LEADER 04086nam 22006855 450 001 9910644265203321 005 20240223142259.0 010 $a3-031-11616-X 024 7 $a10.1007/978-3-031-11616-2 035 $a(MiAaPQ)EBC7179179 035 $a(Au-PeEL)EBL7179179 035 $a(CKB)26020962900041 035 $a(DE-He213)978-3-031-11616-2 035 $a(PPN)267811012 035 $a(EXLCZ)9926020962900041 100 $a20230116d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAlgebraic Curves and Riemann Surfaces for Undergraduates$b[electronic resource] $eThe Theory of the Donut /$fby Anil Nerode, Noam Greenberg 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (456 pages) 311 08$aPrint version: Nerode, Anil Algebraic Curves and Riemann Surfaces for Undergraduates Cham : Springer International Publishing AG,c2023 9783031116155 320 $aIncludes bibliographical references and index. 327 $a1 Introduction -- Part I Algebraic curves -- 2 Algebra -- 3 Affine space -- 4 Projective space -- 5 Tangents -- 6 Bézout?s theorem -- 7 The elliptic group -- Part II Riemann Surfaces -- 8 Quasi-Euclidean spaces -- 9 Connectedness, smooth and simple -- 10 Path integrals -- 11 Complex differentiation -- 12 Riemann surfaces -- Part III Curves and surfaces -- 13 Curves are surfaces -- 14 Elliptic functions and the isomorphism theorem -- 15 Puiseux theory -- 16 A brief history of elliptic functions. 330 $aThe theory relating algebraic curves and Riemann surfaces exhibits the unity of mathematics: topology, complex analysis, algebra and geometry all interact in a deep way. This textbook offers an elementary introduction to this beautiful theory for an undergraduate audience. At the heart of the subject is the theory of elliptic functions and elliptic curves. A complex torus (or ?donut?) is both an abelian group and a Riemann surface. It is obtained by identifying points on the complex plane. At the same time, it can be viewed as a complex algebraic curve, with addition of points given by a geometric ?chord-and-tangent? method. This book carefully develops all of the tools necessary to make sense of this isomorphism. The exposition is kept as elementary as possible and frequently draws on familiar notions in calculus and algebra to motivate new concepts. Based on a capstone course given to senior undergraduates, this book is intended as a textbook for courses at this level and includes a large number of class-tested exercises. The prerequisites for using the book are familiarity with abstract algebra, calculus and analysis, as covered in standard undergraduate courses. 606 $aAlgebraic geometry 606 $aFunctions of complex variables 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aAlgebraic Geometry 606 $aFunctions of a Complex Variable 606 $aGlobal Analysis and Analysis on Manifolds 606 $aCorbes algebraiques$2thub 606 $aGeometria algebraica$2thub 606 $aSuperfícies de Riemann$2thub 608 $aLlibres electrònics$2thub 615 0$aAlgebraic geometry. 615 0$aFunctions of complex variables. 615 0$aGlobal analysis (Mathematics). 615 0$aManifolds (Mathematics). 615 14$aAlgebraic Geometry. 615 24$aFunctions of a Complex Variable. 615 24$aGlobal Analysis and Analysis on Manifolds. 615 7$aCorbes algebraiques 615 7$aGeometria algebraica 615 7$aSuperfícies de Riemann 676 $a515.93 700 $aNerode$b Anil$f1932-$048991 702 $aGreenberg$b Noam 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910644265203321 996 $aAlgebraic Curves and Riemann Surfaces for Undergraduates$93004754 997 $aUNINA