Ziegler, Günter M.
Overview
Works:  100 works in 470 publications in 9 languages and 6,486 library holdings 

Genres:  Anecdotes Popular works Documentary films Pictorial works History Biography 
Roles:  Author, Editor, Contributor, Collector, Interviewee 
Classifications:  QA36, 510 
Publication Timeline
.
Most widely held works by
Günter M Ziegler
Proofs from the book by
Martin Aigner(
Book
)
172 editions published between 1998 and 2015 in 10 languages and held by 2,159 WorldCat member libraries worldwide
The mathematical heroes of this book are 'perfect proofs': brilliant ideas, clever connections & wonderful observations that bring new insight & surprising perspectives on basic & challenging problems from number theory, geometry, analysis, combinatorics & graph theory. 30 examples are presented
172 editions published between 1998 and 2015 in 10 languages and held by 2,159 WorldCat member libraries worldwide
The mathematical heroes of this book are 'perfect proofs': brilliant ideas, clever connections & wonderful observations that bring new insight & surprising perspectives on basic & challenging problems from number theory, geometry, analysis, combinatorics & graph theory. 30 examples are presented
Lectures on polytopes by
Günter M Ziegler(
Book
)
49 editions published between 1993 and 2007 in 4 languages and held by 632 WorldCat member libraries worldwide
"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."Page 4 of cover
49 editions published between 1993 and 2007 in 4 languages and held by 632 WorldCat member libraries worldwide
"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."Page 4 of cover
Do I count? : stories from mathematics by
Günter M Ziegler(
Book
)
19 editions published between 2010 and 2014 in English and German and held by 598 WorldCat member libraries worldwide
The subject of mathematics is not something distant, strange, and abstract that you can only learn aboutand often dislikein school. It is in everyday situations, such as housekeeping, communications, traffic, and weather reports. Taking you on a trip into the world of mathematics, Do I Count? Stories from Mathematics describes in a clear and captivating way the people behind the numbers and the places where mathematics is made. Written by top scientist and engaging storyteller Günter M. Ziegler and translated by Thomas von Foerster, the book presents mathematics and mathematicians in a manner that you have not previously encountered. It guides you on a scenic tour through the field, pointing out which beds were useful in constructing which theorems and which notebooks list the prizes for solving particular problems. Forgoing esoteric areas, the text relates mathematics to celebrities, history, travel, politics, science and technology, weather, clever puzzles, and the future. Can bees count? Is 13 bad luck? Are there equations for everything? What's the real practical value of the Pythagorean Theorem? Are there Sudoku puzzles with fewer than 17 entries and just one solution? Where and how do mathematicians work? Who invented proofs and why do we need them? Why is there no Nobel Prize for mathematics? What kind of life did Paul Erdős lead? Find out the answers to these and other questions in this entertaining book of stories. You'll see that everyone counts, but no computation is needed
19 editions published between 2010 and 2014 in English and German and held by 598 WorldCat member libraries worldwide
The subject of mathematics is not something distant, strange, and abstract that you can only learn aboutand often dislikein school. It is in everyday situations, such as housekeeping, communications, traffic, and weather reports. Taking you on a trip into the world of mathematics, Do I Count? Stories from Mathematics describes in a clear and captivating way the people behind the numbers and the places where mathematics is made. Written by top scientist and engaging storyteller Günter M. Ziegler and translated by Thomas von Foerster, the book presents mathematics and mathematicians in a manner that you have not previously encountered. It guides you on a scenic tour through the field, pointing out which beds were useful in constructing which theorems and which notebooks list the prizes for solving particular problems. Forgoing esoteric areas, the text relates mathematics to celebrities, history, travel, politics, science and technology, weather, clever puzzles, and the future. Can bees count? Is 13 bad luck? Are there equations for everything? What's the real practical value of the Pythagorean Theorem? Are there Sudoku puzzles with fewer than 17 entries and just one solution? Where and how do mathematicians work? Who invented proofs and why do we need them? Why is there no Nobel Prize for mathematics? What kind of life did Paul Erdős lead? Find out the answers to these and other questions in this entertaining book of stories. You'll see that everyone counts, but no computation is needed
