An Accompaniment to Higher Mathematics Paperback - 1996
by George R. Exner
First line
The argument of this chapter is simple: to understand the abstract ideas of mathematics you need to attach to them concrete examples.
From the rear cover
This text prepares undergraduate mathematics students to meet two challenges in the study of mathematics, namely, to read mathematics independently and to understand and write proofs. The book begins by teaching how to read mathematics actively, constructing examples, extreme cases, and non-examples to aid in understanding an unfamiliar theorem or definition (a technique familiar to any mathematician, but rarely taught); it provides practice by indicating explicitly where work with pencil and paper must interrupt reading. The book then turns to proofs, showing in detail how to discover the structure of a potential proof from the form of the theorem (especially the conclusion). It shows the logical structure behind proof farms (especially quantifier arguments), and analyzes, thoroughly, the often sketchy coding of these forms in proofs as they are ordinarily written. The common introductory material (such as sets and functions) is used for the numerous exercises, and the book concludes with a set of "Laboratories" on these topics in which the student can practice the skills learned in the earlier chapters. Intended for use as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology, the book may also be used as the main text for a "transitions" course bridging the gap between calculus and higher mathematics.
Details
- Title An Accompaniment to Higher Mathematics
- Author George R. Exner
- Binding Paperback
- Edition Corrected
- Pages 200
- Volumes 1
- Language ENG
- Publisher Springer, -
- Date 1996-01-05
- Illustrated Yes
- Features Bibliography, Illustrated, Index
- ISBN 9780387946177 / 0387946179
- Weight 1.06 lbs (0.48 kg)
- Dimensions 9.57 x 6.31 x 0.6 in (24.31 x 16.03 x 1.52 cm)
- Library of Congress subjects Proof theory
- Library of Congress Catalog Number 95044884
- Dewey Decimal Code 511.3
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