Overview
- Offers a fresh approach to a core subject
- Provides a gentle and clear introduction without sacrificing rigour or accuracy
- Includes worked examples and exercises designed to reinforce the underlying concepts
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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About this book
From the point of view of strict logic, a rigorous course on real analysis should precede a course on calculus. Strict logic, is, however, overruled by both history and practicality. Historically, calculus, with its origins in the 17th century, came first, and made rapid progress on the basis of informal intuition. Not until well through the 19th century was it possible to claim that the edifice was constructed on sound logical foundations. As for practicality, every university teacher knows that students are not ready for even a semi-rigorous course on analysis until they have acquired the intuitions and the sheer technical skills that come from a traditional calculus course. 1 Real analysis, I have always thought, is the pons asinorv.m of modern mathematics. This shows, I suppose, how much progress we have made in two thousand years, for it is a great deal more sophisticated than the Theorem of Pythagoras, which once received that title. All who have taught the subject know how patient one has to be, for the ideas take root gradually, even in students of good ability. This is not too surprising, since it took more than two centuries for calculus to evolve into what we now call analysis, and even a gifted student, guided by an expert teacher, cannot be expected to grasp all of the issues immediately.
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Table of contents (9 chapters)
Authors and Affiliations
Bibliographic Information
Book Title: Real Analysis
Authors: John M. Howie
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-1-4471-0341-7
Publisher: Springer London
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag London 2001
Softcover ISBN: 978-1-85233-314-0Published: 28 March 2001
eBook ISBN: 978-1-4471-0341-7Published: 06 December 2012
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: X, 276
Number of Illustrations: 13 b/w illustrations
Topics: Analysis, Real Functions