, both simple magic squares and also ones with additional properties.

  • Algebraic and Discrete Mathematical Methods for Modern Biology

    • 1st Edition
    • Raina Robeva
    • English
    Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems. Each chapter begins with a question from modern biology, followed by the description of certain mathematical methods and theory appropriate in the search of answers. Every topic provides a fast-track pathway through the problem by presenting the biological foundation, covering the relevant mathematical theory, and highlighting connections between them. Many of the projects and exercises embedded in each chapter utilize specialized software, providing students with much-needed familiarity and experience with computing applications, critical components of the "modern biology" skill set. This book is appropriate for mathematics courses such as finite mathematics, discrete structures, linear algebra, abstract/modern algebra, graph theory, probability, bioinformatics, statistics, biostatistics, and modeling, as well as for biology courses such as genetics, cell and molecular biology, biochemistry, ecology, and evolution.

  • Progress in Combinatorial Optimization

    • 1st Edition
    • William R. Pulleyblank
    • English
    Progress in Combinatorial Optimization provides information pertinent to the fundamental aspects of combinatorial optimization. This book discusses how to determine whether or not a particular structure exists. Organized into 21 chapters, this book begins with an overview of a polar characterization of facets of polyhedra obtained by lifting facets of lower dimensional polyhedra. This text then discusses how to obtain bounds on the value of the objective in a graph partitioning problem in terms of spectral information about the graph. Other chapters consider the notion of a triangulation of an oriented matroid and show that oriented matroid triangulation yield triangulations of the underlying polytopes. This book discusses as well the selected results and problems on perfect ad imperfect graphs. The final chapter deals with the weighted parity problem for gammoids, which can be reduced to the weighted graphic matching problem. This book is a valuable resource for mathematicians and research workers.

  • Generating Functionology

    • 2nd Edition
    • Herbert S. Wilf
    • English
    This is the Second Edition of the highly successful introduction to the use of generating functions and series in combinatorial mathematics. This new edition includes several new areas of application, including the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences. An appendix on using the computer algebra programs MAPLE(r) and Mathematica(r) to generate functions is also included. The book provides a clear, unified introduction to the basic enumerative applications of generating functions, and includes exercises and solutions, many new, at the end of each chapter.

  • Algorithmic Aspects of Combinatorics

    • 1st Edition
    • Volume 2
    • English

  • Random Graphs '83

    • 1st Edition
    • Volume 28
    • A. Rucinski + 1 more
    • English
    The range of random graph topics covered in this volume includes structure, colouring, algorithms, mappings, trees, network flows, and percolation. The papers also illustrate the application of probability methods to Ramsey's problems, the application of graph theory methods to probability, and relations between games on graphs and random graphs.

  • Advances in Graph Theory

    • 1st Edition
    • Volume 3
    • English

  • Studies in Integer Programming

    • 1st Edition
    • Volume 1
    • English

  • Random Graphs '85

    • 1st Edition
    • Volume 33
    • M. Karonski + 1 more
    • English
    Covering a wide range of Random Graphs subjects, this volume examines series-parallel networks, properties of random subgraphs of the n-cube, random binary and recursive trees, random digraphs, induced subgraphs and spanning trees in random graphs as well as matchings, hamiltonian cycles and closure in such structures. Papers in this collection also illustrate various aspects of percolation theory and its applications, properties of random lattices and random walks on such graphs, random allocation schemes, pseudo-random graphs and reliability of planar networks. Several open problems that were presented during a special session at the Seminar are also included at the end of the volume.

  • Combinatorics '86

    • 1st Edition
    • Volume 37
    • M. Marchi + 2 more
    • English
    Recent developments in all aspects of combinatorial and incidence geometry are covered in this volume, including their links with the foundations of geometry, graph theory and algebraic structures, and the applications to coding theory and computer science.Topics covered include Galois geometries, blocking sets, affine and projective planes, incidence structures and their automorphism groups. Matroids, graph theory and designs are also treated, along with weak algebraic structures such as near-rings, near-fields, quasi-groups, loops, hypergroups etc., and permutation sets and groups.The vitality of combinatorics today lies in its important interactions with computer science. The problems which arise are of a varied nature and suitable techniques to deal with them have to be devised for each situation; one of the special features of combinatorics is the often sporadic nature of solutions, stemming from its links with number theory. The branches of combinatorics are many and various, and all of them are represented in the 56 papers in this volume.

