Lectures on Polytopes: Updated Seventh Printing of the First Edition
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1995
|
| Series: | Graduate Texts in Mathematics
152 |
| Subjects: | |
| Online Access: | DE-4325 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 (XI, 370 Seiten) Illustrationen |
| ISBN: | 9781461384311 9780387943657 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4613-8431-1 |
Staff View
MARC
| LEADER | 00000nam a2200000zcb4500 | ||
|---|---|---|---|
| 001 | BV042420706 | ||
| 003 | DE-604 | ||
| 005 | 20250310 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1995 xx a||| o|||| 00||| eng d | ||
| 020 | |a 9781461384311 |c Online |9 978-1-4613-8431-1 | ||
| 020 | |a 9780387943657 |c Print |9 978-0-387-94365-7 | ||
| 024 | 7 | |a 10.1007/978-1-4613-8431-1 |2 doi | |
| 035 | |a (OCoLC)879623872 | ||
| 035 | |a (DE-599)BVBBV042420706 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 |a DE-4325 | ||
| 082 | 0 | |a 516 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Ziegler, Günter M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Lectures on Polytopes |b Updated Seventh Printing of the First Edition |c by Günter M. Ziegler |
| 264 | 1 | |a New York, NY |b Springer New York |c 1995 | |
| 300 | |a 1 Online-Ressource (XI, 370 Seiten) |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Graduate Texts in Mathematics |v 152 |x 0072-5285 | |
| 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 | |8 1\p |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 2\p |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-0-387-94329-9 |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-1-4613-8431-1 |x Verlag |3 Volltext |
| 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 | |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027856123 | |
| 966 | e | |u https://doi.org/10.1007/978-1-4613-8431-1 |l DE-4325 |p ZDB-2-SEB |q UTN_Einzeltitelkauf_2025 |x Verlag |3 Volltext | |
Record in the Search Index
| _version_ | 1826205447232684032 |
|---|---|
| adam_text | |
| any_adam_object | |
| author | Ziegler, Günter M. |
| author_facet | Ziegler, Günter M. |
| author_role | aut |
| author_sort | Ziegler, Günter M. |
| author_variant | g m z gm gmz |
| building | Verbundindex |
| bvnumber | BV042420706 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)879623872 (DE-599)BVBBV042420706 |
| 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 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000zcb4500</leader><controlfield tag="001">BV042420706</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20250310</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1995 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="020" ind1=" " ind2=" "><subfield code="a">9780387943657</subfield><subfield code="c">Print</subfield><subfield code="9">978-0-387-94365-7</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)879623872</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042420706</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-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-4325</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">Ziegler, Günter M.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Lectures on Polytopes</subfield><subfield code="b">Updated Seventh Printing of the First Edition</subfield><subfield code="c">by Günter M. Ziegler</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">1995</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (XI, 370 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="0" ind2=" "><subfield code="a">Graduate Texts in Mathematics</subfield><subfield code="v">152</subfield><subfield code="x">0072-5285</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="8">1\p</subfield><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">2\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</subfield><subfield code="z">978-0-387-94329-9</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="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="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="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><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="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027856123</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-4325</subfield><subfield code="p">ZDB-2-SEB</subfield><subfield code="q">UTN_Einzeltitelkauf_2025</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| genre | 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content |
| genre_facet | Aufgabensammlung |
| id | DE-604.BV042420706 |
| illustrated | Illustrated |
| indexdate | 2025-03-10T11:13:51Z |
| institution | BVB |
| isbn | 9781461384311 9780387943657 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856123 |
| oclc_num | 879623872 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 DE-4325 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 DE-4325 |
| physical | 1 Online-Ressource (XI, 370 Seiten) Illustrationen |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive ZDB-2-SEB UTN_Einzeltitelkauf_2025 |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Graduate Texts in Mathematics |
| spelling | Ziegler, Günter M. Verfasser aut Lectures on Polytopes Updated Seventh Printing of the First Edition by Günter M. Ziegler New York, NY Springer New York 1995 1 Online-Ressource (XI, 370 Seiten) Illustrationen txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 152 0072-5285 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 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Polytop (DE-588)4175324-0 s 2\p DE-604 Erscheint auch als Druck-Ausgabe 978-0-387-94329-9 https://doi.org/10.1007/978-1-4613-8431-1 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 | Ziegler, Günter M. Lectures on Polytopes Updated Seventh Printing of the First Edition Mathematics Geometry Mathematik Polytop (DE-588)4175324-0 gnd |
| subject_GND | (DE-588)4175324-0 (DE-588)4143389-0 |
| title | Lectures on Polytopes Updated Seventh Printing of the First Edition |
| title_auth | Lectures on Polytopes Updated Seventh Printing of the First Edition |
| title_exact_search | Lectures on Polytopes Updated Seventh Printing of the First Edition |
| title_full | Lectures on Polytopes Updated Seventh Printing of the First Edition by Günter M. Ziegler |
| title_fullStr | Lectures on Polytopes Updated Seventh Printing of the First Edition by Günter M. Ziegler |
| title_full_unstemmed | Lectures on Polytopes Updated Seventh Printing of the First Edition by Günter M. Ziegler |
| title_short | Lectures on Polytopes |
| title_sort | lectures on polytopes updated seventh printing of the first edition |
| title_sub | Updated Seventh Printing of the First Edition |
| 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 |
| work_keys_str_mv | AT zieglergunterm lecturesonpolytopesupdatedseventhprintingofthefirstedition |