Convex polytopes by
Branko Grünbaum(
Book
)
9 editions published in 2003 in English and held by 362 WorldCat member libraries worldwide
"The appearance of Grünbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise beautiful unexplored land for future research. The appearance of the new edition is going to be another moment of grace. Kaibel, Klee and Ziegler were able to update the convex polytope saga in a clear, accurate, lively, and inspired way." (Gil Kalai, The Hebrew University of Jerusalem) "The original book of Grünbaum has provided the central reference for work in this active area of mathematics for the past 35 years ... I first consulted this book as a graduate student in 1967; yet, even today, I am surprised again and again by what I find there. It is an amazingly complete reference for work on this subject up to that time and continues to be a major influence on research to this day." (Louis J. Billera, Cornell University) "The original edition of Convex Polytopes inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again." (Peter McMullen, University College London)
9 editions published in 2003 in English and held by 362 WorldCat member libraries worldwide
"The appearance of Grünbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise beautiful unexplored land for future research. The appearance of the new edition is going to be another moment of grace. Kaibel, Klee and Ziegler were able to update the convex polytope saga in a clear, accurate, lively, and inspired way." (Gil Kalai, The Hebrew University of Jerusalem) "The original book of Grünbaum has provided the central reference for work in this active area of mathematics for the past 35 years ... I first consulted this book as a graduate student in 1967; yet, even today, I am surprised again and again by what I find there. It is an amazingly complete reference for work on this subject up to that time and continues to be a major influence on research to this day." (Louis J. Billera, Cornell University) "The original edition of Convex Polytopes inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again." (Peter McMullen, University College London)
Polytopes : combinatorics and computation by
Gil Kalai(
Book
)
12 editions published in 2000 in English and held by 203 WorldCat member libraries worldwide
Questions that arose from linear programming and combinatorial optimization have been a driving force for modern polytope theory, such as the diameter questions motivated by the desire to understand the complexity of the simplex algorithm, or the need to study facets for use in cutting plane procedures. In addition, algorithms now provide the means to computationally study polytopes, to compute their parameters such as flag vectors, graphs and volumes, and to construct examples of large complexity. The papers of this volume thus display a wide panorama of connections of polytope theory with other fields. Areas such as discrete and computational geometry, linear and combinatorial optimization, and scientific computing have contributed a combination of questions, ideas, results, algorithms and, finally, computer programs
12 editions published in 2000 in English and held by 203 WorldCat member libraries worldwide
Questions that arose from linear programming and combinatorial optimization have been a driving force for modern polytope theory, such as the diameter questions motivated by the desire to understand the complexity of the simplex algorithm, or the need to study facets for use in cutting plane procedures. In addition, algorithms now provide the means to computationally study polytopes, to compute their parameters such as flag vectors, graphs and volumes, and to construct examples of large complexity. The papers of this volume thus display a wide panorama of connections of polytope theory with other fields. Areas such as discrete and computational geometry, linear and combinatorial optimization, and scientific computing have contributed a combination of questions, ideas, results, algorithms and, finally, computer programs
Mathematik  das ist doch keine Kunst! by
Günter M Ziegler(
Book
)
6 editions published in 2013 in German and held by 107 WorldCat member libraries worldwide
Wo wir nur einen Herrnhuter Stern sehen oder einen kunstvollen Knoten, zeigt uns der "Popstar unter den Mathematikern" Günter Ziegler die Mathematik in ihrer ganzen Schönheit. In diesem außergewöhnlichen Buch betrachtet der Geometrieprofessor 24 Bilder, die nur auf den ersten Blick nichts mit Mathematik zu tun haben
