Ziegler, Günter M.
Overview
Works:  106 works in 480 publications in 5 languages and 6,527 library holdings 

Genres:  Anecdotes Popular works Documentary films Pictorial works History Biography 
Roles:  Author, Editor, Contributor, Collector, Interviewee 
Publication Timeline
.
Most widely held works by
Günter M Ziegler
Proofs from the book by
Martin Aigner(
Book
)
108 editions published between 1998 and 2014 in 6 languages and held by 1,718 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
108 editions published between 1998 and 2014 in 6 languages and held by 1,718 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
Do I count? : stories from mathematics by
Günter M Ziegler(
Book
)
18 editions published between 2010 and 2017 in English and German and held by 617 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
18 editions published between 2010 and 2017 in English and German and held by 617 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 360 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 360 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)
Raisonnements divins by
Martin Aigner(
Book
)
35 editions published between 2002 and 2017 in French and English and held by 233 WorldCat member libraries worldwide
Regroupe quelques démonstrations mathématiques choisies pour leur élégance. Différents domaines sont abordés : théorie des nombres, géométrie, analyse combinatoire et théorie des graphes. Propose aussi bien des résultats établis depuis longtemps que des théorèmes récemment démontrés
35 editions published between 2002 and 2017 in French and English and held by 233 WorldCat member libraries worldwide
Regroupe quelques démonstrations mathématiques choisies pour leur élégance. Différents domaines sont abordés : théorie des nombres, géométrie, analyse combinatoire et théorie des graphes. Propose aussi bien des résultats établis depuis longtemps que des théorèmes récemment démontrés
Polytopes : combinatorics and computation by
Gil Kalai(
Book
)
13 editions published in 2000 in English and held by 205 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
13 editions published in 2000 in English and held by 205 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 109 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 109 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
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
Colors of math by
Ekaterina Olegovna Eremenko(
Visual
)
3 editions published in 2012 in English and French and held by 11 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 11 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
Discrete differential geometry by
Alexander I Bobenko(
Book
)
8 editions published in 2008 in English and Undetermined 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 particip
8 editions published in 2008 in English and Undetermined 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 particip
Shellability of chessboard complexes by
Günter M Ziegler(
Book
)
4 editions published between 1992 and 1998 in English and German and held by 10 WorldCat member libraries worldwide
Abstract: "The matchings in a complete bipartite graph form a simplicial complex, which in many cases has strong structural properties. We use an equivalent description as chessboard complexes: the complexes of all nontaking rook positions on chessboards of various shapes. In this paper we construct 'certificate kshapes' [sigma](m, n, k) such that if the shape A contains some [sigma](m, n, k), then the (k1)skeleton of the chessboard complex [delta](A) is vertex decomposable in the sense of Provan & Billera. This covers, in particular, the case of rectangular chessboards A=[m]x[n], for which [delta](A) is vertex decomposable if n [> or =] 2m1, and the [formula]skeleton is vertex decomposable in general
4 editions published between 1992 and 1998 in English and German and held by 10 WorldCat member libraries worldwide
Abstract: "The matchings in a complete bipartite graph form a simplicial complex, which in many cases has strong structural properties. We use an equivalent description as chessboard complexes: the complexes of all nontaking rook positions on chessboards of various shapes. In this paper we construct 'certificate kshapes' [sigma](m, n, k) such that if the shape A contains some [sigma](m, n, k), then the (k1)skeleton of the chessboard complex [delta](A) is vertex decomposable in the sense of Provan & Billera. This covers, in particular, the case of rectangular chessboards A=[m]x[n], for which [delta](A) is vertex decomposable if n [> or =] 2m1, and the [formula]skeleton is vertex decomposable in general
Randomized simplex algorithms on Klee Minty cubes by
Bernd Gärtner(
Book
)
4 editions published in 1994 in English and German and held by 9 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."
4 editions published in 1994 in English and German and held by 9 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."
Vision als Aufgabe das LeibnizUniversum im 21. Jahrhundert(
Book
)
2 editions published in 2016 in German and held by 8 WorldCat member libraries worldwide
2 editions published in 2016 in German and held by 8 WorldCat member libraries worldwide
Pi und Co. : Kaleidoskop der Mathematik(
Book
)
3 editions published in 2008 in German and held by 2 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
3 editions published in 2008 in German and held by 2 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
Oriented matroids(
Book
)
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
Oriented matroids are a very natural mathematical concept which presents itself in many different guises, and which has connections and applications to many different areas. These include discrete and computational geometry, combinatorics, convexity, topology, algebraic geometry, operations research, computer science and theoretical chemistry. This is the first comprehensive or accessible account of the subject. This book is intended for a diverse audience: graduate students who wish to learn the subject from scratch, researchers in the various fields of application who want to concentrate on certain aspects of the theory, specialists who need a thorough reference work, and others at points in between. A list of exercises and open problems ends each chapter, and the work is rounded off by an uptodate and exhaustive reference list
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
Oriented matroids are a very natural mathematical concept which presents itself in many different guises, and which has connections and applications to many different areas. These include discrete and computational geometry, combinatorics, convexity, topology, algebraic geometry, operations research, computer science and theoretical chemistry. This is the first comprehensive or accessible account of the subject. This book is intended for a diverse audience: graduate students who wish to learn the subject from scratch, researchers in the various fields of application who want to concentrate on certain aspects of the theory, specialists who need a thorough reference work, and others at points in between. A list of exercises and open problems ends each chapter, and the work is rounded off by an uptodate and exhaustive reference list
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
Das BUCH der Beweise(
)
1 edition published in 2010 in German and held by 0 WorldCat member libraries worldwide
1 edition published in 2010 in German and held by 0 WorldCat member libraries worldwide
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Related Identities
 Aigner, Martin 1942 Author
 Hofmann, Karl Heinrich Illustrator
 Klee, Victor Editor
 Kaibel, Volker Editor
 Grünbaum, Branko Author
 Puech, Nicolas Translator
 Kalai, Gil 1955 Author Editor
 Behrends, Ehrhard 1946 Editor
 Gritzmann, Peter Editor
 Björner, Anders Editor Honoree Author Contributor Collector
Useful Links
Associated Subjects
Algebra Beutelspacher, Albrecht Combinatorial analysis Combinatorial optimization Computer science Convex polytopes Discrete geometry Discrete groups Distribution (Probability theory) Geometry Geometry, Differential Germany Global analysis (Mathematics) Global differential geometry Graph theory Italy Linear programming Mathematical recreations Mathematicians Mathematics MathematicsPhilosophy MathematicsStudy and teaching Number theory Oriented matroids Polytopes Reasoning
Alternative Names
Cigler, Ginter 1963
Günter M. Ziegler
Günter M. Ziegler doorverwijspagina
Günter M. Ziegler Duits wiskundige
Günter M. Ziegler German mathematician
Günter M. Ziegler mathématicien allemand
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.
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