Lectures on Polytopes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York ; Heidelberg ; Dordrecht ; London
Springer
2007
|
| Edition: | Updated seventh printing of the first edition |
| Series: | Graduate texts in mathematics
152 |
| Subjects: | |
| Online Access: | DE-188 Volltext |
| Item Description: | Based on a graduate course given at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The clear and straightforward presentation features many illustrations, and provides complete proofs for most theorems. The material requires only linear algebra as a prerequisite, but takes the reader quickly from the basics to topics of recent research, including a number of unanswered questions. The lectures introduce the basic facts about polytopes, with an emphasis on the methods that yield the results (Fourier-Motzkin elimination, Schlegel diagrams, shellability, Gale transforms, and oriented matroids), discuss important examples and elegant constructions (cyclic and neighborly polytopes, zonotopes, Minkowski sums, permutahedra and associhedra, fiber polytopes, and the Lawrence construction), show the excitement of current work in the field (Kalai's new diameter bounds, construction of non-rational polytopes, the Bohne-Dress tiling theorem, the upper-bound theorem), and nonextendable shellings) |
| Physical Description: | 1 Online-Ressource (xiii, 373 Seiten) Illustrationen |
| ISBN: | 9781461384311 |
| DOI: | 10.1007/978-1-4613-8431-1 |
Staff View
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| spelling | Ziegler, Günter M. 1963- Verfasser (DE-588)121062155 aut Lectures on Polytopes by Günter M. Ziegler Updated seventh printing of the first edition New York ; Heidelberg ; Dordrecht ; London Springer 2007 1 Online-Ressource (xiii, 373 Seiten) Illustrationen txt rdacontent c rdamedia cr rdacarrier Graduate texts in mathematics 152 Based on a graduate course given at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The clear and straightforward presentation features many illustrations, and provides complete proofs for most theorems. The material requires only linear algebra as a prerequisite, but takes the reader quickly from the basics to topics of recent research, including a number of unanswered questions. The lectures introduce the basic facts about polytopes, with an emphasis on the methods that yield the results (Fourier-Motzkin elimination, Schlegel diagrams, shellability, Gale transforms, and oriented matroids), discuss important examples and elegant constructions (cyclic and neighborly polytopes, zonotopes, Minkowski sums, permutahedra and associhedra, fiber polytopes, and the Lawrence construction), show the excitement of current work in the field (Kalai's new diameter bounds, construction of non-rational polytopes, the Bohne-Dress tiling theorem, the upper-bound theorem), and nonextendable shellings) Mathematics Geometry Mathematik Polytop (DE-588)4175324-0 gnd rswk-swf (DE-588)4143389-0 Aufgabensammlung gnd-content Polytop (DE-588)4175324-0 s 1\p DE-604 Erscheint auch als Druck-Ausgabe, Hardcover 978-0-387-94329-9 Erscheint auch als Druck-Ausgabe, Paperback 978-0-387-94365-7 Graduate texts in mathematics 152 (DE-604)BV035421258 152 https://doi.org/10.1007/978-1-4613-8431-1 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ziegler, Günter M. 1963- Lectures on Polytopes Graduate texts in mathematics Mathematics Geometry Mathematik Polytop (DE-588)4175324-0 gnd |
| subject_GND | (DE-588)4175324-0 (DE-588)4143389-0 |
| title | Lectures on Polytopes |
| title_auth | Lectures on Polytopes |
| title_exact_search | Lectures on Polytopes |
| title_full | Lectures on Polytopes by Günter M. Ziegler |
| title_fullStr | Lectures on Polytopes by Günter M. Ziegler |
| title_full_unstemmed | Lectures on Polytopes by Günter M. Ziegler |
| title_short | Lectures on Polytopes |
| title_sort | lectures on polytopes |
| topic | Mathematics Geometry Mathematik Polytop (DE-588)4175324-0 gnd |
| topic_facet | Mathematics Geometry Mathematik Polytop Aufgabensammlung |
| url | https://doi.org/10.1007/978-1-4613-8431-1 |
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