The Art of Proof: Basic Training for Deeper Mathematics (Undergraduate Texts in Mathematics) - Softcover

Beck, Matthias; Geoghegan, Ross

Softcover

ISBN 10: 1493940864 ISBN 13: 9781493940868

Publisher: Springer, 2016

Synopsis

Written to accompany a one- or two-semester course, this text combines rigor and wit to cover a plethora of topics from integers to uncountable sets. It teaches methods such as axiom, theorem, and proof through the mathematics rather than in abstract isolation.

About this title

From the Back Cover

The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. Some of the proofs are presented in detail, while others (some with hints) may be assigned to the student or presented by the instructor. The authors recommend that the two parts of the book -- Discrete and Continuous -- be given equal attention. The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions.

About the Author

Matthias Beck received his initial training in mathematics in Würzburg, Germany, received his Ph.D. in mathematics from Temple University, and is now associate professor of mathematics at San Francisco State University. He is the recipient of the 2013 MAA Haimo Award for Distinguished College or University Teaching of Mathematics. He is the author of a previously published Springer book, Computing the Continuous Discretely (with Sinai Robins).

Ross Geoghegan received his initial training in mathematics in Dublin, Ireland, received his Ph.D. in mathematics from Cornell University, and is now professor of mathematics at the State University of New York at Binghamton. He is the author of a previously published Springer book, Topological Methods in Group Theory.

Edition details

• Publisher: Springer
• Publication date: 2016
• ISBN 10: 1493940864
• ISBN 13: 9781493940868
• Binding: Paperback
• Language: English
• Number of pages: 203