Joseph J. Rotman: Journey into Mathematics: An Introduction to Proofs

Journey into Mathematics: An Introduction to Proofs



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Author: Joseph J. Rotman
Number of Pages: 256 pages
Published Date: 27 Dec 2006
Publisher: Dover Publications Inc.
Publication Country: New York, United States
Language: English
ISBN: 9780486453064
Download Link: Click Here
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Students learn how to read and write proofs by actually reading and writing them, asserts author Joseph J. Rotman, adding that merely "reading" about mathematics is no substitute for "doing" mathematics. In addition to teaching how to interpret and construct proofs, Professor Rotman's introductory text imparts other valuable mathematical tools and illustrates the intrinsic beauty and interest of mathematics. "Journey into Mathematics "offers a coherent story, with intriguing historical and etymological asides. The three-part treatment begins with the mechanics of writing proofs, including some very elementary mathematics--induction, binomial coefficients, and polygonal areas--that allow students to focus on the proofs without the distraction of absorbing unfamiliar ideas at the same time. Once they have acquired some geometric experience with the simpler classical notion of limit, they proceed to considerations of the area and circumference of circles. The text concludes with examinations of complex numbers and their application, via De Moivre's theorem, to real numbers.