Algebraic Curves and Riemann Surfaces for Undergraduates : Springer : 9783031116155 : 3031116151 : 17 Jan 2023 : 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 cou