LEADER 04190nam 22006375 450 001 9910480566603321 005 20200704032512.0 010 $a1-4612-1005-4 024 7 $a10.1007/978-1-4612-1005-4 035 $a(CKB)3400000000089356 035 $a(SSID)ssj0000821498 035 $a(PQKBManifestationID)11448333 035 $a(PQKBTitleCode)TC0000821498 035 $a(PQKBWorkID)10878738 035 $a(PQKB)11654783 035 $a(DE-He213)978-1-4612-1005-4 035 $a(MiAaPQ)EBC3075098 035 $a(PPN)237994267 035 $a(EXLCZ)993400000000089356 100 $a20121227d1991 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aNumbers$b[electronic resource] /$fby Heinz-Dieter Ebbinghaus, Hans Hermes, Friedrich Hirzebruch, Max Koecher, Klaus Mainzer, Jürgen Neukirch, Alexander Prestel, Reinhold Remmert ; edited by John H. Ewing 205 $a1st ed. 1991. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1991. 215 $a1 online resource (XVIII, 398 p.) 225 1 $aReadings in Mathematics ;$v123 300 $aTranslation of: Zahlen. 300 $a"With 24 illustrations." 311 $a0-387-97202-1 311 $a0-387-97497-0 320 $aIncludes bibliographical references. 327 $aA. 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. 330 $aA book about numbers sounds rather dull. This one is not. Instead it is a lively story about one thread of mathematics-the concept of "number"­ told by eight authors and organized into a historical narrative that leads the reader from ancient Egypt to the late twentieth century. It is a story that begins with some of the simplest ideas of mathematics and ends with some of the most complex. It is a story that mathematicians, both amateur and professional, ought to know. Why write about numbers? Mathematicians have always found it diffi­ cult to develop broad perspective about their subject. While we each view our specialty as having roots in the past, and sometimes having connec­ tions to other specialties in the present, we seldom see the panorama of mathematical development over thousands of years. Numbers attempts to give that broad perspective, from hieroglyphs to K-theory, from Dedekind cuts to nonstandard analysis. 410 0$aReadings in Mathematics ;$v123 606 $aNumber theory 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 615 0$aNumber theory. 615 14$aNumber Theory. 676 $a512/.7 700 $aEbbinghaus$b Heinz-Dieter$4aut$4http://id.loc.gov/vocabulary/relators/aut$046491 702 $aHermes$b Hans$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aHirzebruch$b Friedrich$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aKoecher$b Max$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMainzer$b Klaus$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aNeukirch$b Jürgen$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aPrestel$b Alexander$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aRemmert$b Reinhold$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aEwing$b John H$4edt$4http://id.loc.gov/vocabulary/relators/edt 906 $aBOOK 912 $a9910480566603321 996 $aNumbers$9924836 997 $aUNINA