Happy Holidays! Over 120,000 eBooks at just 19.99 each— Pick a favorite today

Proofs from THE BOOK

Authors: Aigner, Martin, Ziegler, Günter M.

  • Revised and enlarged fifth edition
  • Four new chapters
  • Presents some recent jewels and surprises
see more benefits

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-662-44205-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.99
price for USA
  • ISBN 978-3-662-44204-3
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
Softcover $59.99
price for USA
  • ISBN 978-3-662-49592-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

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 questio

ns so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... "

SIGACT News, December 2011.

About the authors

Martin Aigner received his Ph.D. from the University of Vienna and has been professor of mathematics at the Freie Universität Berlin since 1974. He has published in various fields of combinatorics and graph theory and is the author of several monographs on discrete mathematics, among them the Springer books Combinatorial Theory and A Course on Enumeration. Martin Aigner is a recipient of the 1996 Lester R. Ford Award for mathematical exposition of the Mathematical Association of America MAA.

 

Günter M. Ziegler received his Ph.D. from M.I.T. and has been professor of mathematics in Berlin – first at TU Berlin, now at Freie Universität – since 1995. He has published in discrete mathematics, geometry, topology, and optimization, including the Lectures on Polytopes with Springer, as well as „Do I Count? Stories from Mathematics“. Günter M. Ziegler is a recipient of the 2006 Chauvenet Prize of the MAA for his expository writing and the 2008 Communicator award of the German Science Foundation.

 

Martin Aigner and Günter M. Ziegler have started their work on Proofs from THE BOOK in 1995 together with Paul Erdös. The first edition of this book appeared in 1998 – it has since been translated into 13 languages: Brazilian, Chinese, German, Farsi, French, Hungarian, Italian, Japanese, Korean, Polish, Russian, Spanish, and Turkish.

Reviews

“This book by Aigner and Ziegler, now in its fifth edition, seeks to pay homage to the late Paul Erdõs by attempting to provide an approximation of ‘The Book.’ … Throughout, illustrations and figures are used to support the arguments in the main text; these can greatly help the readability of the proofs, especially for novices like me. … the book is a marvelous project and this new edition provides a good amount of fresh material.” (Harry Strange, Computing Reviews, March, 2015)


Table of contents (44 chapters)

  • Six proofs of the infinity of primes

    Aigner, Martin (et al.)

    Pages 3-8

  • Bertrand’s postulate

    Aigner, Martin (et al.)

    Pages 9-14

  • Binomial coefficients are (almost) never powers

    Aigner, Martin (et al.)

    Pages 15-18

  • Representing numbers as sums of two squares

    Aigner, Martin (et al.)

    Pages 19-24

  • The law of quadratic reciprocity

    Aigner, Martin (et al.)

    Pages 25-32

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-662-44205-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.99
price for USA
  • ISBN 978-3-662-44204-3
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
Softcover $59.99
price for USA
  • ISBN 978-3-662-49592-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Proofs from THE BOOK
Authors
Copyright
2014
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-44205-0
DOI
10.1007/978-3-662-44205-0
Hardcover ISBN
978-3-662-44204-3
Softcover ISBN
978-3-662-49592-6
Edition Number
5
Number of Pages
VIII, 308
Number of Illustrations and Tables
246 b/w illustrations, 9 illustrations in colour
Topics