  • Surveys in Combinatorial Optimization

    • 1st Edition
    • Volume 31
    • S. Martello + 3 more
    • English
    A collection of papers surveying recent progress in the field of Combinatorial Optimization.Topics examined include theoretical and computational aspects (Boolean Programming, Probabilistic Analysis of Algorithms, Parallel Computer Models and Combinatorial Algorithms), well-known combinatorial problems (such as the Linear Assignment Problem, the Quadratic Assignment Problem, the Knapsack Problem and Steiner Problems in Graphs) and more applied problems (such as Network Synthesis and Dynamic Network Optimization, Single Facility Location Problems on Networks, the Vehicle Routing Problem and Scheduling Problems).

  • Combinatorial Design Theory

    • 1st Edition
    • Volume 34
    • C.J. Colbourn + 1 more
    • English
    Combinatorial design theory is a vibrant area of combinatorics, connecting graph theory, number theory, geometry, and algebra with applications in experimental design, coding theory, and numerous applications in computer science.This volume is a collection of forty-one state-of-the-art research articles spanning all of combinatorial design theory. The articles develop new methods for the construction and analysis of designs and related combinatorial configurations; both new theoretical methods, and new computational tools and results, are presented. In particular, they extend the current state of knowledge on Steiner systems, Latin squares, one-factorizations, block designs, graph designs, packings and coverings, and develop recursive and direct constructions.The contributions form an overview of the current diversity of themes in design theory for those peripherally interested, while researchers in the field will find it to be a major collection of research advances. The volume is dedicated to Alex Rosa, who has played a major role in fostering and developing combinatorial design theory.

  • Linear and Combinatorial Optimization in Ordered Algebraic Structures

    • 1st Edition
    • Volume 10
    • English

  • Combinatorics 79. Part II

    • 1st Edition
    • Volume 9
    • English

  • Combinatorial Mathematics, Optimal Designs, and Their Applications

    • 1st Edition
    • Volume 6
    • English

  • Combinatorics 79. Part I

    • 1st Edition
    • Volume 8
    • English

  • Topics on Steiner Systems

    • 1st Edition
    • Volume 7
    • English

  • Trees and Hills: Methodology for Maximizing Functions of Systems of Linear Relations

    • 1st Edition
    • Volume 22
    • R. Greer
    • English

  • Computational Theory of Iterative Methods

    • 1st Edition
    • Volume 15
    • Ioannis Argyros
    • English
    The book is designed for researchers, students and practitioners interested in using fast and efficient iterative methods to approximate solutions of nonlinear equations. The following four major problems are addressed. Problem 1: Show that the iterates are well defined. Problem 2: concerns the convergence of the sequences generated by a process and the question of whether the limit points are, in fact solutions of the equation. Problem 3: concerns the economy of the entire operations. Problem 4: concerns with how to best choose a method, algorithm or software program to solve a specific type of problem and its description of when a given algorithm succeeds or fails. The book contains applications in several areas of applied sciences including mathematical programming and mathematical economics. There is also a huge number of exercises complementing the theory.

  • Introduction to Probability Models

    • 9th Edition
    • Sheldon M. Ross
    • English
    Introduction to Probability Models, Ninth Edition, is the primary text for a first undergraduate course in applied probability. This updated edition of Ross's classic bestseller provides an introduction to elementary probability theory and stochastic processes, and shows how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. With the addition of several new sections relating to actuaries, this text is highly recommended by the Society of Actuaries. This book now contains a new section on compound random variables that can be used to establish a recursive formula for computing probability mass functions for a variety of common compounding distributions; a new section on hiddden Markov chains, including the forward and backward approaches for computing the joint probability mass function of the signals, as well as the Viterbi algorithm for determining the most likely sequence of states; and a simplified approach for analyzing nonhomogeneous Poisson processes. There are also additional results on queues relating to the conditional distribution of the number found by an M/M/1 arrival who spends a time t in the system; inspection paradox for M/M/1 queues; and M/G/1 queue with server breakdown. Furthermore, the book includes new examples and exercises, along with compulsory material for new Exam 3 of the Society of Actuaries. This book is essential reading for professionals and students in actuarial science, engineering, operations research, and other fields in applied probability.

