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An Accompaniment to Higher Mathematics (Undergraduate Texts in Mathematics)

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An Accompaniment to Higher Mathematics (Undergraduate Texts in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

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.

Description:

Includes bibliographical references (p. [189]-190) and index.

Table of Contents

Introduction.- Examples.- Informal Language and Proof.- Formal Language and Proof.- Laboratories.- Theoretical Apologia.- Hints.- References.- Index.

Product Details

ISBN:
9780387946177
Author:
Exner, George
Publisher:
Springer
Author:
Exner, George R.
Location:
New York, NY
Subject:
Logic
Subject:
Mathematical Analysis
Subject:
Proof theory
Subject:
"Corrected second printing"--T.p. verso.
Subject:
Analysis
Subject:
Topology
Subject:
Mathematics-Logic and Philosophy
Subject:
Mathematical Logic and Foundations
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Global analysis (Mathematics)
Subject:
Logic, symbolic and mathematical
Copyright:
Edition Number:
2
Edition Description:
1st ed. 1996. Corr. 3rd printing
Series:
Undergraduate Texts in Mathematics
Series Volume:
104-143
Publication Date:
September 1997
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
217
Dimensions:
235 x 155 mm 1090 gr

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Related Subjects

History and Social Science » Economics » General
Reference » Science Reference » Technology
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » Logic and Philosophy
Science and Mathematics » Mathematics » Real Analysis
Science and Mathematics » Mathematics » Set Theory
Science and Mathematics » Mathematics » Topology

An Accompaniment to Higher Mathematics (Undergraduate Texts in Mathematics) New Trade Paper
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$67.25 In Stock
Product details 217 pages Springer-Verlag - English 9780387946177 Reviews:
"Synopsis" by , 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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