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- catalog abstract "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 famililar 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 forms (especially quantifier arguments), and analyzes, thoroughly, the often sketchy coding of these forms in proofs as they are ordinarily written. The common introductroy 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 gab between calculus and higher mathematics.".
- catalog contributor b9872937.
- catalog created "c1996.".
- catalog date "1996".
- catalog date "c1996.".
- catalog dateCopyrighted "c1996.".
- catalog description "Includes bibliographical references (p. [189]-190) and index.".
- catalog description "Introduction -- Examples -- Informal Language and Proof -- Formal Language and Proof -- Laboratories -- Theoretical Apologia -- Hints -- References -- Index.".
- catalog description "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 famililar 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 forms (especially quantifier arguments), and analyzes, thoroughly, the often sketchy coding of these forms in proofs as they are ordinarily written. The common introductroy 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 gab between calculus and higher mathematics.".
- catalog extent "xvii, 198 p. :".
- catalog identifier "0387946179 (hardcover : alk. paper)".
- catalog isPartOf "Undergraduate texts in mathematics".
- catalog issued "1996".
- catalog issued "c1996.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "511.3 20".
- catalog subject "Global analysis (Mathematics).".
- catalog subject "Mathematics.".
- catalog subject "Proof theory.".
- catalog subject "QA9.54 .E96 1996".
- catalog subject "Topology.".
- catalog tableOfContents "Introduction -- Examples -- Informal Language and Proof -- Formal Language and Proof -- Laboratories -- Theoretical Apologia -- Hints -- References -- Index.".
- catalog title "An accompaniment to higher mathematics / George R. Exner.".
- catalog type "text".