Foundations of Real and Abstract Analysis

Douglas S. Bridges

ISBN 10: 1475771614 / ISBN 13: 9781475771619

Edité par Springer New York, Chapman And Hall/CRC Mär 2013, 2013

A propos de cet article

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 344 pp. Englisch.

N° de réf. du vendeur 9781475771619

Détails bibliographiques

• Titre: Foundations of Real and Abstract Analysis
• Éditeur: Springer New York, Chapman And Hall/CRC Mär 2013
• Date de parution: 2013
• Langue: anglais
• ISBN à 10 chiffres: 1475771614
• ISBN à 13 chiffres: 9781475771619
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 235 L x 155 H x 19 P (en millimètres) 235 millimètres de largeur par 155 millimètres de hauteur par 19 millimètres de profondeur
• Poids: 522 grammes

A propos de ce titre

Synopsis

This book represents a first course in the theory of metric, normed, and Hilbert spaces, and is intended (i) for mathematicians, physicists, and others who may need only one course that provides the elements of that subject, and (ii) as a foundation for more advanced courses in analysis, topology, and geometry for pure mathematicians. Prerequisites is a knowledge of the basic ideas of limits and continuity.