  • Dictionary of Distances

    • 1st Edition
    • Michel-Marie Deza + 1 more
    • English
    This book comes out of need and urgency (expressed especially in areas of Information Retrieval with respect to Image, Audio, Internet and Biology) to have a working tool to compare data.The book will provide powerful resource for all researchers using Mathematics as well as for mathematicians themselves. In the time when over-specialization and terminology fences isolate researchers, this Dictionary try to be "centripedal" and "oikoumeni", providing some access and altitude of vision but without taking the route of scientific vulgarisation. This attempted balance is the main philosophy of this Dictionary which defined its structure and style.Key features:- Unicity: it is the first book treating the basic notion of Distance in whole generality.- Interdisciplinarity: this Dictionary is larger in scope than majority of thematic dictionaries.- Encyclopedicity: while an Encyclopedia of Distances seems now too difficult to produce, this book (by its scope, short introductions and organization) provides the main material for it and for future tutorials on some parts of this material.- Applicability: the distances, as well as distance-related notions and paradigms, are provided in ready-to-use fashion.- Worthiness: the need and urgency for such dictionary was great in several huge areas, esp. Information Retrieval, Image Analysis, Speech Recognition and Biology.- Accessibility: the definitions are easy to locate by subject or, in Index, by alphabetic order; the introductions and definitions are reader-friendly and maximally independent one from another; still the text is structured, in the 3D HTML style, by hyperlink-like boldfaced references to similar definitions.

  • Discrete Dynamical Systems, Bifurcations and Chaos in Economics

    • 1st Edition
    • Volume 204
    • Wei-Bin Zhang
    • English
    This book is a unique blend of difference equations theory and its exciting applications to economics. It deals with not only theory of linear (and linearized) difference equations, but also nonlinear dynamical systems which have been widely applied to economic analysis in recent years. It studies most important concepts and theorems in difference equations theory in a way that can be understood by anyone who has basic knowledge of calculus and linear algebra. It contains well-known applications and many recent developments in different fields of economics. The book also simulates many models to illustrate paths of economic dynamics.

  • Linear Discrete Parabolic Problems

    • 1st Edition
    • Volume 203
    • Nikolai Bakaev
    • English
    This volume introduces a unified, self-contained study of linear discrete parabolic problems through reducing the starting discrete problem to the Cauchy problem for an evolution equation in discrete time. Accessible to beginning graduate students, the book contains a general stability theory of discrete evolution equations in Banach space and gives applications of this theory to the analysis of various classes of modern discretization methods, among others, Runge-Kutta and linear multistep methods as well as operator splitting methods.Key features:* Presents a unified approach to examining discretization methods for parabolic equations.* Highlights a stability theory of discrete evolution equations (discrete semigroups) in Banach space.* Deals with both autonomous and non-autonomous equations as well as with equations with memory.* Offers a series of numerous well-posedness and convergence results for various discretization methods as applied to abstract parabolic equations; among others, Runge-Kutta and linear multistep methods as well as certain operator splitting methods.* Provides comments of results and historical remarks after each chapter.

  • Handbook of Knot Theory

    • 1st Edition
    • William Menasco + 1 more
    • English
    This book is a survey of current topics in the mathematical theory of knots. For a mathematician, a knot is a closed loop in 3-dimensional space: imagine knotting an extension cord and then closing it up by inserting its plug into its outlet. Knot theory is of central importance in pure and applied mathematics, as it stands at a crossroads of topology, combinatorics, algebra, mathematical physics and biochemistry.

  • Submodular Functions and Optimization

    • 2nd Edition
    • Volume 58
    • Satoru Fujishige
    • English
    It has widely been recognized that submodular functions play essential roles in efficiently solvable combinatorial optimization problems. Since the publication of the 1st edition of this book fifteen years ago, submodular functions have been showing further increasing importance in optimization, combinatorics, discrete mathematics, algorithmic computer science, and algorithmic economics, and there have been made remarkable developments of theory and algorithms in submodular functions. The 2nd edition of the book supplements the 1st edition with a lot of remarks and with new two chapters: "Submodular Function Minimization" and "Discrete Convex Analysis." The present 2nd edition is still a unique book on submodular functions, which is essential to students and researchers interested in combinatorial optimization, discrete mathematics, and discrete algorithms in the fields of mathematics, operations research, computer science, and economics.

  • Algorithmic Graph Theory and Perfect Graphs

    • 2nd Edition
    • Volume 57
    • Martin Charles Golumbic
    • English
    Algorithmic Graph Theory and Perfect Graphs, first published in 1980, has become the classic introduction to the field. This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems. It remains a stepping stone from which the reader may embark on one of many fascinating research trails. The past twenty years have been an amazingly fruitful period of research in algorithmic graph theory and structured families of graphs. Especially important have been the theory and applications of new intersection graph models such as generalizations of permutation graphs and interval graphs. These have lead to new families of perfect graphs and many algorithmic results. These are surveyed in the new Epilogue chapter in this second edition.

