This revised and enlarged 5th variation beneficial properties 4 new chapters, which include hugely unique and pleasant proofs for classics resembling the spectral theorem from linear algebra, a few newer jewels just like the non-existence of the Borromean earrings and different surprises.

**From the Reviews**

"... inside of PFTB (Proofs from The ebook) is certainly a glimpse of mathematical heaven, the place shrewdpermanent insights and gorgeous principles mix in miraculous and wonderful methods. there's significant wealth inside of its pages, one gem after one other. ... Aigner and Ziegler... write: "... all we provide is the examples that we have got chosen, hoping that our readers will proportion our enthusiasm approximately tremendous principles, shrewdpermanent insights and lovely observations." I do. ... "

*Notices of the AMS, August 1999*

"... This e-book is a excitement to carry and to examine: considerable margins, great pictures, instructive photos and lovely drawings ... it's a excitement to learn to boot: the fashion is apparent and interesting, the extent is as regards to hassle-free, the required heritage is given individually and the proofs are extraordinary. ..."

*LMS e-newsletter, January 1999*

"Martin Aigner and Günter Ziegler succeeded admirably in placing jointly a wide choice of theorems and their proofs that will unquestionably be within the e-book of Erdös. The theorems are so basic, their proofs so dependent and the rest open questio

ns so fascinating that each mathematician, despite speciality, can make the most of examining this publication. ... "

*SIGACT information, December 2011.*