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Foundations of Real and Abstract Analysis by Douglas S. Bridges at Abbey's Bookshop,
Foundations of Real and Abstract Analysis
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Douglas S. Bridges

Foundations of Real and Abstract Analysis

Douglas S. Bridges

$130.95   $105.07

Paperback

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English
Springer-Verlag New York Inc.
07 March 2013
Management decision making; Operational research; Real analysis, real variables
Series: Graduate Texts in Mathematics
The core of this book, Chapters three through five, presents a course on metric, normed, and Hilbert spaces at the senior/graduate level. The motivation for each of these chapters is the generalisation of a particular attribute of the n Euclidean space R: in Chapter 3, that attribute is distance; in Chapter 4, length; and in Chapter 5, inner product. In addition to the standard topics that, arguably, should form part of the armoury of any graduate student in mathematics, physics, mathematical economics, theoretical statistics,. . . , this part of the book contains many results and exercises that are seldom found in texts on analysis at this level. Examples of the latter are Wong’s Theorem (3.3.12) showing that the Lebesgue covering property is equivalent to the uniform continuity property, and Motzkin’s result (5. 2. 2) that a nonempty closed subset of Euclidean space has the unique closest point property if and only if it is convex. The sad reality today is that, perceiving them as one of the harder parts of their mathematical studies, students contrive to avoid analysis courses at almost any cost, in particular that of their own educational and technical deprivation. Many universities have at times capitulated to the negative demand of students for analysis courses and have seriously watered down their expectations of students in that area. As a result, mathematics majors are graduating, sometimes with high honours, with little exposure to anything but a rudimentary course or two on real and complex analysis, often without even an introduction to the Lebesgue integral.
By:  
Imprint:   Springer-Verlag New York Inc.
Country of Publication:   United States
Edition:   Softcover reprint of the original 1st ed. 1998
Volume:   174
Dimensions:   Height: 235mm,  Width: 155mm,  Spine: 18mm
Weight:   528g
ISBN:   9781475771619
ISBN 10:   1475771614
Series:   Graduate Texts in Mathematics
Pages:   322
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active

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