001452252 000__ 03268cam\a22004697a\4500
001452252 001__ 1452252
001452252 003__ OCoLC
001452252 005__ 20230310003347.0
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001452252 007__ cr\un\nnnunnun
001452252 008__ 230128s2022\\\\sz\\\\\\ob\\\\001\0\eng\d
001452252 020__ $$a9783031116162$$q(electronic bk.)
001452252 020__ $$a303111616X$$q(electronic bk.)
001452252 020__ $$z3031116151
001452252 020__ $$z9783031116155
001452252 0247_ $$a10.1007/978-3-031-11616-2$$2doi
001452252 035__ $$aSP(OCoLC)1362500169
001452252 040__ $$aYDX$$beng$$cYDX$$dGW5XE
001452252 049__ $$aISEA
001452252 050_4 $$aQA565
001452252 08204 $$a516.3/52$$223/eng/20230130
001452252 1001_ $$aNerode, Anil,$$d1932-$$eauthor.
001452252 24510 $$aAlgebraic curves and Riemann surfaces for undergraduates :$$bthe theory of the donut /$$cAnil Nerode, Noam Greenberg.
001452252 260__ $$aCham :$$bSpringer,$$c2022.
001452252 300__ $$a1 online resource
001452252 504__ $$aIncludes bibliographical references and index.
001452252 5050_ $$a1 Introduction -- Part I Algebraic curves -- 2 Algebra -- 3 Affine space -- 4 Projective space -- 5 Tangents -- 6 Bezouts theorem -- 7 The elliptic group -- Part II Riemann Surfaces -- 8 Quasi-Euclidean spaces -- 9 Connectedness, smooth and simple -- 10 Path integrals -- 11 Complex differentiation -- 12 Riemann surfaces -- Part III Curves and surfaces -- 13 Curves are surfaces -- 14 Elliptic functions and the isomorphism theorem -- 15 Puiseux theory -- 16 A brief history of elliptic functions.
001452252 506__ $$aAccess limited to authorized users.
001452252 520__ $$aThe theory relating algebraic curves and Riemann surfaces exhibits the unity of mathematics: topology, complex analysis, algebra and geometry all interact in a deep way. This textbook offers an elementary introduction to this beautiful theory for an undergraduate audience. At the heart of the subject is the theory of elliptic functions and elliptic curves. A complex torus (or "donut") is both an abelian group and a Riemann surface. It is obtained by identifying points on the complex plane. At the same time, it can be viewed as a complex algebraic curve, with addition of points given by a geometric "chord-and-tangent" method. This book carefully develops all of the tools necessary to make sense of this isomorphism. The exposition is kept as elementary as possible and frequently draws on familiar notions in calculus and algebra to motivate new concepts. Based on a capstone course given to senior undergraduates, this book is intended as a textbook for courses at this level and includes a large number of class-tested exercises. The prerequisites for using the book are familiarity with abstract algebra, calculus and analysis, as covered in standard undergraduate courses.
001452252 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed January 30, 2023).
001452252 650_0 $$aCurves, Algebraic.
001452252 650_0 $$aGeometry, Algebraic.
001452252 650_0 $$aRiemann surfaces.
001452252 655_0 $$aElectronic books.
001452252 7001_ $$aGreenberg, Noam,$$eauthor.
001452252 77608 $$iPrint version: $$z3031116151$$z9783031116155$$w(OCoLC)1330690603
001452252 852__ $$bebk
001452252 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-11616-2$$zOnline Access$$91397441.1
001452252 909CO $$ooai:library.usi.edu:1452252$$pGLOBAL_SET
001452252 980__ $$aBIB
001452252 980__ $$aEBOOK
001452252 982__ $$aEbook
001452252 983__ $$aOnline
001452252 994__ $$a92$$bISE