Classical Topology and Combinatorial Group Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1993
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Graduate Texts in Mathematics
72 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Königsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does not understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the visualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connections to other parts of mathematics which make topology an important as well as a beautiful subject |
| Beschreibung: | 1 Online-Ressource (XII, 336 p) |
| ISBN: | 9781461243724 9780387979700 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-4372-4 |
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Datensatz im Suchindex
| _version_ | 1804153092011196416 |
|---|---|
| any_adam_object | |
| author | Stillwell, John |
| author_facet | Stillwell, John |
| author_role | aut |
| author_sort | Stillwell, John |
| author_variant | j s js |
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512.482 512.55 |
| dewey-sort | 3512.482 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-4372-4 |
| edition | Second Edition |
| format | Electronic eBook |
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| isbn | 9781461243724 9780387979700 |
| issn | 0072-5285 |
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| spelling | Stillwell, John Verfasser aut Classical Topology and Combinatorial Group Theory by John Stillwell Second Edition New York, NY Springer New York 1993 1 Online-Ressource (XII, 336 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 72 0072-5285 In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Königsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does not understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the visualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connections to other parts of mathematics which make topology an important as well as a beautiful subject Mathematics Topological Groups Topology Topological Groups, Lie Groups Mathematik Kombinatorik (DE-588)4031824-2 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Kombinatorische Topologie (DE-588)4137530-0 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Topologie (DE-588)4060425-1 s Gruppentheorie (DE-588)4072157-7 s Kombinatorik (DE-588)4031824-2 s 2\p DE-604 Kombinatorische Gruppentheorie (DE-588)4219556-1 s 3\p DE-604 Kombinatorische Topologie (DE-588)4137530-0 s 4\p DE-604 Graduate Texts in Mathematics 72 (DE-604)BV035421258 72 https://doi.org/10.1007/978-1-4612-4372-4 Verlag 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 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Stillwell, John Classical Topology and Combinatorial Group Theory Graduate Texts in Mathematics Mathematics Topological Groups Topology Topological Groups, Lie Groups Mathematik Kombinatorik (DE-588)4031824-2 gnd Gruppentheorie (DE-588)4072157-7 gnd Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd Topologie (DE-588)4060425-1 gnd Kombinatorische Topologie (DE-588)4137530-0 gnd |
| subject_GND | (DE-588)4031824-2 (DE-588)4072157-7 (DE-588)4219556-1 (DE-588)4060425-1 (DE-588)4137530-0 (DE-588)4123623-3 |
| title | Classical Topology and Combinatorial Group Theory |
| title_auth | Classical Topology and Combinatorial Group Theory |
| title_exact_search | Classical Topology and Combinatorial Group Theory |
| title_full | Classical Topology and Combinatorial Group Theory by John Stillwell |
| title_fullStr | Classical Topology and Combinatorial Group Theory by John Stillwell |
| title_full_unstemmed | Classical Topology and Combinatorial Group Theory by John Stillwell |
| title_short | Classical Topology and Combinatorial Group Theory |
| title_sort | classical topology and combinatorial group theory |
| topic | Mathematics Topological Groups Topology Topological Groups, Lie Groups Mathematik Kombinatorik (DE-588)4031824-2 gnd Gruppentheorie (DE-588)4072157-7 gnd Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd Topologie (DE-588)4060425-1 gnd Kombinatorische Topologie (DE-588)4137530-0 gnd |
| topic_facet | Mathematics Topological Groups Topology Topological Groups, Lie Groups Mathematik Kombinatorik Gruppentheorie Kombinatorische Gruppentheorie Topologie Kombinatorische Topologie Lehrbuch |
| url | https://doi.org/10.1007/978-1-4612-4372-4 |
| volume_link | (DE-604)BV035421258 |
| work_keys_str_mv | AT stillwelljohn classicaltopologyandcombinatorialgrouptheory |