Numbers

Buch | Softcover
398 Seiten
1990
Springer-Verlag New York Inc.
978-0-387-97497-2 (ISBN)

Lese- und Medienproben

Numbers - Heinz-Dieter Ebbinghaus, Hans Hermes
80,24 inkl. MwSt
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.

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.

Reihe/Serie Graduate Texts in Mathematics ; 123
Readings in Mathematics
Einführung K. Lamotke
Übersetzer H.L.S. Orde
Zusatzinfo XVIII, 398 p.
Verlagsort New York, NY
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Naturwissenschaften Physik / Astronomie
ISBN-10 0-387-97497-0 / 0387974970
ISBN-13 978-0-387-97497-2 / 9780387974972
Zustand Neuware
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