Geometry and topology:
Geometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. This book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples. The treatment emphas...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2005
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| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 URL des Erstveröffentlichers |
| Zusammenfassung: | Geometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. This book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples. The treatment emphasises coordinate systems and the coordinate changes that generate symmetries. The discussion moves from Euclidean to non-Euclidean geometries, including spherical and hyperbolic geometry, and then on to affine and projective linear geometries. Group theory is introduced to treat geometric symmetries, leading to the unification of geometry and group theory in the Erlangen program. An introduction to basic topology follows, with the Möbius strip, the Klein bottle and the surface with g handles exemplifying quotient topologies and the homeomorphism problem. Topology combines with group theory to yield the geometry of transformation groups,having applications to relativity theory and quantum mechanics. A final chapter features historical discussions and indications for further reading. With minimal prerequisites, the book provides a first glimpse of many research topics in modern algebra, geometry and theoretical physics. The book is based on many years' teaching experience, and is thoroughly class-tested. There are copious illustrations, and each chapter ends with a wide supply of exercises. Further teaching material is available for teachers via the web, including assignable problem sheets with solutions |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xviii, 196 pages) |
| ISBN: | 9780511807510 |
| DOI: | 10.1017/CBO9780511807510 |
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| 520 | |a Geometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. This book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples. The treatment emphasises coordinate systems and the coordinate changes that generate symmetries. The discussion moves from Euclidean to non-Euclidean geometries, including spherical and hyperbolic geometry, and then on to affine and projective linear geometries. Group theory is introduced to treat geometric symmetries, leading to the unification of geometry and group theory in the Erlangen program. An introduction to basic topology follows, with the Möbius strip, the Klein bottle and the surface with g handles exemplifying quotient topologies and the homeomorphism problem. Topology combines with group theory to yield the geometry of transformation groups,having applications to relativity theory and quantum mechanics. A final chapter features historical discussions and indications for further reading. With minimal prerequisites, the book provides a first glimpse of many research topics in modern algebra, geometry and theoretical physics. The book is based on many years' teaching experience, and is thoroughly class-tested. There are copious illustrations, and each chapter ends with a wide supply of exercises. Further teaching material is available for teachers via the web, including assignable problem sheets with solutions | ||
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Datensatz im Suchindex
| _version_ | 1804176886784327680 |
|---|---|
| any_adam_object | |
| author | Reid, Miles |
| author_facet | Reid, Miles |
| author_role | aut |
| author_sort | Reid, Miles |
| author_variant | m r mr |
| building | Verbundindex |
| bvnumber | BV043943155 |
| classification_rvk | SK 280 SK 340 SK 370 SK 380 |
| collection | ZDB-20-CBO |
| ctrlnum | (ZDB-20-CBO)CR9780511807510 (OCoLC)850742714 (DE-599)BVBBV043943155 |
| dewey-full | 516 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516 |
| dewey-search | 516 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511807510 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T07:39:19Z |
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| isbn | 9780511807510 |
| language | English |
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| spelling | Reid, Miles Verfasser aut Geometry and topology Miles Reid, Balázs Szendrői Geometry & Topology Cambridge Cambridge University Press 2005 1 online resource (xviii, 196 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) Geometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. This book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples. The treatment emphasises coordinate systems and the coordinate changes that generate symmetries. The discussion moves from Euclidean to non-Euclidean geometries, including spherical and hyperbolic geometry, and then on to affine and projective linear geometries. Group theory is introduced to treat geometric symmetries, leading to the unification of geometry and group theory in the Erlangen program. An introduction to basic topology follows, with the Möbius strip, the Klein bottle and the surface with g handles exemplifying quotient topologies and the homeomorphism problem. Topology combines with group theory to yield the geometry of transformation groups,having applications to relativity theory and quantum mechanics. A final chapter features historical discussions and indications for further reading. With minimal prerequisites, the book provides a first glimpse of many research topics in modern algebra, geometry and theoretical physics. The book is based on many years' teaching experience, and is thoroughly class-tested. There are copious illustrations, and each chapter ends with a wide supply of exercises. Further teaching material is available for teachers via the web, including assignable problem sheets with solutions Geometry Topology Topologie (DE-588)4060425-1 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Topologie (DE-588)4060425-1 s 2\p DE-604 Geometrie (DE-588)4020236-7 s 3\p DE-604 Szendrői, Balázs Sonstige oth Erscheint auch als Druckausgabe 978-0-521-61325-5 Erscheint auch als Druckausgabe 978-0-521-84889-3 https://doi.org/10.1017/CBO9780511807510 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Reid, Miles Geometry and topology Geometry Topology Topologie (DE-588)4060425-1 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4060425-1 (DE-588)4020236-7 (DE-588)4123623-3 |
| title | Geometry and topology |
| title_alt | Geometry & Topology |
| title_auth | Geometry and topology |
| title_exact_search | Geometry and topology |
| title_full | Geometry and topology Miles Reid, Balázs Szendrői |
| title_fullStr | Geometry and topology Miles Reid, Balázs Szendrői |
| title_full_unstemmed | Geometry and topology Miles Reid, Balázs Szendrői |
| title_short | Geometry and topology |
| title_sort | geometry and topology |
| topic | Geometry Topology Topologie (DE-588)4060425-1 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Geometry Topology Topologie Geometrie Lehrbuch |
| url | https://doi.org/10.1017/CBO9780511807510 |
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