Logo - springer
Slogan - springer

Mathematics | The Art of Proof (Reviews)

The Art of Proof

Basic Training for Deeper Mathematics

Beck, Matthias, Geoghegan, Ross

2010, XXII, 182 p. 23 illus.

Available Formats:

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.


(net) price for USA

ISBN 978-1-4419-7023-7

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase

learn more about Springer eBooks

add to marked items


Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.


(net) price for USA

ISBN 978-1-4419-7022-0

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days

add to marked items

From the reviews:

"The Art of Proof is a surprising union of rigor with taste and wit.  The authors take a hard-core axiomatic approach, but the writing is never dry.  Instead, topics are carefully chosen and meticulously developed with grace and humor, careful attention to detail, and just the right number of skill-building exercises and thought-provoking problems.

"The text is spare—well under two hundred pages—but contains a thorough axiomatic development of the integers and the reals, along with non-standard optional topics such as Cayley graphs and generating functions.  Instead of the standard scattershot "symbolic logic-set theory-functions-proof by contradiction-zzzz..." books, this text keeps its focus on just a few fundamental ideas, of which induction is the most important.  This helps my students to  feel that they are participants in a grand undertaking—the construction of a number system—rather than passive victims of one proof technique after another." —Paul Zeitz (Mathematics Professor at the University of San Francisco)

“This qualitative transition presents a most acute pedagogical challenge. … This book does feature definite mathematical content, contrasting with works that aim at decoupling purely logical apparatus from strictly mathematical concerns. … The authors write with the authority of research mathematicians and clearly mean to open that avenue to students. Summing Up: Recommended. Upper-division undergraduates through professionals.” (D. V. Feldman, Choice, Vol. 48 (8), April, 2011)

“This book offers an approach well-balanced between rigor and clarifying simplification. Dilbert and Foxtrot cartoons with philosophical quotes presage the introduction of axioms and preliminary propositions. This graceful and witty blend succeeds well in a textbook for a post-calculus course transitioning a student to higher mathematics. The Art of Proof can also well serve independent readers looking for a solitary path to a vista on higher mathematics.” (Tom Schulte, The Mathematical Association of America, November, 2010)

“This is an undergraduate text to extend, in a deeper and formal way, the usual initial knowledge of mathematics. The book deals with classical topics like integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, uncountable sets … . The publication may be useful for people using the book to teach a course on the above mentioned topics. … The aim behind this textbook is teaching how to read and write mathematics as well as understanding key methods and concepts.” (Claudi Alsina, Zentralblatt MATH, Vol. 1198, 2010)



Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Mathematical Logic and Foundations.

Additional information