Author | Ebbinghaus, Heinz-Dieter. author |
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Title | Numbers [electronic resource] / by Heinz-Dieter Ebbinghaus, Hans Hermes, Friedrich Hirzebruch, Max Koecher, Klaus Mainzer, Jรผrgen Neukirch, Alexander Prestel, Reinhold Remmert |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1991 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1005-4 |
Descript | XVIII, 398 p. online resource |
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. Hamiltonโs Quaternions -- 8. The Isomorphism Theorems of FROBENIUS, HOPF and GELFAND-MAZUR -- 9. CAYLEY Numbers or Alternative Division Algebras -- 10. Composition Algebras. HURWITZโs 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