Numbers
著者
書誌事項
Numbers
（Graduate texts in mathematics, 123 . Readings in mathematics）
Springer-Verlag, c1990
- : us : hard
- : us : soft
- : gw : hard
- : gw : soft
- タイトル別名
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Zahlen, Grundwissen Mathematik 1
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注記
Authors: H.-D. Ebbinghaus, H. Hermes, F. Hirzebruch, M. Koecher, K. Mainzer, J. Neukirch, A. Prestel, R. Remmert
Includes bibliographical references and indexes
内容説明・目次
- 巻冊次
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: us : hard ISBN 9780387972022
内容説明
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 A, ? Why was Hamilton obsessed with quaternions? What was the prospect for quaternionic analysis in the 19th century? This is the story about one of the major threads of mathematics over thousands of years. It is a story that will give the reader both a glimpse of the mystery surrounding imaginary numbers in the 17th century and also a view of some major developments in the 20th.
- 巻冊次
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: us : soft ISBN 9780387974972
内容説明
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.
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.
- 巻冊次
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: gw : soft ISBN 9783540974970
内容説明
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 6? Why was Hamilton obsessed with quaternions? What was the prospect for "quaternionic analysis" in the 19th century? This is the story about one of the major threads of mathematics over thousands of years. It is a story that will give the reader both a glimpse of the mystery surrounding imaginary numbers in the 17th century and also a view of some major developments in the 20th.
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