6 editions published in 2013 in German and held by 107 WorldCat member libraries worldwide
Wo wir nur einen Herrnhuter Stern sehen oder einen kunstvollen Knoten, zeigt uns der "Popstar unter den Mathematikern" Günter Ziegler die Mathematik in ihrer ganzen Schönheit. In diesem außergewöhnlichen Buch betrachtet der Geometrieprofessor 24 Bilder, die nur auf den ersten Blick nichts mit Mathematik zu tun haben
Das Buch der Beweise by
Martin Aigner(
)
1 edition published in 2015 in German and held by 58 WorldCat member libraries worldwide
1 edition published in 2015 in German and held by 58 WorldCat member libraries worldwide
Using the BorsukUlam theorem : lectures on topological methods in combinatorics and geometry by
Jiří Matoušek(
Book
)
16 editions published between 2003 and 2010 in English and held by 48 WorldCat member libraries worldwide
A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not so widely understood. They are scattered in research papers or outlined in surveys, and they often use topological notions not commonly known among combinatorialists or computer scientists. This book is the first textbook treatment of a significant part of such results. It focuses on socalled equivariant methods, based on the BorsukUlam theorem and its generalizations. The topological tools are intentionally kept on a very elementary level (for example, homology theory and homotopy groups are completely avoided). No prior knowledge of algebraic topology is assumed, only a background in undergraduate mathematics, and the required topological notions and results are gradually explained. At the same time, many substantial combinatorial results are covered, sometimes with some of the most important results, such as Kneser's conjecture, showing them from various points of view. The history of the presented material, references, related results, and more advanced methods are surveyed in separate subsections. The text is accompanied by numerous exercises, of varying difficulty. Many of the exercises actually outline additional results that did not fit in the main text. The book is richly illustrated, and it has a detailed index and an extensive bibliography. This text started with a onesemester graduate course the author taught in fall 1993 in Prague. The transcripts of the lectures by the participants served as a basis of the first version. Some years later, a course partially based on that text was taught by Gunter M. Ziegler in Berlin. The book is based on a thoroughly rewritten version prepared during a predoctoral course the author taught at the ETH Zurich in fall 2001. Most of the material was covered in the course: Chapter 1 was assigned as an introductory reading text, and the other chapters were presented in approximately 30 hours of teaching (by 45 minutes), with some omissions throughout and with only a sketchy presentation of the last chapter
16 editions published between 2003 and 2010 in English and held by 48 WorldCat member libraries worldwide
A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not so widely understood. They are scattered in research papers or outlined in surveys, and they often use topological notions not commonly known among combinatorialists or computer scientists. This book is the first textbook treatment of a significant part of such results. It focuses on socalled equivariant methods, based on the BorsukUlam theorem and its generalizations. The topological tools are intentionally kept on a very elementary level (for example, homology theory and homotopy groups are completely avoided). No prior knowledge of algebraic topology is assumed, only a background in undergraduate mathematics, and the required topological notions and results are gradually explained. At the same time, many substantial combinatorial results are covered, sometimes with some of the most important results, such as Kneser's conjecture, showing them from various points of view. The history of the presented material, references, related results, and more advanced methods are surveyed in separate subsections. The text is accompanied by numerous exercises, of varying difficulty. Many of the exercises actually outline additional results that did not fit in the main text. The book is richly illustrated, and it has a detailed index and an extensive bibliography. This text started with a onesemester graduate course the author taught in fall 1993 in Prague. The transcripts of the lectures by the participants served as a basis of the first version. Some years later, a course partially based on that text was taught by Gunter M. Ziegler in Berlin. The book is based on a thoroughly rewritten version prepared during a predoctoral course the author taught at the ETH Zurich in fall 2001. Most of the material was covered in the course: Chapter 1 was assigned as an introductory reading text, and the other chapters were presented in approximately 30 hours of teaching (by 45 minutes), with some omissions throughout and with only a sketchy presentation of the last chapter
