Geometry of Surfaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1992
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Geometry used to be the basis of a mathematical education; today it is not even a standard undergraduate topic. Much as I deplore this situation, I welcome the opportunity to make a fresh start. Classical geometry is no longer an adequate basis for mathematics or physics-both of which are becoming increasingly geometric-and geometry can no longer be divorced from algebra, topology, and analysis. Students need a geometry of greater scope, and the fact that there is no room for geometry in the curriculum un til the third or fourth year at least allows us to assume some mathematical background. What geometry should be taught? I believe that the geometry of surfaces of constant curvature is an ideal choice, for the following reasons: 1. It is basically simple and traditional. We are not forgetting euclidean geometry but extending it enough to be interesting and useful. The extensions offer the simplest possible introduction to fundamentals of modem geometry: curvature, group actions, and covering spaces. 2. The prerequisites are modest and standard. A little linear algebra (mostly 2 x 2 matrices), calculus as far as hyperbolic functions, ba sic group theory (subgroups and cosets), and basic topology (open, closed, and compact sets) |
| Physical Description: | 1 Online-Ressource (XI, 236p. 164 illus) |
| ISBN: | 9781461209294 9780387977430 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-1-4612-0929-4 |
Staff View
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042419678 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1992 |||| o||u| ||||||eng d | ||
| 020 | |a 9781461209294 |c Online |9 978-1-4612-0929-4 | ||
| 020 | |a 9780387977430 |c Print |9 978-0-387-97743-0 | ||
| 024 | 7 | |a 10.1007/978-1-4612-0929-4 |2 doi | |
| 035 | |a (OCoLC)863754665 | ||
| 035 | |a (DE-599)BVBBV042419678 | ||
| 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 516 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Stillwell, John |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Geometry of Surfaces |c by John Stillwell |
| 264 | 1 | |a New York, NY |b Springer New York |c 1992 | |
| 300 | |a 1 Online-Ressource (XI, 236p. 164 illus) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Universitext |x 0172-5939 | |
| 500 | |a Geometry used to be the basis of a mathematical education; today it is not even a standard undergraduate topic. Much as I deplore this situation, I welcome the opportunity to make a fresh start. Classical geometry is no longer an adequate basis for mathematics or physics-both of which are becoming increasingly geometric-and geometry can no longer be divorced from algebra, topology, and analysis. Students need a geometry of greater scope, and the fact that there is no room for geometry in the curriculum un til the third or fourth year at least allows us to assume some mathematical background. What geometry should be taught? I believe that the geometry of surfaces of constant curvature is an ideal choice, for the following reasons: 1. It is basically simple and traditional. We are not forgetting euclidean geometry but extending it enough to be interesting and useful. The extensions offer the simplest possible introduction to fundamentals of modem geometry: curvature, group actions, and covering spaces. 2. The prerequisites are modest and standard. A little linear algebra (mostly 2 x 2 matrices), calculus as far as hyperbolic functions, ba sic group theory (subgroups and cosets), and basic topology (open, closed, and compact sets) | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Geometry | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Konstante Krümmung |0 (DE-588)4287357-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Fläche |0 (DE-588)4129864-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Fläche |0 (DE-588)4129864-0 |D s |
| 689 | 0 | 1 | |a Konstante Krümmung |0 (DE-588)4287357-5 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4612-0929-4 |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:BVB01-027855095 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804153090583035904 |
|---|---|
| any_adam_object | |
| author | Stillwell, John |
| author_facet | Stillwell, John |
| author_role | aut |
| author_sort | Stillwell, John |
| author_variant | j s js |
| building | Verbundindex |
| bvnumber | BV042419678 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863754665 (DE-599)BVBBV042419678 |
| 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 | 10.1007/978-1-4612-0929-4 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02804nmm a2200469zc 4500</leader><controlfield tag="001">BV042419678</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1992 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461209294</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4612-0929-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780387977430</subfield><subfield code="c">Print</subfield><subfield code="9">978-0-387-97743-0</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4612-0929-4</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)863754665</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042419678</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">516</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="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Geometry