E-Book, Englisch, 182 Seiten
Beck / Geoghegan The Art of Proof
1. Auflage 2010
ISBN: 978-1-4419-7023-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
Basic Training for Deeper Mathematics
E-Book, Englisch, 182 Seiten
Reihe: Undergraduate Texts in Mathematics
ISBN: 978-1-4419-7023-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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. 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.
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 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.
