02182cam a22002655a 4500
1617537
20171216160932.0
951002t1996 nyua frb 001 0 eng d
95044884
0387946179 (hardcover : alk. paper)
9780387946177
DLC
eng
DLC
DLC
EG-ScBUE
511.3
EXN
22
Exner, George R.
An accompaniment to higher mathematics /
George R. Exner.
New York :
Springer,
c.1996.
xvii, 198 p. :
ill. ;
25 cm.
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.
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