02372cam a2200325 i 4500 1617537 EG-ScBUE 20240908093807.0 951002t1996 nyua f b 001 0 eng d 0387946179 (hardcover : alk. paper) 9780387946177 DLC eng rda DLC DLC EG-ScBUE 511.3 EXN 22 Exner, George R., author. An accompaniment to higher mathematics / George R. Exner. New York : Springer, [1996] c1996 xvii, 198 pages : illustrations ; 25 cm. rdacontent text txt unmediated rdamedia n volume nc rdacarrier Undergraduate texts in mathematics Includes bibliographical references and index. 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. Proof theory. BUEsh 6607 BUEsh ENGGEN December2017 Reading book ddc BB 25712 25684 0 0 ddc 0 0 Alahram MAIN MAIN 1ST 2017-12-16 Purchase 158.40 24641 0 511.3 EXN 000042655 2025-07-15 00:00:00 2017-12-16 BB