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This book describes and summarizes past work in important areas of combinatorics and computation, as well as gives directions for researchers working in these areas in the 21st century. It contains primarily survey papers and presents original research by Peter Fishburn, Jim Ho Kwak, Jaeun Lee, K H Kim, F W Roush and Susan Williams. The papers deal with some of the most exciting and promising developments in the areas of coding theory in relation to number theory, lattice theory and its applications, graph theory and its applications, topological techniques in combinatorics, symbolic dynamics and mathematical social science.
This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.
Algebraic and Combinatorial Computational Biology introduces students and researchers to a panorama of powerful and current methods for mathematical problem-solving in modern computational biology. Presented in a modular format, each topic introduces the biological foundations of the field, covers specialized mathematical theory, and concludes by highlighting connections with ongoing research, particularly open questions. The work addresses problems from gene regulation, neuroscience, phylogenetics, molecular networks, assembly and folding of biomolecular structures, and the use of clustering methods in biology. A number of these chapters are surveys of new topics that have not been previously compiled into one unified source. These topics were selected because they highlight the use of technique from algebra and combinatorics that are becoming mainstream in the life sciences. - Integrates a comprehensive selection of tools from computational biology into educational or research programs - Emphasizes practical problem-solving through multiple exercises, projects and spinoff computational simulations - Contains scalable material for use in undergraduate and graduate-level classes and research projects - Introduces the reader to freely-available professional software - Supported by illustrative datasets and adaptable computer code
This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.
This book was first published in 2003. Combinatorica, an extension to the popular computer algebra system Mathematica®, is the most comprehensive software available for teaching and research applications of discrete mathematics, particularly combinatorics and graph theory. This book is the definitive reference/user's guide to Combinatorica, with examples of all 450 Combinatorica functions in action, along with the associated mathematical and algorithmic theory. The authors cover classical and advanced topics on the most important combinatorial objects: permutations, subsets, partitions, and Young tableaux, as well as all important areas of graph theory: graph construction operations, invariants, embeddings, and algorithmic graph theory. In addition to being a research tool, Combinatorica makes discrete mathematics accessible in new and exciting ways to a wide variety of people, by encouraging computational experimentation and visualization. The book contains no formal proofs, but enough discussion to understand and appreciate all the algorithms and theorems it contains.
This book describes algorithms of mathematical methods and illustrates their application with examples. The mathematical background needed is elementary algebra and calculus.
This is the most readable and thorough graduate textbook and reference for combinatorics, covering enumeration, graphs, sets, and methods.
This combinatorics text 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. It presents the computer and software algorithms in pseudo-code and incorporates definitions, theorems, proofs, examples, and nearly 300 illustrations as pedagogical elements of the exposition. Numerous problems, solutions, and hints reinforce basic skills and assist with creative problem solving. The author also offers a website with extensive graph theory informational resources as well as a computational engine to help with calculations for some of the exercises.
The book is an introduction to the theory of convex polytopes and polyhedral sets, to algebraic geometry, and to the connections between these fields, known as the theory of toric varieties. The first part of the book covers the theory of polytopes and provides large parts of the mathematical background of linear optimization and of the geometrical aspects in computer science. The second part introduces toric varieties in an elementary way.
Distributed Computing Through Combinatorial Topology describes techniques for analyzing distributed algorithms based on award winning combinatorial topology research. The authors present a solid theoretical foundation relevant to many real systems reliant on parallelism with unpredictable delays, such as multicore microprocessors, wireless networks, distributed systems, and Internet protocols. Today, a new student or researcher must assemble a collection of scattered conference publications, which are typically terse and commonly use different notations and terminologies. This book provides a self-contained explanation of the mathematics to readers with computer science backgrounds, as well as explaining computer science concepts to readers with backgrounds in applied mathematics. The first section presents mathematical notions and models, including message passing and shared-memory systems, failures, and timing models. The next section presents core concepts in two chapters each: first, proving a simple result that lends itself to examples and pictures that will build up readers' intuition; then generalizing the concept to prove a more sophisticated result. The overall result weaves together and develops the basic concepts of the field, presenting them in a gradual and intuitively appealing way. The book's final section discusses advanced topics typically found in a graduate-level course for those who wish to explore further. - Named a 2013 Notable Computer Book for Computing Methodologies by Computing Reviews - Gathers knowledge otherwise spread across research and conference papers using consistent notations and a standard approach to facilitate understanding - Presents unique insights applicable to multiple computing fields, including multicore microprocessors, wireless networks, distributed systems, and Internet protocols - Synthesizes and distills material into a simple, unified presentation with examples, illustrations, and exercises