Complex Algebraic Curves [Paperback]

This book introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.Using only basic undergraduate mathematical techniques, the author introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.Using only basic undergraduate mathematical techniques, the author introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.This development of the theory of complex algebraic curves was one of the peaks of nineteenth century mathematics. They have many fascinating properties and arise in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.1. Introduction and background; 2. Foundations; 3. Algebraic properties; 4. Topological properties; 5. Riemann surfaces; 6. Differentials on Riemann surfaces; 7. Singular curves; Appendices. Kirwan should succeed admirably with her goal of showing senior undergraduates who perhaps do not plan to study mathematics beyond the bachelor's degree 'how the basic ideas of pure mathematics they had studied in previous years could be brought together in one of the showpieces of mathematics.' Choice ...worth serious consideration for those planning to teach such a course, and perhaps even more importantly, as an inspiration for mathematicians to offer such a course. The book offers us plenty to work with, and is an excellent contribution. S. Zdravkovska and Daniel M. Burns, Jr., Mathematical Reviews At last an introduction to the theory of algebraic curves lã#