Universitext

Techniques of Constructive Analysis

Authors: Bridges, Douglas S., Vita, Luminita Simona

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About this Textbook

This text provides a rigorous, wide-ranging introduction to modern constructive analysis for anyone with a strong mathematical background who is interested in the challenge of developing mathematics algorithmically. The authors begin by outlining the history of constructive mathematics, and the logic and set theory that are used throughout the book. They then present a new construction of the real numbers, followed by the fundamentals of the constructive theory of metric and normed spaces; the lambda-technique (a special method that enables one to prove many results that appear, at first sight, to be nonconstructive); finite- dimensional and Hilbert spaces; and convexity, separation, and Hahn-Banach theorems. The book ends with a long chapter in which the work of the preceding ones is applied to operator theory and other aspects of functional analysis. Many results and proofs, especially in the later chapters, are of relatively recent origin.

The intended readership includes advanced undergraduates, postgraduates, and professional researchers in mathematics and theoretical computer science. With this book, the authors hope to spread the message that doing mathematics constructively is interesting and challenging, and produces new, deep computational information.

Reviews

From the reviews:

"Constructive mathematics is often mistakenly thought to be a branch of formal logic, or to involve recursive function theory. The recent Bridges-Vîta textbook is an exemplar of perseverance in efforts to correct this situation. For students at the graduate level it is an excellent introduction to constructive mathematics: for the more experienced reader it is a portal to some of the latest research using constructive methods." (Mark Mandelkern, Zentralblatt MATH, Vol. 1107 (9), 2007)

"Bridges and Vita (both, Univ. of Canterbury, New Zealand) offer a book, written jointly by an associate (Bridges) of the famous Errett Bishop … . Thorough index; plentiful exercises and references. Eminently suitable. Summing Up: Recommended. Upper-division undergraduates through faculty." (F. E. J. Linton, CHOICE, Vol. 44 (11), August, 2007)

"The authors have written a valuable introduction to constructive analysis, devoting the larger part of their space and efforts to subjects from constructive functional analysis, a field to which they have made important contributions themselves. … Without a doubt, this well-written book shows constructive analysis to be a serious and important subject. The authors, who have thought on their subject long and deeply, deserve our thanks." (Wim Veldman, Mathematical Reviews, Issue 2008 a)


Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook 50,28 €
price for Spain (gross)
  • ISBN 978-0-387-38147-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Softcover 62,39 €
price for Spain (gross)
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Bibliographic Information

Bibliographic Information
Book Title
Techniques of Constructive Analysis
Authors
Series Title
Universitext
Copyright
2006
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-38147-3
DOI
10.1007/978-0-387-38147-3
Softcover ISBN
978-0-387-33646-6
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XVI, 215
Topics