Numbers

Front Cover
Springer Science & Business Media, 1991 - Mathematics - 391 pages
A book about numbers sounds rather dull. This one is not. Instead it is a lively story about one thread of mathematics-the concept of "number" told by eight authors and organized into a historical narrative that leads the reader from ancient Egypt to the late twentieth century. It is a story that begins with some of the simplest ideas of mathematics and ends with some of the most complex. It is a story that mathematicians, both amateur and professional, ought to know. Why write about numbers? Mathematicians have always found it diffi cult to develop broad perspective about their subject. While we each view our specialty as having roots in the past, and sometimes having connec tions to other specialties in the present, we seldom see the panorama of mathematical development over thousands of years. Numbers attempts to give that broad perspective, from hieroglyphs to K-theory, from Dedekind cuts to nonstandard analysis.
 

Contents

Natural Numbers Integers and Rational Numbers
9
Real Numbers
27
Complex Numbers
55
The Fundamental Theorem of Algebra
97
What is 𝛑?
123
The pAdic Numbers
155
Real Division Algebras
179
Introduction
181
CAYLEY Numbers or Alternative Division Algebras
249
Composition Algebras HURWITZs TheoremVectorProduct Algebras
265
Division Algebras and Topology
281
Infinitesimals Games and Sets
303
Nonstandard Analysis
305
Numbers and Games
329
Set Theory and Mathematics
355
Name Index
381

Repertory Basic Concepts from the Theory of Algebras
183
Hamiltons Quaternions
189
The Isomorphism Theorems of FROBENIUS HOPF and GELFANDMAJOR
221
Subject Index
387
Portraits of Famous Mathematicians
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