LEADER 04948nam 22007695 450 001 9910300243903321 005 20220223180536.0 010 $a1-4939-3264-0 024 7 $a10.1007/978-1-4939-3264-1 035 $a(CKB)3710000000653417 035 $a(SSID)ssj0001666095 035 $a(PQKBManifestationID)16454784 035 $a(PQKBTitleCode)TC0001666095 035 $a(PQKBWorkID)15000328 035 $a(PQKB)10305735 035 $a(DE-He213)978-1-4939-3264-1 035 $a(MiAaPQ)EBC5595097 035 $a(PPN)193442442 035 $a(EXLCZ)993710000000653417 100 $a20160415d2015 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aTurning Points in the History of Mathematics /$fby Hardy Grant, Israel Kleiner 205 $a1st ed. 2015. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Birkhäuser,$d2015. 215 $a1 online resource (IX, 109 p. 51 illus., 13 illus. in color.) 225 1 $aCompact Textbooks in Mathematics,$x2296-4568 300 $aBibliographic Level Mode of Issuance: Monograph 311 0 $a1-4939-3263-2 327 $aAxiomatics - Euclid's and Hilbert's: From Material to Formal -- Solution by Radicals of the Cubic: From Equations to Groups and from Real to Complex Numbers -- Analytic Geometry: From the Marriage of Two Fields to the Birth of a Third -- Probability: From Games of Chance to an Abstract Theory -- Calculus: From Tangents and Areas to Derivatives and Integrals -- Gaussian Integers: From Arithmetic to Arithmetics -- Non-Euclidean Geometry: From One Geometry to Many -- Hypercomplex Numbers: From Algebra to Algebras -- The Infinite: From Potential to Actual -- Philosophy of Mathematics: From Hilbert to Gödel -- Some Further Turning Points -- Index. 330 $aThis book explores some of the major turning points in the history of mathematics, ranging from ancient Greece to the present, demonstrating the drama that has often been a part of its evolution. Studying these breakthroughs, transitions, and revolutions, their stumbling-blocks and their triumphs, can help illuminate the importance of the history of mathematics for its teaching, learning, and appreciation. Some of the turning points considered are the rise of the axiomatic method (most famously in Euclid), and the subsequent major changes in it (for example, by David Hilbert); the ?wedding,? via analytic geometry, of algebra and geometry; the ?taming? of the infinitely small and the infinitely large; the passages from algebra to algebras, from geometry to geometries, and from arithmetic to arithmetics; and the revolutions in the late nineteenth and early twentieth centuries that resulted from Georg Cantor?s creation of transfinite set theory. The origin of each turning point is discussed, along with the mathematicians involved and some of the mathematics that resulted. Problems and projects are included in each chapter to extend and increase understanding of the material. Substantial reference lists are also provided. Turning Points in the History of Mathematics will be a valuable resource for teachers of, and students in, courses in mathematics or its history. The book should also be of interest to anyone with a background in mathematics who wishes to learn more about the important moments in its development. 410 0$aCompact Textbooks in Mathematics,$x2296-4568 606 $aMathematics 606 $aHistory 606 $aMathematics 606 $aSocial sciences 606 $aGeometry 606 $aAlgebra 606 $aHistory of Mathematical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M23009 606 $aMathematics Education$3https://scigraph.springernature.com/ontologies/product-market-codes/O25000 606 $aMathematics in the Humanities and Social Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M32000 606 $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 615 0$aMathematics. 615 0$aHistory. 615 0$aMathematics. 615 0$aSocial sciences. 615 0$aGeometry. 615 0$aAlgebra. 615 14$aHistory of Mathematical Sciences. 615 24$aMathematics Education. 615 24$aMathematics in the Humanities and Social Sciences. 615 24$aGeometry. 615 24$aAlgebra. 676 $a510.9 700 $aGrant$b Hardy$4aut$4http://id.loc.gov/vocabulary/relators/aut$0348028 702 $aKleiner$b Israel$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300243903321 996 $aTurning Points in the History of Mathematics$92504780 997 $aUNINA