Topology with applications
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Topology with applications

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Published by János Bolyai Mathematical Society in Budapest, Hungary .
Written in English

Subjects:

  • Topology -- Congresses.

Book details:

Edition Notes

Statementedited by A. Császár.
GenreCongresses.
SeriesBolyai Society mathematical studies -- 4
ContributionsCsáczár, Akos., Bolyai János Matematikai Társulat., Colloquium on Topology (7th : 1993 : Szekszárd, Hungary)
Classifications
LC ClassificationsQA611.A1 C64 1993
The Physical Object
Pagination465 p. :
Number of Pages465
ID Numbers
Open LibraryOL22245063M
ISBN 109638022841

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Topology, as a well-defined mathematical discipline, originates in the early part of the twentieth century, but some isolated results can be traced back several centuries. Among these are certain questions in geometry investigated by Leonhard lfcmalta.com paper on the Seven Bridges of Königsberg is regarded as one of the first practical applications of topology. Topology plays a huge role in contemporary condensed matter physics, and many top-notch researchers have made a career of ite.g. Xiao-Liang Qi at Stanford. There are more applications of topology to condensed matter physics than I can begin to enumerate (the above linked page names several), but I'll highlight two: Dislocations in crystals. This note covers the following topics: Background in set theory, Topology, Connected spaces, Compact spaces, Metric spaces, Normal spaces, Algebraic topology and homotopy theory, Categories and paths, Path lifting and covering spaces, Global topology: applications, Quotients, gluing and simplicial complexes, Galois theory of covering spaces. A Concise Course in Algebraic Topology. University of Chicago Press, [$18] — Good for getting the big picture. Perhaps not as easy for a beginner as the preceding book. • G E Bredon. Topology and Geometry. Springer GTM , [$70] — Includes basics on smooth manifolds, and even some point-set topology.

both the mathematics and the applications are taught side-by-side. this text is densely illustrated and suitable for self-study or as part of a course. pdf chapters are available for free for personal use: do not distribute! this is a self-published book, using amazon's createspace for print-on-demand. Brings Readers Up to Speed in This Important and Rapidly Growing Area Supported by many examples in mathematics, physics, economics, engineering, and other disciplines, Essentials of Topology with Applications provides a clear, insightful, and thorough introduction to the basics of modern topology. This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. This book presents three topology optimization methods together with examples and explanations of how topology optimization is a powerful tool for the design of structures. It also includes three software tools which allow the reader to try for themselves the three presented topology optimization methods.