Combinatorial Algebraic Topology

Author: Dimitry Kozlov

Publisher: Springer Science & Business Media

ISBN: 9783540730514

Category: Mathematics

Page: 390

View: 8587

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.

Morse Theory

Smooth and Discrete

Author: Kevin P Knudson

Publisher: World Scientific Publishing Company

ISBN: 9814630985

Category: Mathematics

Page: 196

View: 8728

Morse Theory: Smooth and Discrete serves as an introduction to classical smooth Morse theory and to Forman's discrete Morse theory, highlighting the parallels between the two subjects. This is the first time both smooth and discrete Morse theory have been treated in a single volume. This makes the book a valuable resource for students and professionals working in topology and discrete mathematics. With a strong focus on examples, the text is suitable for advanced undergraduates or beginning graduate students.

Mathematical Reviews

Author: N.A

Publisher: N.A


Category: Mathematics

Page: N.A

View: 8159

Topology for Computing

Author: Afra J. Zomorodian

Publisher: Cambridge University Press

ISBN: 9781139442633

Category: Computers

Page: N.A

View: 453

The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.

Algorithms in Combinatorial Geometry

Author: Herbert Edelsbrunner

Publisher: Springer Science & Business Media

ISBN: 9783540137221

Category: Computers

Page: 423

View: 6228

This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems. Combinatorial investigations play an important role in this study.

Algorithmic and Combinatorial Algebra

Author: L.A. Bokut',G.P.. Kukin

Publisher: Springer Science & Business Media

ISBN: 9780792323136

Category: Computers

Page: 384

View: 1260

Even three decades ago, the words 'combinatorial algebra' contrasting, for in stance, the words 'combinatorial topology,' were not a common designation for some branch of mathematics. The collocation 'combinatorial group theory' seems to ap pear first as the title of the book by A. Karras, W. Magnus, and D. Solitar [182] and, later on, it served as the title of the book by R. C. Lyndon and P. Schupp [247]. Nowadays, specialists do not question the existence of 'combinatorial algebra' as a special algebraic activity. The activity is distinguished not only by its objects of research (that are effectively given to some extent) but also by its methods (ef fective to some extent). To be more exact, we could approximately define the term 'combinatorial algebra' for the purposes of this book, as follows: So we call a part of algebra dealing with groups, semi groups , associative algebras, Lie algebras, and other algebraic systems which are given by generators and defining relations {in the first and particular place, free groups, semigroups, algebras, etc. )j a part in which we study universal constructions, viz. free products, lINN-extensions, etc. j and, finally, a part where specific methods such as the Composition Method (in other words, the Diamond Lemma, see [49]) are applied. Surely, the above explanation is far from covering the full scope of the term (compare the prefaces to the books mentioned above).

Combinatorial and Computational Geometry

Author: Jacob E. Goodman,Janos Pach,Emo Welzl

Publisher: Cambridge University Press

ISBN: 9780521848626

Category: Computers

Page: 616

View: 9218

This 2005 book deals with interest topics in Discrete and Algorithmic aspects of Geometry.

Combinatorial and Computational Mathematics

Author: Sungpyo Hong,Jin Ho Kwah,Ki Hang Kim,Fred W Roush

Publisher: World Scientific

ISBN: 9814490687

Category: Mathematics

Page: 288

View: 4943

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. Contents:Monte-Carlo and Quasi-Monte-Carlo Methods for Numerical Integration (H Faure)Theoretical Approaches to Judgement and Choice (P Fishburn)Combinatorial Aspects of Mathematical Social Science (K H Kim & F W Roush)Twelve Views of Matroid Theory (J P S Kung)Enumeration of Graph Coverings, Surface Branched Coverings and Related Group Theory (J H Kwak & J Lee)An Overview of the Poset of Irreducibles (G Markowsky)Number Theory and Public-Key Cryptography (D Pointcheval)Some Applications of Graph Theory (F Roberts)Duality and Its Consequences for Ordered Cohomology of Finite Type Subshifts (K H Kim et al.)Simple Maximum Likelihood Methods for the Optical Mapping Problem (V Dancík & M S Waterman) Readership: Researchers, graduate students and advanced undergraduates in combinatorics and computational mathematics. Keywords:Combinatorics;Computation;Coding Theory;Number Theory;Lattice Theory;Graph Theory;Topological Techniques;Symbolic Dynamics;Mathematical Social Science

Computational Algebraic Geometry

Author: Hal Schenck

Publisher: Cambridge University Press

ISBN: 9780521536509

Category: Mathematics

Page: 193

View: 6354

This 2003 book investigates interplay between algebra and geometry. Covers: homological algebra, algebraic combinatorics and algebraic topology, and algebraic geometry.