Pi und Co. : Kaleidoskop der Mathematik(
Book
)
6 editions published between 2008 and 2016 in German and held by 15 WorldCat member libraries worldwide
Mathematik ist eine äußerst vielseitige, lebendige Wissenschaft. Von ihren großen Themen wie Zahlen, Unendlichkeiten, Dimensionen und Wahrscheinlichkeiten spannen die Autoren einen Bogen bis hin zu aktuellen Anwendungen in der Logistik, der Finanzwelt, der Kryptographie, der Medizin und anderen Gebieten. Breit gefächert wie die Mathematik ist auch das Spektrum der Beiträge. Leicht verständliche, unterhaltsame Texte finden sich ebenso wie anspruchsvollere mathematische Herausforderungen. Das Buch ist also eine Einladung an jeden, seinen eigenen Zugang zu dieser spannenden und abenteurreichen Wissenschaft zu finden
6 editions published between 2008 and 2016 in German and held by 15 WorldCat member libraries worldwide
Mathematik ist eine äußerst vielseitige, lebendige Wissenschaft. Von ihren großen Themen wie Zahlen, Unendlichkeiten, Dimensionen und Wahrscheinlichkeiten spannen die Autoren einen Bogen bis hin zu aktuellen Anwendungen in der Logistik, der Finanzwelt, der Kryptographie, der Medizin und anderen Gebieten. Breit gefächert wie die Mathematik ist auch das Spektrum der Beiträge. Leicht verständliche, unterhaltsame Texte finden sich ebenso wie anspruchsvollere mathematische Herausforderungen. Das Buch ist also eine Einladung an jeden, seinen eigenen Zugang zu dieser spannenden und abenteurreichen Wissenschaft zu finden
Optimal Bounds for the Colored Tverberg Problem by Pavle V. M Blagojevic(
)
1 edition published in 2009 in German and held by 15 WorldCat member libraries worldwide
1 edition published in 2009 in German and held by 15 WorldCat member libraries worldwide
Shellability of chessboard complexes by
Günter M Ziegler(
Book
)
4 editions published between 1992 and 1998 in English and German and held by 14 WorldCat member libraries worldwide
The notion of vertex decomposability is a very convenient tool to prove shellability of such combinatorially defined simplicial complexes. We establish a relation between vertex decomposability and the CL shellability technique (for posets) of Björner & Wachs."
4 editions published between 1992 and 1998 in English and German and held by 14 WorldCat member libraries worldwide
The notion of vertex decomposability is a very convenient tool to prove shellability of such combinatorially defined simplicial complexes. We establish a relation between vertex decomposability and the CL shellability technique (for posets) of Björner & Wachs."
Randomized simplex algorithms on Klee Minty cubes by
Bernd Gärtner(
Book
)
6 editions published in 1994 in English and German and held by 13 WorldCat member libraries worldwide
Abstract: "We investigate the behavior of randomized simplex algorithms on special linear programs. For this, we develop combinatorial models for the KleeMinty cubes [16] and similar linear programs with exponential decreasing paths. The analysis of two randomized pivot rules on the KleeMinty cubes leads to (nearly) quadratic lower bounds for the complexity of linear programming with random pivots. Thus we disprove two bounds conjectured in the literature. At the same time, we establish quadratic upper bounds for random pivots on the linear programs under investigation. This motivates the question whether some randomized pivot rules possibly have quadratic worstcase behavior on general linear programs."
6 editions published in 1994 in English and German and held by 13 WorldCat member libraries worldwide
Abstract: "We investigate the behavior of randomized simplex algorithms on special linear programs. For this, we develop combinatorial models for the KleeMinty cubes [16] and similar linear programs with exponential decreasing paths. The analysis of two randomized pivot rules on the KleeMinty cubes leads to (nearly) quadratic lower bounds for the complexity of linear programming with random pivots. Thus we disprove two bounds conjectured in the literature. At the same time, we establish quadratic upper bounds for random pivots on the linear programs under investigation. This motivates the question whether some randomized pivot rules possibly have quadratic worstcase behavior on general linear programs."
