An accompaniment to higher mathematics / George R. Exner.Material type: TextSeries: Undergraduate texts in mathematicsPublication details: New York : Springer, c.1996.Description: xvii, 198 p. : ill. ; 25 cmISBN:
- 0387946179 (hardcover : alk. paper)
- 511.3 EXN 22
|Item type||Current library||Call number||Vol info||Status||Date due||Barcode||Item holds|
|Book - Borrowing||Central Library First floor||511.3 EXN (Browse shelf(Opens below))||24641||Available||000042655|
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|511.3 DIM Discrete Mathematical Problems with Medical Applications :||511.3 DNA DNA computing :||511.3 DNA DNA computing :||511.3 EXN An accompaniment to higher mathematics /||511.3 GER Introduction to mathematical structures and proofs /||511.3 GOD Introducing the theory of computation /||511.3 GOL Logics of time and computation /|
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.