MATH 421 Algebraic Geometry (Not offered 2006-2007; to be offered 2007-2008) (Q)
Algebraic Geometry studies the geometry of polynomials and lies in the
intersection of a tremendous amount of current mathematics, ranging from
number theory to robotics. This course will be an introduction, emphasizing
curves in the plane. In particular, we will study conics and cubics (books are
written about the geometry of cubics; the depth of the ideas involved with cubics
is amazing). Fundamental notions such as projective space, elliptic integrals,
algebraic varieties, genus of a curve, the Riemann-Roch theorem, and rational
points will be introduced.
Evaluation will be based primarily on homework and exams.
Prerequisites: Mathematics 312 or 315 or 317 or permission of instructor.