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Table of contents (23 chapters)
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Front Matter
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From Calculus to Analysis
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Front Matter
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Number
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Front Matter
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Geometry
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Front Matter
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Keywords
About this book
What shall we say of this metamorphosis in passing from finite to infinite? Galileo, Two New Sciences As its title suggests, this book was conceived as a prologue to the study of "Why the calculus works"--otherwise known as analysis. It is in fact a critical reexamination of the infinite processes arising in elementary math ematics: Part II reexamines rational and irrational numbers, and their representation as infinite decimals; Part III examines our ideas of length, area, and volume; and Part IV examines the evolution of the modern function-concept. The book may be used in a number of ways: firstly, as a genuine pro logue to analysis; secondly, as a supplementary text within an analysis course, providing a source of elementary motivation, background and ex amples; thirdly, as a kind of postscript to elementary analysis-as in a senior undergraduate course designed to reinforce students' understanding of elementary analysis and of elementary mathematics by considering the mathematical and historical connections between them. But the contents of the book should be of interest to a much wider audience than this including teachers, teachers in training, students in their last year at school, and others interested in mathematics.
Authors and Affiliations
Bibliographic Information
Book Title: Infinite Processes
Book Subtitle: Background to Analysis
Authors: A. Gardiner
DOI: https://doi.org/10.1007/978-1-4612-5654-0
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag New York Inc. 1982
Softcover ISBN: 978-1-4612-5656-4Published: 12 October 2011
eBook ISBN: 978-1-4612-5654-0Published: 06 December 2012
Edition Number: 1
Number of Pages: X, 306
Topics: Real Functions