A Course in Modern Geometries:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2001
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Undergraduate Texts in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | A Course in Modern Geometries is designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. Chapter 1 presents several finite geometries in an axiomatic framework. Chapter 2 continues the synthetic approach as it introduces Euclid's geometry and ideas of non-Euclidean geometry. In Chapter 3, a new introduction to symmetry and hands-on explorations of isometries precedes the extensive analytic treatment of isometries, similarities and affinities. A new concluding section explores isometries of space. Chapter 4 presents plane projective geometry both synthetically and analytically. The extensive use of matrix representations of groups of transformations in Chapters 3-4 reinforces ideas from linear algebra and serves as excellent preparation for a course in abstract algebra. The new Chapter 5 uses a descriptive and exploratory approach to introduce chaos theory and fractal geometry, stressing the self-similarity of fractals and their generation by transformations from Chapter 3. Each chapter includes a list of suggested resources for applications or related topics in areas such as art and history. The second edition also includes pointers to the web location of author-developed guides for dynamic software explorations of the Poincaré model, isometries, projectivities, conics and fractals. Parallel versions of these explorations are available for "Cabri Geometry" and "Geometer's Sketchpad". Judith N. Cederberg is an associate professor of mathematics at St. Olaf College in Minnesota |
| Beschreibung: | 1 Online-Ressource (XX, 442 p) |
| ISBN: | 9781475734904 9781441931931 |
| ISSN: | 0172-6056 |
| DOI: | 10.1007/978-1-4757-3490-4 |
Internformat
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Datensatz im Suchindex
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| author | Cederberg, Judith N. |
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| 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 | 10.1007/978-1-4757-3490-4 |
| edition | Second Edition |
| format | Electronic eBook |
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| isbn | 9781475734904 9781441931931 |
| issn | 0172-6056 |
| language | English |
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| spelling | Cederberg, Judith N. Verfasser aut A Course in Modern Geometries by Judith N. Cederberg Second Edition New York, NY Springer New York 2001 1 Online-Ressource (XX, 442 p) txt rdacontent c rdamedia cr rdacarrier Undergraduate Texts in Mathematics 0172-6056 A Course in Modern Geometries is designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. Chapter 1 presents several finite geometries in an axiomatic framework. Chapter 2 continues the synthetic approach as it introduces Euclid's geometry and ideas of non-Euclidean geometry. In Chapter 3, a new introduction to symmetry and hands-on explorations of isometries precedes the extensive analytic treatment of isometries, similarities and affinities. A new concluding section explores isometries of space. Chapter 4 presents plane projective geometry both synthetically and analytically. The extensive use of matrix representations of groups of transformations in Chapters 3-4 reinforces ideas from linear algebra and serves as excellent preparation for a course in abstract algebra. The new Chapter 5 uses a descriptive and exploratory approach to introduce chaos theory and fractal geometry, stressing the self-similarity of fractals and their generation by transformations from Chapter 3. Each chapter includes a list of suggested resources for applications or related topics in areas such as art and history. The second edition also includes pointers to the web location of author-developed guides for dynamic software explorations of the Poincaré model, isometries, projectivities, conics and fractals. Parallel versions of these explorations are available for "Cabri Geometry" and "Geometer's Sketchpad". Judith N. Cederberg is an associate professor of mathematics at St. Olaf College in Minnesota Mathematics Geometry Mathematik Geometrie (DE-588)4020236-7 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Geometrie (DE-588)4020236-7 s 2\p DE-604 https://doi.org/10.1007/978-1-4757-3490-4 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 |
| spellingShingle | Cederberg, Judith N. A Course in Modern Geometries Mathematics Geometry Mathematik Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4123623-3 |
| title | A Course in Modern Geometries |
| title_auth | A Course in Modern Geometries |
| title_exact_search | A Course in Modern Geometries |
| title_full | A Course in Modern Geometries by Judith N. Cederberg |
| title_fullStr | A Course in Modern Geometries by Judith N. Cederberg |
| title_full_unstemmed | A Course in Modern Geometries by Judith N. Cederberg |
| title_short | A Course in Modern Geometries |
| title_sort | a course in modern geometries |
| topic | Mathematics Geometry Mathematik Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Mathematics Geometry Mathematik Geometrie Lehrbuch |
| url | https://doi.org/10.1007/978-1-4757-3490-4 |
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