Israel Kleiner

Excursions in the History of Mathematics

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Birkhäuser / Birkhäuser Boston / Springer, Basel
• Artikelnr. des Verlages: 978-0-8176-8267-5
• 2012
• Seitenzahl: 372
• Erscheinungstermin: 1. Dezember 2011
• Englisch
• Abmessung: 241mm x 160mm x 25mm
• Gewicht: 694g
• ISBN-13: 9780817682675
• ISBN-10: 0817682678
• Artikelnr.: 33836585

Inhaltsangabe

A. Number Theory.- 1. Highlights in the History of Number Theory: 1700 BC - 2008.- 2. Fermat: The Founder of Modern Number Theory.- 3. Fermat's Last Theorem: From Fermat to Wiles.- B. Calculus/Analysis.- 4. A History of the Infinitely Small and the Infinitely Large in Calculus, with Remarks for the Teacher.- 5. A Brief History of the Function Concept.- 6. More on the History of Functions, Including Remarks on Teaching.- C. Proof.- 7. Highlights in the Practice of Proof: 1600 BC - 2009.- 8. Paradoxes: What are they Good for?.- 9. Principle of Continuity: 16th - 19th centuries.- 10. Proof: A Many-Splendored Thing.- D. Courses Inspired by History.- 11. Numbers as a Source of Mathematical Ideas.- 12. History of Complex Numbers, with a Moral for Teachers.- 13. A History-of-Mathematics Course for Teachers, Based on Great Quotations.- 14. Famous Problems in Mathematics.- E. Brief Biographies of Selected Mathematicians.- 15. The Biographies.- Index.

Rezensionen

From the reviews:
"The book under review was written with two main goals in mind: (1) to arose mathematics teachers' interest in the history of mathematics, and (2) to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component. ... The book can serve teachers of mathematics as well as mathematicians who want to get to know historical background of their subjects. It can be also useful to those teaching or studying the history of mathematics." (Roman Murawski, Zentralblatt MATH, Vol. 1230, 2012)