04199nam 22006375 450 991078922540332120230825135236.01-4612-1005-410.1007/978-1-4612-1005-4(CKB)3400000000089356(SSID)ssj0000821498(PQKBManifestationID)11448333(PQKBTitleCode)TC0000821498(PQKBWorkID)10878738(PQKB)11654783(DE-He213)978-1-4612-1005-4(MiAaPQ)EBC3075098(PPN)237994267(EXLCZ)99340000000008935620121227d1991 u| 0engurnn#008mamaatxtccrNumbers[electronic resource] /by Heinz-Dieter Ebbinghaus, Hans Hermes, Friedrich Hirzebruch, Max Koecher, Klaus Mainzer, Jürgen Neukirch, Alexander Prestel, Reinhold Remmert ; edited by John H. Ewing1st ed. 1991.New York, NY :Springer New York :Imprint: Springer,1991.1 online resource (XVIII, 398 p.)Readings in Mathematics ;123Translation of: Zahlen."With 24 illustrations."0-387-97202-1 0-387-97497-0 Includes bibliographical references.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.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.Readings in Mathematics ;123Number theoryNumber Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Number theory.Number Theory.512/.7Ebbinghaus Heinz-Dieter1939-authttp://id.loc.gov/vocabulary/relators/aut1068399Hermes Hansauthttp://id.loc.gov/vocabulary/relators/autHirzebruch Friedrichauthttp://id.loc.gov/vocabulary/relators/autKoecher Maxauthttp://id.loc.gov/vocabulary/relators/autMainzer Klausauthttp://id.loc.gov/vocabulary/relators/autNeukirch Jürgenauthttp://id.loc.gov/vocabulary/relators/autPrestel Alexanderauthttp://id.loc.gov/vocabulary/relators/autRemmert Reinholdauthttp://id.loc.gov/vocabulary/relators/autEwing John Hedthttp://id.loc.gov/vocabulary/relators/edtBOOK9910789225403321Numbers3840258UNINA