Excursions in the History of Mathematics

2012
ISBN: 978-0-8176-8267-5
Verlag: Birkhäuser Boston

Buch, Englisch, 347 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 723 g

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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Kleiner, Israel

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik

Inhaltsverzeichnis

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.