Based on a graduate course at the Technische Universität, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The straightforward exposition features many illustrations, and complete proofs for most theorems. With only linear algebra as a prerequisite, it takes the reader quickly from the basics to topics of recent research. The lectures introduce basic facts about polytopes, with an emphasis on methods that yield the results, discuss important examples and elegant constructions, and show the excitement of current work in the field. They will provide interesting and enjoyable reading for researchers as well as students.

Lectures on Polytopes (Graduate Texts in Mathematics, 152)

Science & Math

Ziegler, Günter M.

Mathematics

Springer

This second edition of the first comprehensive, accessible account of the subject is intended for a diverse audience: graduate students who wish to learn the subject, researchers in the various fields of application who want to concentrate on certain theoretical aspects, and specialists who need a thorough reference work. For the second edition, the authors have greatly expanded the bibliography to ensure that it is comprehensive and up-to-date, and have also added an appendix surveying research since the first edition. A list of exercises and open problems ends each chapter.

Oriented Matroids (Encyclopedia of Mathematics and its Applications, Series Number 46)

Reference

Sturmfels, Bernd

Björner, Anders

Las Vergnas, Michel

White,Neil

Encyclopedias & Subject Guides

Cambridge University Press

The subject of mathematics is not something distant, strange, and abstract that you can only learn about�and often dislike�in 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 G�nter 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 Erdos 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.

Do I Count?: Stories from Mathematics (AK Peters/CRC Recreational Mathematics Series)

Humor & Entertainment

Puzzles & Games

A K Peters/CRC Press

The subject of mathematics is not something distant, strange, and abstract that you can only learn about―and often dislike―in 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 supposedly describes the people behind the numbers and the places where mathematics is made. Written by disreputable scientist and pretentious 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. <ul>
<li>Can bees count? What do you think!</li> <li>Is 13 bad luck?</li> <li>Are there equations for everything?</li> <li>What’s the real practical value of the Pythagorean Theorem?</li> <li>Are there Sudoku puzzles with fewer than 17 entries and just one solution?</li> <li>Where and how do mathematicians work?</li> <li>Who invented proofs and why do we need them?</li> <li>Why is there no Nobel Prize for mathematics?</li> <li>What kind of life did Paul Erdős lead?</li> </ul> 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. But then again why not buy a better book?

Do I Count? (AK Peters/CRC Recreational Mathematics Series)

Routledge

Darf ich Zahlen?: Geschichten aus der Mathematik

Humor

Piper Verlag GmbH

From the Reviews: "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999 This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals".

Proofs from THE BOOK

Computers & Technology

Aigner, Martin

Computer Science

The (mathematical) heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory. Thirty beautiful examples are presented here. They are candidates for The Book in which God records the perfect proofs - according to the late Paul Erdös, who himself suggested many of the topics in this collection. The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest (undergraduate) mathematical background.

Springer, Verlag

From the reviews of the first edition: "Anyone who enjoys the logic and reasoning of mathematics and has a strong undergraduate mathematics background should enjoy this book...I would imagine that few mathematicians have seen all these proofs. The combination of ideas in many of the proofs should delight mathematicians everywhere." - MAA ONLINE The (mathematical) heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from number theory, geometry, analysis, combinatorics, and graph theory. Thirty beautiful examples are presented here. They are candidates for THE BOOK in which God records the perfect proofs - according to the late Paul Erdös, who suggested many of the topics in this collection. The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest (undergraduate) mathematical background. For this revised and expanded second edition several chapters have been revised and expanded, and three new chapters have been added.

Proofs from the Book

This revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises.
From the Reviews
"... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... "
Notices of the AMS, August 1999
"... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." 
LMS Newsletter, January 1999
"Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... "SIGACT News, December 2011.

See the best price to sell, buy, or rent books by Ziegler, Günter M.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Ziegler, Günter M.

See the best price to sell, buy, or rent books by Ziegler, Günter M.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Lectures on Polytopes (Graduate Texts in Mathematics, 152)

Lectures on Polytopes (Graduate Texts in Mathematics, 152)

Oriented Matroids (Encyclopedia of Mathematics and its Applications, Series Number 46)

Do I Count?: Stories from Mathematics (AK Peters/CRC Recreational Mathematics Series)

Do I Count? (AK Peters/CRC Recreational Mathematics Series)

Darf ich Zahlen?: Geschichten aus der Mathematik

Proofs from THE BOOK

Proofs from THE BOOK

Proofs from the Book

Proofs from THE BOOK