  • Discrete Optimization

    The State of the Art
    • 1st Edition
    • Volume 11
    • E. Boros + 1 more
    • English
    One of the most frequently occurring types of optimization problems involves decision variables which have to take integer values. From a practical point of view, such problems occur in countless areas of management, engineering, administration, etc., and include such problems as location of plants or warehouses, scheduling of aircraft, cutting raw materials to prescribed dimensions, design of computer chips, increasing reliability or capacity of networks, etc. This is the class of problems known in the professional literature as "discrete optimization" problems. While these problems are of enormous applicability, they present many challenges from a computational point of view. This volume is an update on the impressive progress achieved by mathematicians, operations researchers, and computer scientists in solving discrete optimization problems of very large sizes. The surveys in this volume present a comprehensive overview of the state of the art in discrete optimization and are written by the most prominent researchers from all over the world.This volume describes the tremendous progress in discrete optimization achieved in the last 20 years since the publication of Discrete Optimization '77, Annals of Discrete Mathematics, volumes 4 and 5, 1979 (Elsevier). It contains surveys of the state of the art written by the most prominent researchers in the field from all over the world, and covers topics like neighborhood search techniques, lift and project for mixed 0-1 programming, pseudo-Boolean optimization, scheduling and assignment problems, production planning, location, bin packing, cutting planes, vehicle routing, and applications to graph theory, mechanics, chip design, etc.Key features:• state of the art surveys• comprehensiveness• prominent authors• theoretical, computational and applied aspects.This book is a reprint of Discrete Applied Mathematics Volume 23, Numbers 1-3

  • Codes on Euclidean Spheres

    • 1st Edition
    • Volume 63
    • T. Ericson + 1 more
    • English
    Codes on Euclidean spheres are often referred to as spherical codes. They are of interest from mathematical, physical and engineering points of view. Mathematically the topic belongs to the realm of algebraic combinatorics, with close connections to number theory, geometry, combinatorial theory, and - of course - to algebraic coding theory. The connections to physics occur within areas like crystallography and nuclear physics. In engineering spherical codes are of central importance in connection with error-control in communication systems. In that context the use of spherical codes is often referred to as "coded modulation." The book offers a first complete treatment of the mathematical theory of codes on Euclidean spheres. Many new results are published here for the first time. Engineering applications are emphasized throughout the text. The theory is illustrated by many examples. The book also contains an extensive table of best known spherical codes in dimensions 3-24, including exact constructions.

  • Discrete Optimization I

    • 1st Edition
    • Volume 4
    • English

  • Handbook of Coding Theory

    Part 2: Connections, Part 3: Applications
    • 1st Edition
    • Volume II
    • Bozzano G Luisa
    • English
    The second volume of this work contains Parts 2 and 3 of the "Handbook of Coding Theory". Part 2, "Connections", is devoted to connections between coding theory and other branches of mathematics and computer science. Part 3, "Applications", deals with a variety of applications for coding.

  • Stream Ciphers and Number Theory

    • 1st Edition
    • Volume 55
    • T.W. Cusick + 2 more
    • English
    This book is almost entirely concerned with stream ciphers, concentrating on a particular mathematical model for such ciphers which are called additive natural stream ciphers. These ciphers use a natural sequence generator to produce a periodic keystream. Full definitions of these concepts are given in Chapter 2.This book focuses on keystream sequences which can be analysed using number theory. It turns out that a great deal of information can be deducted about the cryptographic properties of many classes of sequences by applying the terminology and theorems of number theory. These connections can be explicitly made by describing three kinds of bridges between stream ciphering problems and number theory problems. A detailed summary of these ideas is given in the introductory Chapter 1.Many results in the book are new, and over seventy percent of these results described in this book are based on recent research results.

  • Covering Codes

    • 1st Edition
    • Volume 54
    • G. Cohen + 3 more
    • English
    The problems of constructing covering codes and of estimating their parameters are the main concern of this book. It provides a unified account of the most recent theory of covering codes and shows how a number of mathematical and engineering issues are related to covering problems.Scientists involved in discrete mathematics, combinatorics, computer science, information theory, geometry, algebra or number theory will find the book of particular significance. It is designed both as an introductory textbook for the beginner and as a reference book for the expert mathematician and engineer.A number of unsolved problems suitable for research projects are also discussed.

