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Sinopsis
Designed for students preparing to engage in their first struggles to understand and write proofs and to read mathematics independently, this is well suited as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology. The book teaches in detail how to construct examples and non-examples to help understand a new theorem or definition; it shows how to discover the outline of a proof in the form of the theorem and how logical structures determine the forms that proofs may take. Throughout, the text asks the reader to pause and work on an example or a problem before continuing, and encourages the student to engage the topic at hand and to learn from failed attempts at solving problems. The book may also be used as the main text for a "transitions" course bridging the gap between calculus and higher mathematics. The whole concludes with a set of "Laboratories" in which students can practice the skills learned in the earlier chapters on set theory and function theory.
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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.
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An Accompaniment to Higher Mathematics (Undergraduate Texts in Mathematics)
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An Accompaniment to Higher Mathematics
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Springer New York, 1996
ISBN 10: 0387946179
ISBN 13: 9780387946177
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An Accompaniment to Higher Mathematics
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Paperback. Condición: Good. No Jacket. Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less. Nº de ref. del artículo: G0387946179I3N00
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An Accompaniment to Higher Mathematics
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Paperback. Condición: Very Good. No Jacket. Former library book; May have limited writing in cover pages. Pages are unmarked. ~ ThriftBooks: Read More, Spend Less. Nº de ref. del artículo: G0387946179I4N10
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An Accompaniment to Higher Mathematics (Undergraduate Texts in Mathematics)
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An Accompaniment to Higher Mathematics
Publicado por
Springer-Verlag, NY, 1996
ISBN 10: 0387946179
ISBN 13: 9780387946177
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Librería: Florida Mountain Book Co., Datil, NM, Estados Unidos de America
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Condición: Near Fine. Hardcover, [xvii], 198 pages. Near Fine condition. Size 9.5"x6.25". This book "is well suited as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology. The book teaches in detail how to construct examples and non-examples to help understand a new theorem or definition; it shows how to discover the outline of a proof in the form of the theorem and how logical structures determine the forms that proofs may take.' Book has very light exterior shelfwear, else As New, clean and unmarked. Nº de ref. del artículo: 009822
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An Accompaniment to Higher Mathematics (Undergraduate Texts in Mathematics)
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An accompaniment to higher mathematics / George R. Exner / Undergraduate texts in mathematics
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New York ; Berlin ; Singapore ; Tokyo ; Heidelberg ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara : Springer, 1996
ISBN 10: 0387946179
ISBN 13: 9780387946177
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Librería: Roland Antiquariat UG haftungsbeschränkt, Weinheim, Alemania
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Hardcover. 1st ed. 1996. XVII, 198 S. : graph. Darst. ; 24 cm 1st ed. 1996. Unread book. Very good condition. Minimum traces of storage. 9780387946177 Sprache: Englisch Gewicht in Gramm: 454. Nº de ref. del artículo: 201740
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An Accompaniment to Higher Mathematics (Undergraduate Texts in Mathematics)
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Accompaniment to Higher Mathematics
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