Excursions in the History of Mathematics

• Κύριος συγγραφέας: Kleiner, Israel (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston : Birkhäuser Boston, 2012.
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; History.; Mathematical logic.; Number theory.; Mathematics > Study and teaching.; History of Mathematical Sciences.; Mathematics Education.; Number Theory.; Analysis.; Mathematical Logic and Foundations.; Mathematics, general.

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 who played major roles...

Πίνακας περιεχομένων:

• 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.