Lectures on Polytopes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York ; Heidelberg ; Dordrecht ; London
Springer
2007
|
| Ausgabe: | Updated seventh printing of the first edition |
| Schriftenreihe: | Graduate texts in mathematics
152 |
| Schlagworte: | |
| Online-Zugang: | DE-188 Volltext |
| Beschreibung: | 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) |
| Beschreibung: | 1 Online-Ressource (xiii, 373 Seiten) Illustrationen |
| ISBN: | 9781461384311 |
| DOI: | 10.1007/978-1-4613-8431-1 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV049942890 | ||
| 003 | DE-604 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 241107s2007 xx a||| o|||| 00||| eng d | ||
| 020 | |a 9781461384311 |c Online |9 978-1-4613-8431-1 | ||
| 024 | 7 | |a 10.1007/978-1-4613-8431-1 |2 doi | |
| 035 | |a (OCoLC)1477609023 | ||
| 035 | |a (DE-599)BVBBV049942890 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-188 | ||
| 082 | 0 | |a 516 |2 23 | |
| 084 | |a SK 380 |0 (DE-625)143235: |2 rvk | ||
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Ziegler, Günter M. |d 1963- |e Verfasser |0 (DE-588)121062155 |4 aut | |
| 245 | 1 | 0 | |a Lectures on Polytopes |c by Günter M. Ziegler |
| 250 | |a Updated seventh printing of the first edition | ||
| 264 | 1 | |a New York ; Heidelberg ; Dordrecht ; London |b Springer |c 2007 | |
| 300 | |a 1 Online-Ressource (xiii, 373 Seiten) |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 152 | |
| 500 | |a 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) | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Geometry | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Polytop |0 (DE-588)4175324-0 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4143389-0 |a Aufgabensammlung |2 gnd-content | |
| 689 | 0 | 0 | |a Polytop |0 (DE-588)4175324-0 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe, Hardcover |z 978-0-387-94329-9 |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe, Paperback |z 978-0-387-94365-7 |
| 830 | 0 | |a Graduate texts in mathematics |v 152 |w (DE-604)BV035421258 |9 152 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4613-8431-1 |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 912 | |a ZDB-2-SEB | ||
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035281083 | |
| 966 | e | |u https://doi.org/10.1007/978-1-4613-8431-1 |l DE-188 |p ZDB-2-SEB |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1822483072715587584 |
|---|---|
| adam_text | |
| any_adam_object | |
| author | Ziegler, Günter M. 1963- |
| author_GND | (DE-588)121062155 |
| author_facet | Ziegler, Günter M. 1963- |
| author_role | aut |
| author_sort | Ziegler, Günter M. 1963- |
| author_variant | g m z gm gmz |
| building | Verbundindex |
| bvnumber | BV049942890 |
| classification_rvk | SK 380 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SEB |
| ctrlnum | (OCoLC)1477609023 (DE-599)BVBBV049942890 |
| 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 | 10.1007/978-1-4613-8431-1 |
| edition | Updated seventh printing of the first edition |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV049942890</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">241107s2007 xx a||| o|||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461384311</subfield><subfield code="c">Online</subfield><subfield code="9">978-1-4613-8431-1</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-1-4613-8431-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1477609023</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV049942890</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-188</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">SK 380</subfield><subfield code="0">(DE-625)143235:</subfield><subfield code="2">rvk</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">Ziegler, Günter M.</subfield><subfield code="d">1963-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)121062155</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Lectures on Polytopes</subfield><subfield code="c">by Günter M. Ziegler</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Updated seventh printing of the first edition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York ; Heidelberg ; Dordrecht ; London</subfield><subfield code="b">Springer</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xiii, 373 Seiten)</subfield><subfield code="b">Illustrationen</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">152</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">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)</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">Polytop</subfield><subfield code="0">(DE-588)4175324-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4143389-0</subfield><subfield code="a">Aufgabensammlung</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Polytop</subfield><subfield code="0">(DE-588)4175324-0</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="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe, Hardcover</subfield><subfield code="z">978-0-387-94329-9</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe, Paperback</subfield><subfield code="z">978-0-387-94365-7</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Graduate texts in mathematics</subfield><subfield code="v">152</subfield><subfield code="w">(DE-604)BV035421258</subfield><subfield code="9">152</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-1-4613-8431-1</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</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="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SEB</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-035281083</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">https://doi.org/10.1007/978-1-4613-8431-1</subfield><subfield code="l">DE-188</subfield><subfield code="p">ZDB-2-SEB</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| genre | (DE-588)4143389-0 Aufgabensammlung gnd-content |
| genre_facet | Aufgabensammlung |
| id | DE-604.BV049942890 |
| illustrated | Illustrated |
| indexdate | 2025-01-28T09:08:18Z |
| institution | BVB |
| isbn | 9781461384311 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035281083 |
| oclc_num | 1477609023 |
| open_access_boolean | |
| owner | DE-188 |
| owner_facet | DE-188 |
| physical | 1 Online-Ressource (xiii, 373 Seiten) Illustrationen |
| psigel | ZDB-2-SEB |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| 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 |
| volume_link | (DE-604)BV035421258 |
| work_keys_str_mv | AT zieglergunterm lecturesonpolytopes |