Discrete differential geometry by
Alexander I Bobenko(
Book
)
7 editions published in 2008 in English and held by 11 WorldCat member libraries worldwide
Discrete differential geometry is an active mathematical terrain where differential geometry and discrete geometry meet and interact. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. Current progress in this field is to a large extent stimulated by its relevance for computer graphics and mathematical physics. This collection of essays, which documents the main lectures of the 2004 Oberwolfach Seminar on the topic, as well as a number of additional contributions by key participants, gives a lively, multifacetted introduction to this emerging field
7 editions published in 2008 in English and held by 11 WorldCat member libraries worldwide
Discrete differential geometry is an active mathematical terrain where differential geometry and discrete geometry meet and interact. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. Current progress in this field is to a large extent stimulated by its relevance for computer graphics and mathematical physics. This collection of essays, which documents the main lectures of the 2004 Oberwolfach Seminar on the topic, as well as a number of additional contributions by key participants, gives a lively, multifacetted introduction to this emerging field
Colors of math by
Ekaterina Eremenko(
Visual
)
3 editions published in 2012 in English and French and held by 9 WorldCat member libraries worldwide
"To most people math appears abstract, mysterious. Complicated. Inaccessible. But math is nothing but a different language to express the world. Math can be sensual. Math can be tasted, it smells, it creates sound and color. One can touch it and be touched by it...."  Container
3 editions published in 2012 in English and French and held by 9 WorldCat member libraries worldwide
"To most people math appears abstract, mysterious. Complicated. Inaccessible. But math is nothing but a different language to express the world. Math can be sensual. Math can be tasted, it smells, it creates sound and color. One can touch it and be touched by it...."  Container
On the difference between real and complex arrangements by
Günter M Ziegler(
Book
)
5 editions published between 1991 and 1992 in English and German and held by 8 WorldCat member libraries worldwide
5 editions published between 1991 and 1992 in English and German and held by 8 WorldCat member libraries worldwide
A variant of the Buchberger algorithm for integer programming by
Regina Urbaniak(
Book
)
4 editions published in 1994 in English and German and held by 8 WorldCat member libraries worldwide
Abstract: "In this paper we modify Buchberger's Spair reduction algorithm for computing a Gröbner basis of a toric ideal so as to apply to an integer program in inequality form with fixed right hand sides and fixed upper bounds on the variables. We formulate the algorithm in the original space and interpret the reduction steps geometrically. In fact, three variants of this algorithm are presented and we give elementary proofs for their correctness. A relationship between these (exact) algorithms, iterative improvement heuristics and the KernighanLin procedure is established."
4 editions published in 1994 in English and German and held by 8 WorldCat member libraries worldwide
Abstract: "In this paper we modify Buchberger's Spair reduction algorithm for computing a Gröbner basis of a toric ideal so as to apply to an integer program in inequality form with fixed right hand sides and fixed upper bounds on the variables. We formulate the algorithm in the original space and interpret the reduction steps geometrically. In fact, three variants of this algorithm are presented and we give elementary proofs for their correctness. A relationship between these (exact) algorithms, iterative improvement heuristics and the KernighanLin procedure is established."
Higher Bruhat orders and cyclic hyperplane arrangements by
Günter M Ziegler(
Book
)
5 editions published between 1991 and 1992 in English and German and held by 8 WorldCat member libraries worldwide
5 editions published between 1991 and 1992 in English and German and held by 8 WorldCat member libraries worldwide
Gröbner bases of lattices, corner polyhedra, and integer programming by
Bernd Sturmfels(
Book
)
4 editions published in 1994 in German and English and held by 8 WorldCat member libraries worldwide
Abstract: "We investigate the generating sets ('Gröbner bases') of integer lattices which correspond to the Gröbner bases of the associated binomial ideals. Extending results in [22], we obtain a geometric characterization of the universal Gröbner basis in terms of the vertices and edges of the associated corner polyhedra. We emphasize the special case where the lattice has finite index. In this case the corner polyhedra were studied by Gomory [14], and there is a close connection to the 'group problem in integer programming' [20, p. 363]. We present exponential lower and upper bounds for the size of a reduced Gröbner basis. The initial complex of (the ideal of) a lattice is shown to be dual to the boundary of a certain simple polyhedron."
