Numbers.

Graduate Texts in Mathematics -- Editor's page -- Copyright -- Preface to the English Edition -- Preface to Second Edition -- Preface to First Edition -- Contents -- Introduction -- Part 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 Algebra -- 5 What is π? -- 6 The p-Adic Numbers -- Part B Real Division Algebras -- Introduction -- 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 -- Part C Infinitesimals, Games, and Sets -- 12 Nonstandard Analysis -- 13 Numbers and Games -- 14 Set Theory and Mathematics -- Name Index -- Subject Index -- Portraits of Famous Mathematicians.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.