  • Fractal Imaging

    • 1st Edition
    • Wei-Kao Lu
    • English
    Fractal image compression technology, one of the major digital image compression techniques, has been a well kept secret for many years. While there are many books written on other technologies, such as DCT/JPEG andwavelet theory, few books touch the subject of fractal image compression. Fractal Imaging presents the logic, technology, and various uses of fractal imaging by analyzing a complete, usable fractal image representation system. This detailed work will be a must for engineers interested in building fractal imaging systems. It will also be of interest to the general public, showing how mathematics once again plays a central role in our lives, where art and science intersect.

  • Linear Models

    A Mean Model Approach
    • 1st Edition
    • William R. Moser
    • English
    Linear models, normally presented in a highly theoretical and mathematical style, are brought down to earth in this comprehensive textbook. Linear Models examines the subject from a mean model perspective, defining simple and easy-to-learn rules for building mean models, regression models, mean vectors, covariance matrices and sums of squares matrices for balanced and unbalanced data sets. The author includes both applied and theoretical discussions of the multivariate normal distribution, quadratic forms, maximum likelihood estimation, less than full rank models, and general mixed models. The mean model is used to bring all of these topics together in a coherent presentation of linear model theory.

  • Decision and Discrete Mathematics

    Maths for Decision-Making in Business and Industry
    • 1st Edition
    • I Hardwick
    • English
    This text offers a complete coverage in the Decision Mathematics module, also known as Discrete Mathematics, of the syllabuses of English A-level examination boards. it is a rewritten and modern version of Decision Mathematics (published by Ellis Horwood Ltd in 1986 for The Spode Group, so well known for its development of innovative mathematics teaching). It is also a suitable text for foundation and first year undergraduate courses in qualitative studies or operational research, or for access courses for students needing strengthening in mathematics, or for students who are moving into mathematics from another subject discipline.Compact and concise, it reflects the combined teaching skills and experience of its authors who know exactly what mathematics must be learnt at the readership level today. The text is built up in modular fashion, explaining concepts used in decision mathematics and related operational research, and electronics. It emphasises an understanding of techniques and algorithms, which it relates to real life situations and working problems that will apply throughout future working careers.

  • Handbook of Combinatorics Volume 2

    • 1st Edition
    • Bozzano G Luisa
    • English

  • Handbook of Combinatorics

    • 1st Edition
    • R.L. Graham
    • English

  • Handbook of Combinatorics Volume 1

    • 1st Edition
    • Bozzano G Luisa
    • English
    Handbook of Combinatorics, Volume 1 focuses on basic methods, paradigms, results, issues, and trends across the broad spectrum of combinatorics. The selection first elaborates on the basic graph theory, connectivity and network flows, and matchings and extensions. Discussions focus on stable sets and claw free graphs, nonbipartite matching, multicommodity flows and disjoint paths, minimum cost circulations and flows, special proof techniques for paths and circuits, and Hamilton paths and circuits in digraphs. The manuscript then examines coloring, stable sets, and perfect graphs and embeddings and minors. The book takes a look at random graphs, hypergraphs, partially ordered sets, and matroids. Topics include geometric lattices, structural properties, linear extensions and correlation, dimension and posets of bounded degree, hypergraphs and set systems, stability, transversals, and matchings, and phase transition. The manuscript also reviews the combinatorial number theory, point lattices, convex polytopes and related complexes, and extremal problems in combinatorial geometry. The selection is a valuable reference for researchers interested in combinatorics.

  • Discrete Mathematics

    • 1st Edition
    • Amanda Chetwynd + 1 more
    • English
    As an introduction to discrete mathematics, this text provides a straightforward overview of the range of mathematical techniques available to students. Assuming very little prior knowledge, and with the minimum of technical complication, it gives an account of the foundations of modern mathematics: logic; sets; relations and functions. It then develops these ideas in the context of three particular topics: combinatorics (the mathematics of counting); probability (the mathematics of chance) and graph theory (the mathematics of connections in networks).Worked examples and graded exercises are used throughout to develop ideas and concepts. The format of this book is such that it can be easily used as the basis for a complete modular course in discrete mathematics.

  • Threshold Graphs and Related Topics

    • 1st Edition
    • Volume 56
    • N.V.R. Mahadev + 1 more
    • English
    Threshold graphs have a beautiful structure and possess many important mathematical properties. They have applications in many areas including computer science and psychology. Over the last 20 years the interest in threshold graphs has increased significantly, and the subject continues to attract much attention.The book contains many open problems and research ideas which will appeal to graduate students and researchers interested in graph theory. But above all Threshold Graphs and Related Topics provides a valuable source of information for all those working in this field.