Classical Topology and Combinatorial Group Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer US
1980
|
| 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 Konigsberg, 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 reason 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 mathematicscomplex analysis (Riemann), mechanics (poincare), and group theory (Oehn). It is these connections to other parts of mathematics which make topology an important as well as a beautiful subject |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9781468401103 9781468401127 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4684-0110-3 |
Internformat
MARC
| LEADER | 00000nmm a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042421002 | ||
| 003 | DE-604 | ||
| 005 | 20210216 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1980 |||| o||u| ||||||eng d | ||
| 020 | |a 9781468401103 |c Online |9 978-1-4684-0110-3 | ||
| 020 | |a 9781468401127 |c Print |9 978-1-4684-0112-7 | ||
| 024 | 7 | |a 10.1007/978-1-4684-0110-3 |2 doi | |
| 035 | |a (OCoLC)863873595 | ||
| 035 | |a (DE-599)BVBBV042421002 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 514 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Stillwell, John |d 1942- |e Verfasser |0 (DE-588)128427264 |4 aut | |
| 245 | 1 | 0 | |a Classical Topology and Combinatorial Group Theory |c by John Stillwell |
| 264 | 1 | |a New York, NY |b Springer US |c 1980 | |
| 300 | |a 1 Online-Ressource | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a Graduate Texts in Mathematics |v 72 |x 0072-5285 | |
| 500 | |a In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, 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 reason 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 mathematicscomplex analysis (Riemann), mechanics (poincare), and group theory (Oehn). It is these connections to other parts of mathematics which make topology an important as well as a beautiful subject | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Group theory | |
| 650 | 4 | |a Topology | |
| 650 | 4 | |a Group Theory and Generalizations | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Kombinatorische Topologie |0 (DE-588)4137530-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kombinatorische Gruppentheorie |0 (DE-588)4219556-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kombinatorik |0 (DE-588)4031824-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Topologie |0 (DE-588)4060425-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gruppentheorie |0 (DE-588)4072157-7 |2 gnd |9 rswk-swf |
| 655 | 7 | |8 1\p |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Topologie |0 (DE-588)4060425-1 |D s |
| 689 | 0 | 1 | |a Gruppentheorie |0 (DE-588)4072157-7 |D s |
| 689 | 0 | 2 | |a Kombinatorik |0 (DE-588)4031824-2 |D s |
| 689 | 0 | |8 2\p |5 DE-604 | |
| 689 | 1 | 0 | |a Kombinatorische Gruppentheorie |0 (DE-588)4219556-1 |D s |
| 689 | 1 | 1 | |a Topologie |0 (DE-588)4060425-1 |D s |
| 689 | 1 | |8 3\p |5 DE-604 | |
| 689 | 2 | 0 | |a Kombinatorische Topologie |0 (DE-588)4137530-0 |D s |
| 689 | 2 | |8 4\p |5 DE-604 | |
| 830 | 0 | |a Graduate Texts in Mathematics |v 72 |w (DE-604)BV035421258 |9 72 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4684-0110-3 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027856419 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 3\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 4\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153093564137472 |
|---|---|
| any_adam_object | |
| author | Stillwell, John 1942- |
| author_GND | (DE-588)128427264 |
| author_facet | Stillwell, John 1942- |
| author_role | aut |
| author_sort | Stillwell, John 1942- |
| author_variant | j s js |
| building | Verbundindex |
| bvnumber | BV042421002 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863873595 (DE-599)BVBBV042421002 |
| dewey-full | 514 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514 |
| dewey-search | 514 |
| dewey-sort | 3514 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4684-0110-3 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>04104nmm a2200661zcb4500</leader><controlfield tag="001">BV042421002</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210216 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1980 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781468401103</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4684-0110-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781468401127</subfield><subfield code="c">Print</subfield><subfield code="9">978-1-4684-0112-7</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4684-0110-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863873595</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042421002</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">514</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Stillwell, John</subfield><subfield code="d">1942-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)128427264</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Classical Topology and Combinatorial Group Theory</subfield><subfield code="c">by John Stillwell</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY</subfield><subfield code="b">Springer US</subfield><subfield