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

PaulErdos ? likedtotalkaboutTheBook,inwhichGodmaintainstheperfect proofsformathematicaltheorems,followingthedictumofG. H. Hardythat there is no permanent place for ugly mathematics. Erdos ? also said that you need not believe in God but, as a mathematician, you should believe in The Book. A few years ago, we suggested to him to write up a ?rst (and very modest) approximation to The Book. He was enthusiastic about the idea and, characteristically, went to work immediately, ?lling page after page with his suggestions. Our book was supposed to appear in March 1998 as a present to Erdos ? ’ 85th birthday. With Paul’s unfortunate death in the summer of 1996, he is not listed as a co-author. Instead this book is dedicated to his memory. ? Paul Erdos We have no de?nition or characterization of what constitutes a proof from The Book: all we offer here is the examples that we have selected, h- ing that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations. We also hope that our readers will enjoy this despite the imperfections of our exposition. The selection is to a ? great extent in?uencedby Paul Erdos himself. A largenumberof the topics were suggested by him, and many of the proofs trace directly back to him, or were initiated by his supreme insight in asking the right question or in makingthe rightconjecture. So to a largeextentthisbookre?ectstheviews of Paul Erdos ? as to what should be considered a proof from The Book.

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