David Jordan: A Topological Aperitif

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Cover: 9781848009127 | A Topological Aperitif | David Jordan (u. a.) | Taschenbuch | Englisch

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Sprache: Englisch

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Beschreibung

Topologyhasbeenreferredtoas¿rubber-sheetgeometry¿.Thenameisapt,for the subject is concerned with properties of an object that would be preserved, no matter how much it is stretched, squashed, or distorted, so long as it is not in any way torn apart or glued together. One¿s ?rst reaction might be that such animprecise-soundingsubjectcouldhardlybepartofseriousmathematics,and wouldbeunlikelytohaveapplicationsbeyondtheamusementofsimpleparlour games. This reaction could hardly be further from the truth. Topology is one of the most important and broad-ranging disciplines of modern mathematics. It is a subject of great precision and of breadth of development. It has vastly many applications, some of great importance, ranging from particle physics to cosmology, and from hydrodynamics to algebra and number theory. It is also a subject of great beauty and depth. To appreciate something of this, it is not necessary to delve into the more obscure aspects of mathematical formalism. For topology is, at least initially, a very visual subject. Some of its concepts apply to spaces of large numbers of dimensions, and therefore do not easily submit to reasoning that depends upon direct pictorial representation. But even in such cases, important insights can be obtained from the visual - rusal of a simple geometrical con?guration. Although much modern topology depends upon ?nely tuned abstract algebraic machinery of great mathematical sophistication, the underlying ideas are often very simple and can be appre- ated by the examination of properties of elementary-looking drawings.

Zusammenfassung

Takes a new approach to the subject by choosing a geometrical rather than an algebraic or combinatorial approach

Contains many examples to develop the student's grasp of the subject and their ability to produce rigorous arguments

Includes a foreword written by Roger Penrose

Co-written by Stephen Huggett who gave the LMS Popular Lecture, "Knots", in 2007 which is available on DVD through the LMS Popular Lecture series

Includes supplementary material: [...]

Inhaltsverzeichnis

Foreword (written by Roger Penrose).- Homeomorphic Sets.- Topological Properties.- Equivalent Subsets.- Surfaces and Spaces.- Polyhedra.- Winding Number.- Appendix A: Continuity.- Appendix B: Knots.- Appendix C: History.- Appendix D: Solutions.- Bibliography.- Index.

Details

Erscheinungsjahr:	2009
Fachbereich:	Topologie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Seiten:	164
Inhalt:	ix 152 S. 135 s/w Illustr. 152 p. 135 illus.
ISBN-13:	9781848009127
ISBN-10:	1848009127
Sprache:	Englisch
Herstellernummer:	12457427
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Jordan, David Huggett, Stephen
Auflage:	2nd ed. 2009
Hersteller:	Springer London
Maße:	235 x 178 x 10 mm
Von/Mit:	David Jordan (u. a.)
Erscheinungsdatum:	26.03.2009
Gewicht:	0,298 kg

preigu-id: 101751246