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In recent years graph theory has emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. Robin Wilson's book has been widely used as a text for undergraduate course...s in mathematics, computer science and economics, and as a readable introduction to the subject for non-mathematicians. The opening chapters provide a basic foundation course, containing definitions and examples, connectedness, Eulerian and Hamiltonian paths and cycles, and trees, with a range of applications. This is followed by two chapters on planar graphs and colouring, with special reference to the four-colour theorem. The next chapter deals with transversal theory and connectivity, with applications to network flows. A final chapter on matroid theory ties together material from earlier chapters, and an appendix discusses algorithms and their efficiency.
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This self-contained text on discrete mathematics covers contemporary applications of discrete mathematics, including simulation, probabilistic algorithms, and public-key cryptography. Other topics discussed include logic and sets, relations and functions, number systems, counting... techniques, generating functions, algorithms, and basic simulations. The author includes exercises throughout the sections and at the end of each chapter to illustrate key concepts. He also provides solutions to the problems to ensure further understanding. Numerous supplementary topics are introduced in the appendices and exercise passages to allow for student projects.
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Finite geometry is an important, wide-ranging research area in mathematics with strong connections to algebra and combinatorics. This book introduces parallelisms and spreads. It covers topics such as partial spreads, spreadsets, quasifields, collineations, automorphisms and auto...topisms.
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This is the first book to provide an overview of combinatorial scientific computing (CSC). Bringing together a diverse group of researchers, it addresses many of the challenges faced in high-performance computing (HPC) by setting the stage for accelerated development and deployme...nt of fundamental enabling technologies in HPC. The text focuses on load balancing and parallelization on high-performance computers, large-scale optimization, automatic differentiation of numerical simulation code, and sparse matrix software tools. It also discusses key topics in CSC, important software tools, and special topics and applications.
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Graph partitioning is a theoretical subject with applications in many areas, principally: numerical analysis, programs mapping onto parallel architectures, image segmentation, VLSI design. During the last 40 years, the literature has strongly increased and big improvements have b...een made.
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This major revision of James Oxley's classic Matroid Theory provides a comprehensive introduction to the subject, covering the basics to more advanced topics. With over 700 exercises and proofs of all relevant major theorems, this book is the ideal reference and class text for ac...ademics and graduate students in mathematics and computer science.
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Filling the gap between introductory and encyclopedic treatments, this book provides rich and appealing material for a second course in combinatorial optimization. This book is suitable for graduate students as well as a reference for established researchers.
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In 1736, the mathematician Euler invented graph theory while solving the Konigsberg seven-bridge problem. This book introduces some basic knowledge and the primary methods in graph theory by many interesting problems and games.
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This book introduces the vast wealth of mathematical concepts and methods on which the Internet depends. It illustrates mathematical and algorithmic methods with examples from various fields to show the universality of the concepts presented. The authors provide complete discussi...ons of sequences, exponential growth, algorithms and complexity, randomness, graphs and networks, search engines, parallel and distributed computation, and cryptography. They also address cutting-edge topics, such as game theory, and include a short encyclopedic dictionary of terms related to the Internet.
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Introduces simplified multi-dimensional models of cubes and torus, which keep the character of the original general model, and introduces a combinatorial analysis for combinatorial modelings.
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