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Numbers / by Heinz-Dieter Ebbinghaus, Hans Hermes, Friedrich Hirzebruch, Max Koecher, Klaus Mainzer, Jürgen Neukirch, Alexander Prestel, Reinhold Remmert.

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This is a book about numbers - all kinds of numbers, from integers to p-adics, from rationals to octonions, from reals to infinitesimals. Who first used the standard notation for Â? Why was Hamilton obsessed with quaternions? What was the prospect for "quaternionic analysis" in the 19th ce...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Ebbinghaus, Heinz-Dieter
Other Authors: Hermes, Hans, Hirzebruch, Friedrich, Koecher, Max, Mainzer, Klaus, Neukirch, Jürgen, Prestel, Alexander, Remmert, Reinhold
Format: eBook
Language:English
Published: New York, NY : Springer New York, 1991.
Series:Graduate texts in mathematics. Readings in mathematics ; 123.
Subjects:
Mathematics.
Number theory.
Table of Contents:
  • A. From the Natural Numbers, to the Complex Numbers, to the p-adics
  • 1. Natural Numbers, Integers, and Rational Numbers
  • 2. Real Numbers
  • 3. Complex Numbers
  • 4. The Fundamental Theorem of Algebr
  • 5. What is??
  • 6. The p-Adic Numbers
  • B. Real Division Algebras
  • Repertory. Basic Concepts from the Theory of Algebras
  • 7. Hamilton's Quaternions
  • 8. The Isomorphism Theorems of FROBENIUS, HOPF and GELFAND-MAZUR
  • 9. CAYLEY Numbers or Alternative Division Algebras
  • 10. Composition Algebras. HURWITZ's Theorem-Vector-Product Algebras
  • 11. Division Algebras and Topology
  • C. Infinitesimals, Games, and Sets
  • 12. Nonsiandard Analysis
  • 13. Numbers and Games
  • 14. Set Theory and Mathematics
  • Name Index
  • Portraits of Famous Mathematicians.

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