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Excursions in the History of Mathematics by Israel Kleiner (auth.)[PDF]

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Ebook Details


Title: Excursions in the History of Mathematics
Language: English
Year: 2012
Author(s): Israel Kleiner (auth.)
Publisher: Birkhäuser Basel
Identifier: 0817682678,9780817682675,9780817682682
Format: pdf
Filesize: 3.7M
Pages: 362
Edition: 1
DOI: 10.1007/978-0-8176-8268-2


Ebook Description


This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians—Dedekind, Euler, Gauss, Hilbert, and Weierstrass—who played major roles in the historical events described in the first four parts of the work.

Excursions in the History of Mathematics was written with several goals in mind: to arouse mathematics teachers’ interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses.




Table Of Contents


Front Matter….Pages i-xxi
Front Matter….Pages 1-1
Highlights in the History of Number Theory: 1700 BC– 2008….Pages 3-30
Fermat: The Founder of Modern Number Theory….Pages 31-45
Fermat’s Last Theorem: From Fermat to Wiles….Pages 47-64
Front Matter….Pages 65-65
History of the Infinitely Small and the Infinitely Large in Calculus, with Remarks for the Teacher….Pages 67-101
A Brief History of the Function Concept….Pages 103-124
More on the History of Functions, with Remarks on Teaching….Pages 125-150
Front Matter….Pages 151-151
Highlights in the Practice of Proof: 1600 BC–2009….Pages 153-180
Paradoxes: What Are They Good For?….Pages 181-196
Principle of Continuity: Sixteenth–Nineteenth Centuries….Pages 197-214
Proof: A Many-Splendored Thing….Pages 215-236
Front Matter….Pages 237-237
Numbers as a Source of Mathematical Ideas….Pages 239-259
History of Complex Numbers, with a Moral for Teachers….Pages 261-272
A History-of-Mathematics Course for Teachers, Based on Great Quotations….Pages 273-284
Famous Problems in Mathematics….Pages 285-302
Front Matter….Pages 303-303
The Biographies….Pages 305-342
Back Matter….Pages 343-347

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