02321cam a22002775a 4500001000800000005001700008008004100025010001700066020004000083020001800123040003300141082001900174100002100193245006300214260003500277300003500312490003900347504005100386520138800437650003101825651001001856653002501866942000801891952012701899999001702026161753720171216160932.0951002t1996 nyua frb 001 0 eng d a 95044884 a0387946179 (hardcover : alk. paper) a9780387946177 aDLCbengcDLCdDLCdEG-ScBUE04a511.3bEXN2221 aExner, George R.13aAn accompaniment to higher mathematics /cGeorge R. Exner. aNew York :bSpringer,cc.1996. axvii, 198 p. :bill. ;c25 cm.0 aUndergraduate texts in mathematics aIncludes bibliographical references and index. aThis 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. 7aProof theory.2BUEsh96607 2BUEsh bENGGENcDecember2017 2ddc 00102ddc4070aMAINbMAINc1STd2017-12-16ePurchaseg158.40h24641l0o511.3 EXNp000042655r2022-08-24w2017-12-16yBB c25712d25684