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MATH-217 Introduction to Algebraic Curves
Offered academic year 2011-2012
This course is an introduction to the theory of algebraic curves. We will start with lines and conics from elementary geometry. After a review of the algebra of polynomials we will consider curves in the real affine plane and discuss their singularities and tangents. Later we will discuss curves in more general fields and indicate applications to number theory. Time permitting, we shall see how to extend the real affine plane, by adding points at infinity, to the projective plane, a natural setting for curves. Projective curves and their singularities, tangents, and flexes will be discussed.
Credits: 3
Prerequisites: 208, or consent of instructor. Multivariable calculus, Linear Algebra, and Abstract Algebra are desirable prerequisites, along with some familiarity with the complex numbers
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