04084nam 22006855 450 99650857150331620240223142259.03-031-11616-X10.1007/978-3-031-11616-2(MiAaPQ)EBC7179179(Au-PeEL)EBL7179179(CKB)26020962900041(DE-He213)978-3-031-11616-2(PPN)267811012(EXLCZ)992602096290004120230116d2022 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierAlgebraic Curves and Riemann Surfaces for Undergraduates[electronic resource] The Theory of the Donut /by Anil Nerode, Noam Greenberg1st ed. 2022.Cham :Springer International Publishing :Imprint: Springer,2022.1 online resource (456 pages)Print version: Nerode, Anil Algebraic Curves and Riemann Surfaces for Undergraduates Cham : Springer International Publishing AG,c2023 9783031116155 Includes bibliographical references and index.1 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.The 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.Algebraic geometryFunctions of complex variablesGlobal analysis (Mathematics)Manifolds (Mathematics)Algebraic GeometryFunctions of a Complex VariableGlobal Analysis and Analysis on ManifoldsCorbes algebraiquesthubGeometria algebraicathubSuperfícies de RiemannthubLlibres electrònicsthubAlgebraic geometry.Functions of complex variables.Global analysis (Mathematics).Manifolds (Mathematics).Algebraic Geometry.Functions of a Complex Variable.Global Analysis and Analysis on Manifolds.Corbes algebraiquesGeometria algebraicaSuperfícies de Riemann515.93Nerode Anil1932-48991Greenberg NoamMiAaPQMiAaPQMiAaPQBOOK996508571503316Algebraic Curves and Riemann Surfaces for Undergraduates3004754UNISA