of Surfaces</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 New York</subfield><subfield code="c">1992</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XI, 236p. 164 illus)</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="0" ind2=" "><subfield code="a">Universitext</subfield><subfield code="x">0172-5939</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Geometry used to be the basis of a mathematical education; today it is not even a standard undergraduate topic. Much as I deplore this situation, I welcome the opportunity to make a fresh start. Classical geometry is no longer an adequate basis for mathematics or physics-both of which are becoming increasingly geometric-and geometry can no longer be divorced from algebra, topology, and analysis. Students need a geometry of greater scope, and the fact that there is no room for geometry in the curriculum un til the third or fourth year at least allows us to assume some mathematical background. What geometry should be taught? I believe that the geometry of surfaces of constant curvature is an ideal choice, for the following reasons: 1. It is basically simple and traditional. We are not forgetting euclidean geometry but extending it enough to be interesting and useful. The extensions offer the simplest possible introduction to fundamentals of modem geometry: curvature, group actions, and covering spaces. 2. The prerequisites are modest and standard. A little linear algebra (mostly 2 x 2 matrices), calculus as far as hyperbolic functions, ba sic group theory (subgroups and cosets), and basic topology (open, closed, and compact sets)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Konstante Krümmung</subfield><subfield code="0">(DE-588)4287357-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Fläche</subfield><subfield code="0">(DE-588)4129864-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Fläche</subfield><subfield code="0">(DE-588)4129864-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Konstante Krümmung</subfield><subfield code="0">(DE-588)4287357-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4612-0929-4</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:BVB01-027855095</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></record></collection> |
| id | DE-604.BV042419678 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461209294 9780387977430 |
| issn | 0172-5939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855095 |
| oclc_num | 863754665 |
| 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 (XI, 236p. 164 illus) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Universitext |
| spelling | Stillwell, John Verfasser aut Geometry of Surfaces by John Stillwell New York, NY Springer New York 1992 1 Online-Ressource (XI, 236p. 164 illus) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 Geometry used to be the basis of a mathematical education; today it is not even a standard undergraduate topic. Much as I deplore this situation, I welcome the opportunity to make a fresh start. Classical geometry is no longer an adequate basis for mathematics or physics-both of which are becoming increasingly geometric-and geometry can no longer be divorced from algebra, topology, and analysis. Students need a geometry of greater scope, and the fact that there is no room for geometry in the curriculum un til the third or fourth year at least allows us to assume some mathematical background. What geometry should be taught? I believe that the geometry of surfaces of constant curvature is an ideal choice, for the following reasons: 1. It is basically simple and traditional. We are not forgetting euclidean geometry but extending it enough to be interesting and useful. The extensions offer the simplest possible introduction to fundamentals of modem geometry: curvature, group actions, and covering spaces. 2. The prerequisites are modest and standard. A little linear algebra (mostly 2 x 2 matrices), calculus as far as hyperbolic functions, ba sic group theory (subgroups and cosets), and basic topology (open, closed, and compact sets) Mathematics Geometry Mathematik Konstante Krümmung (DE-588)4287357-5 gnd rswk-swf Fläche (DE-588)4129864-0 gnd rswk-swf Fläche (DE-588)4129864-0 s Konstante Krümmung (DE-588)4287357-5 s 1\p DE-604 https://doi.org/10.1007/978-1-4612-0929-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Stillwell, John Geometry of Surfaces Mathematics Geometry Mathematik Konstante Krümmung (DE-588)4287357-5 gnd Fläche (DE-588)4129864-0 gnd |
| subject_GND | (DE-588)4287357-5 (DE-588)4129864-0 |
| title | Geometry of Surfaces |
| title_auth | Geometry of Surfaces |
| title_exact_search | Geometry of Surfaces |
| title_full | Geometry of Surfaces by John Stillwell |
| title_fullStr | Geometry of Surfaces by John Stillwell |
| title_full_unstemmed | Geometry of Surfaces by John Stillwell |
| title_short | Geometry of Surfaces |
| title_sort | geometry of surfaces |
| topic | Mathematics Geometry Mathematik Konstante Krümmung (DE-588)4287357-5 gnd Fläche (DE-588)4129864-0 gnd |
| topic_facet | Mathematics Geometry Mathematik Konstante Krümmung Fläche |
| url | https://doi.org/10.1007/978-1-4612-0929-4 |
| work_keys_str_mv | AT stillwelljohn geometryofsurfaces |