Algorithmic and Computer Methods for Three-Manifolds
Algorithmic and Computer Methods for Three-Manifolds

Author: A.T. Fomenko

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 343

ISBN-13: 9401706999

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One service mathematics has rendered the human race. It has put common sense back where it belongs. It has put common sense back where it belongs, on the topmost shelf next to the dusty canister labelled discarded nonsense. Eric TBell Every picture tells a story. Advenisement for for Sloan's backache and kidney oils, 1907 The book you have in your hands as you are reading this, is a text on3-dimensional topology. It can serve as a pretty comprehensive text book on the subject. On the other hand, it frequently gets to the frontiers of current research in the topic. If pressed, I would initially classify it as a monograph, but, thanks to the over three hundred illustrations of the geometrical ideas involved, as a rather accessible one, and hence suitable for advanced classes. The style is somewhat informal; more or less like orally presented lectures, and the illustrations more than make up for all the visual aids and handwaving one has at one's command during an actual presentation.

Algorithmic Topology and Classification of 3-Manifolds
Algorithmic Topology and Classification of 3-Manifolds

Author: Sergei Matveev

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 487

ISBN-13: 3662051028

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Here is a thorough review of topics in 3-dimensional topology, derived from a decade of courses taught by the author. The author keeps the exposition to an elementary level by presenting the material mainly from the point of view of special polyhedra and special spines of 3-manifolds. The book culminates with the recognition procedure for Haken manifolds, and includes up-to-date results in computer enumeration of 3-mainfolds. The second edition adds new results, new proofs, and commentaries. Algorithmic Topology and Classification of 3-Manifolds serves as a standard reference for algorithmic 3-dimensional topology for both graduate students and researchers.

Discrete Geometry for Computer Imagery
Discrete Geometry for Computer Imagery

Author: Gunilla Borgefors

Publisher: Springer

Published: 2003-06-29

Total Pages: 544

ISBN-13: 3540444386

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This book constitutes the refereed proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery, DGCI 2000, held in Uppsala, Sweden in December 2000. The 40 revised papers presented together with two invited papers were carefully reviewed and selected from 62 submissions. The papers are organized in topical sections on topology, discrete images, surfaces and volumes, shape representation, and shape understanding.

Knots, Links, Braids and 3-Manifolds
Knots, Links, Braids and 3-Manifolds

Author: Viktor Vasilʹevich Prasolov

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 250

ISBN-13: 0821808982

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This book is an introduction to the remarkable work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its recent modifications and generalizations, including a mathematical treatment of Jones-Witten invariants. The mathematical prerequisites are minimal compared to other monographs in this area. Numerous figures and problems make this book suitable as a graduate level course text or for self-study.

GPU Ray Tracing in Non-Euclidean Spaces
GPU Ray Tracing in Non-Euclidean Spaces

Author: Tiago Novello

Publisher: Morgan & Claypool Publishers

Published: 2022-03-21

Total Pages: 129

ISBN-13: 1636393276

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This book explores the visualization of three-dimensional non-Euclidean spaces using raytracing techniques in Graphics Processing Unit (GPU). This is a trending topic in mathematical visualization that combines the mathematics areas of geometry and topology, with visualization concepts of computer graphics. Several conditions made this a special moment for such topic. On one hand, the development of mathematical research, computer graphics, and algorithms have provided the necessary theoretical framework. On the other hand, the evolution of the technologies and media allows us to be immersed in three-dimensional spaces using Virtual Reality. The content of this book serves both experts in the areas and students. Although this is a short book, it is self-contained since it considers all the ideas, motivations, references, and intuitive explanations of the required fundamental concepts.

Computing and Combinatorics
Computing and Combinatorics

Author: Oscar H. Ibarra

Publisher: Springer

Published: 2003-08-02

Total Pages: 619

ISBN-13: 3540456554

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This book constitutes the refereed proceedings of the 8th Annual International Computing and Combinatorics Conference, COCOON 2002, held in Singapore in August 2002. The 60 revised full papers presented together with three invited contributions were carefully reviewed and selected from 106 submissions. The papers are organized in topical sections on complexity theory, discrete algorithms, computational biology and learning theory, radio networks, automata and formal languages, Internet networks, computational geometry, combinatorial optimization, and quantum computing.

History: fiction or science?. Chronology 1
History: fiction or science?. Chronology 1

Author: A. T. Fomenko

Publisher: Mithec

Published: 2006

Total Pages: 634

ISBN-13: 2913621074

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The author contends that all generaly accepted historical chronology prior to the 16th century is inaccurate, often off by many hundreds or even thousands of years. Volume 1 of a proposed seven volumes.

Knot Theory
Knot Theory

Author: Vassily Olegovich Manturov

Publisher: CRC Press

Published: 2018-04-17

Total Pages: 507

ISBN-13: 1351359126

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Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A-polynomial which give rise to strong invariants of knots and 3-manifolds, in particular, many new unknot detectors. New to this Edition is a discussion of Heegaard-Floer homology theory and A-polynomial of classical links, as well as updates throughout the text. Knot Theory, Second Edition is notable not only for its expert presentation of knot theory’s state of the art but also for its accessibility. It is valuable as a profes-sional reference and will serve equally well as a text for a course on knot theory.