4 editions published in 1994 in German and English and held by 8 WorldCat member libraries worldwide
Abstract: "We investigate the generating sets ('Gröbner bases') of integer lattices which correspond to the Gröbner bases of the associated binomial ideals. Extending results in [22], we obtain a geometric characterization of the universal Gröbner basis in terms of the vertices and edges of the associated corner polyhedra. We emphasize the special case where the lattice has finite index. In this case the corner polyhedra were studied by Gomory [14], and there is a close connection to the 'group problem in integer programming' [20, p. 363]. We present exponential lower and upper bounds for the size of a reduced Gröbner basis. The initial complex of (the ideal of) a lattice is shown to be dual to the boundary of a certain simple polyhedron."
Oriented matroids by
Anders Björner(
Book
)
5 editions published between 1993 and 2000 in English and Undetermined and held by 3 WorldCat member libraries worldwide
First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research
5 editions published between 1993 and 2000 in English and Undetermined and held by 3 WorldCat member libraries worldwide
First comprehensive, accessible account; second edition has expanded bibliography and a new appendix surveying recent research
P [Pi] und Co : Kaleidoskop der Mathematik(
)
1 edition published in 2008 in German and held by 0 WorldCat member libraries worldwide
1 edition published in 2008 in German and held by 0 WorldCat member libraries worldwide
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Related Identities
 Aigner, Martin 1942 Author
 Hofmann, Karl Heinrich Illustrator
 Grünbaum, Branko Author
 Klee, Victor Editor
 Kaibel, Volker Editor
 Kalai, Gil 1955 Author Editor
 Puech, Nicolas Translator
 Behrends, Ehrhard 1946 Editor
 Gritzmann, Peter Editor
 Björner, Anders Editor Honoree Author Contributor Collector
Useful Links
Associated Subjects
Algebra Algebraic topology Beutelspacher, Albrecht Combinatorial analysis Combinatorial enumeration problems Combinatorial geometry Combinatorial optimization Computational complexity Computer algorithms Computer science Convex bodies Convex polytopes Discrete geometry Discrete groups Distribution (Probability theory) Evidence Geometry Geometry, Differential Germany Global analysis (Mathematics) Global differential geometry Graph theory Information theory Integer programming Italy Lattice theory Linear programming Mathematical analysis Mathematical recreations Mathematicians Mathematics MathematicsPhilosophy MathematicsStudy and teaching Matroids Number theory Oriented matroids Polytopes Proof theory Reasoning
Alternative Names
Cigler, Ginter 1963
Günter M. Ziegler
Günter M. Ziegler doorverwijspagina
Günter M. Ziegler Duits wiskundige
Günter M. Ziegler German mathematician
Günter Matias Ziegler desambiguación de Wikipedia
Günter Matias Ziegler matemático alemán
Günter Matthias Ziegler
Günter Matthias Ziegler página de desambiguação de um projeto da Wikimedia
Günter Ziegler grensida
Günter Ziegler tysk matematikar
Günter Ziegler tysk matematiker
Günter Ziegler Wikipediapekerside
Ziegler, G. 1963
Ziegler, G.M.
Ziegler, G. M. 1963
Ziegler, Günter 1963
Ziegler, Günter M.
Ziegler, M. 1963
Гинтер М. Циглер
지글러, 귄터 M. 1963
찌글러, 귄터 M. 1963
치글러, 귄터 M. 1963
ギュンター・ツィーグラー
ツィーグラー, G. M.
Languages
English
(225)
German (46)
French (37)
Italian (8)
Japanese (7)
Chinese (4)
Polish (2)
Spanish (2)
Portuguese (1)
German (46)
French (37)
Italian (8)
Japanese (7)
Chinese (4)
Polish (2)
Spanish (2)
Portuguese (1)
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