Effective Computational Geometry for Curves and Surfaces

Author: Jean-Daniel Boissonnat,Monique Teillaud

Publisher: Springer Science & Business Media

ISBN: 3540332596

Category: Mathematics

Page: 344

View: 2337

This book covers combinatorial data structures and algorithms, algebraic issues in geometric computing, approximation of curves and surfaces, and computational topology. Each chapter fully details and provides a tutorial introduction to important concepts and results. The focus is on methods which are both well founded mathematically and efficient in practice. Coverage includes references to open source software and discussion of potential applications of the presented techniques.

Distributed Computing Through Combinatorial Topology

Author: Maurice Herlihy,Dmitry Kozlov,Sergio Rajsbaum

Publisher: Newnes

ISBN: 0124047289

Category: Computers

Page: 336

View: 5765

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

Foundations of Computational Mathematics, Minneapolis 2002

Author: Society for the Foundation of Computational Mathematics

Publisher: Cambridge University Press

ISBN: 9780521542531

Category: Mathematics

Page: 206

View: 6949

This volume, first published in 2004, contains the plenary invited talks given at main conference in the subject.

Algebra and Algebraic Topology

Author: Ched E. Stedman

Publisher: Nova Publishers

ISBN: 9781600211874

Category: Mathematics

Page: 159

View: 2245

Gathers results in pure and applied algebra, including algebraic topology from researchers around the globe.

Computational Homology

Author: Tomasz Kaczynski,Konstantin Mischaikow,Marian Mrozek

Publisher: Springer Science & Business Media

ISBN: 0387215972

Category: Mathematics

Page: 482

View: 7905

Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.

Algorithmic and Quantitative Real Algebraic Geometry

DIMACS Workshop, Algorithmic and Quantitative Aspects of Real Algebraic, Geometry in Mathematics and Computer Science, March 12-16, 2001, DIMACS Center

Author: Saugata Basu,Laureano González-Vega

Publisher: American Mathematical Soc.

ISBN: 9780821871027

Category: Mathematics

Page: 219

View: 9588

Algorithmic and quantitative aspects in real algebraic geometry are becoming increasingly important areas of research because of their roles in other areas of mathematics and computer science. The papers in this volume collectively span several different areas of current research. The articles are based on talks given at the DIMACS Workshop on ''Algorithmic and Quantitative Aspects of Real Algebraic Geometry''. Topics include deciding basic algebraic properties of real semi-algebraic sets, application of quantitative results in real algebraic geometry towards investigating the computational complexity of various problems, algorithmic and quantitative questions in real enumerative geometry, new approaches towards solving decision problems in semi-algebraic geometry, as well as computing algebraic certificates, and applications of real algebraic geometry to concrete problems arising in robotics and computer graphics. The book is intended for researchers interested in computational methods in algebra.

Algorithms in Real Algebraic Geometry

Author: Saugata Basu,Richard Pollack,Marie-Françoise Roy

Publisher: Springer Science & Business Media

ISBN: 9783540009733

Category: Mathematics

Page: 602

View: 449

This is the first graduate textbook on the algorithmic aspects of real algebraic geometry. The main ideas and techniques presented form a coherent and rich body of knowledge. Mathematicians will find relevant information about the algorithmic aspects.

Computer Algebra Handbook

Foundations · Applications · Systems

Author: Johannes Grabmeier,Erich Kaltofen,Volker Weispfenning

Publisher: Springer Science & Business Media

ISBN: 3642558267

Category: Computers

Page: 637

View: 1944

This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.

Graph Algorithms in the Language of Linear Algebra

Author: Jeremy Kepner,John Gilbert

Publisher: SIAM

ISBN: 0898719909

Category: Mathematics

Page: 375

View: 5007

An introduction to graph algorithms accessible to those without a computer science background.

Solving Polynomial Equations

Foundations, Algorithms, and Applications

Author: Alicia Dickenstein,Ioannis Z Emiris

Publisher: Springer Science & Business Media

ISBN: 3540273573

Category: Mathematics

Page: 426

View: 6966

The subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in di?erent branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems.