Numbers

H.-D. Ebbinghaus ... [et al.] ; with an introduction by K. Lamotke ; translated by H.L.S. Orde ; edited by J.H. Ewing

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.

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[目次]

  • 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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この本の情報

書名 Numbers
著作者等 Ebbinghaus, Heinz-Dieter
Ewing, John H.
Hermes, H.
Hirzebruch, Friedrich
Koecher, Max
Mainzer, Klaus
Neukirch, Jürgen
Prestel, Alexander
Remmert, Reinhold
etc.
書名別名 Zahlen, Grundwissen Mathematik 1
シリーズ名 Graduate texts in mathematics
出版元 Springer-Verlag
刊行年月 c1990
版表示 1st ed. 1991. Corr. 3rd printing 1996
ページ数 xviii, 391 p.
大きさ 25 cm
ISBN 0387974970
3540972021
3540974970
0387972021
NCID BA10726367
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言語 英語
原文言語 ドイツ語
出版国 アメリカ合衆国
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