Numbers
Author(s)
Bibliographic Information
Numbers
（Graduate texts in mathematics, 123 . Readings in mathematics）
Springer, 1995 printing, c1991
Corr. 3rd print
- : pbk
- Other Title
-
Zahlen, Grundwissen Mathematik 1
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Note
Includes bibliographical references and indexes
Description and Table of Contents
Description
This book is about all kinds of numbers, from rationals to octonians, reals to infinitesimals. It is a story about a major thread of mathematics over thousands of years, and it answers everything from why Hamilton was obsessed with quaternions to what the prospect was for quaternionic analysis in the 19th century. It glimpses the mystery surrounding imaginary numbers in the 17th century and views some major developments of the 20th century.
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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