code="c">1980</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Graduate Texts in Mathematics</subfield><subfield code="v">72</subfield><subfield code="x">0072-5285</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, 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 reason 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 mathematicscomplex analysis (Riemann), mechanics (poincare), and group theory (Oehn). It is these connections to other parts of mathematics which make topology an important as well as a beautiful subject</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Group theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Topology</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Group Theory and Generalizations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kombinatorische Topologie</subfield><subfield code="0">(DE-588)4137530-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kombinatorische Gruppentheorie</subfield><subfield code="0">(DE-588)4219556-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kombinatorik</subfield><subfield code="0">(DE-588)4031824-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Topologie</subfield><subfield code="0">(DE-588)4060425-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Gruppentheorie</subfield><subfield code="0">(DE-588)4072157-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="8">1\p</subfield><subfield code="0">(DE-588)4123623-3</subfield><subfield code="a">Lehrbuch</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Topologie</subfield><subfield code="0">(DE-588)4060425-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Gruppentheorie</subfield><subfield code="0">(DE-588)4072157-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Kombinatorik</subfield><subfield code="0">(DE-588)4031824-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Kombinatorische Gruppentheorie</subfield><subfield code="0">(DE-588)4219556-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Topologie</subfield><subfield code="0">(DE-588)4060425-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">3\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Kombinatorische Topologie</subfield><subfield code="0">(DE-588)4137530-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">4\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Graduate Texts in Mathematics</subfield><subfield code="v">72</subfield><subfield code="w">(DE-604)BV035421258</subfield><subfield code="9">72</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4684-0110-3</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027856419</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">3\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">4\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV042421002 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781468401103 9781468401127 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856419 |
| oclc_num | 863873595 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Springer US |
| record_format | marc |
| series | Graduate Texts in Mathematics |
| series2 | Graduate Texts in Mathematics |
| spelling | Stillwell, John 1942- Verfasser (DE-588)128427264 aut Classical Topology and Combinatorial Group Theory by John Stillwell New York, NY Springer US 1980 1 Online-Ressource 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 Konigsberg, 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 reason 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 mathematicscomplex analysis (Riemann), mechanics (poincare), and group theory (Oehn). It is these connections to other parts of mathematics which make topology an important as well as a beautiful subject Mathematics Group theory Topology Group Theory and Generalizations Mathematik Kombinatorische Topologie (DE-588)4137530-0 gnd rswk-swf Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Topologie (DE-588)4060425-1 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 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/10.1007/978-1-4684-0110-3 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 1942- Classical Topology and Combinatorial Group Theory Graduate Texts in Mathematics Mathematics Group theory Topology Group Theory and Generalizations Mathematik Kombinatorische Topologie (DE-588)4137530-0 gnd Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd Kombinatorik (DE-588)4031824-2 gnd Topologie (DE-588)4060425-1 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4137530-0 (DE-588)4219556-1 (DE-588)4031824-2 (DE-588)4060425-1 (DE-588)4072157-7 (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 Group theory Topology Group Theory and Generalizations Mathematik Kombinatorische Topologie (DE-588)4137530-0 gnd Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd Kombinatorik (DE-588)4031824-2 gnd Topologie (DE-588)4060425-1 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Mathematics Group theory Topology Group Theory and Generalizations Mathematik Kombinatorische Topologie Kombinatorische Gruppentheorie Kombinatorik Topologie Gruppentheorie Lehrbuch |
| url | https://doi.org/10.1007/978-1-4684-0110-3 |
| volume_link | (DE-604)BV035421258 |
| work_keys_str_mv | AT stillwelljohn classicaltopologyandcombinatorialgrouptheory |