Instructor: Chad Schoen
Time and Place: MWF 8:45 - 9:35, room 205 Physics Building.
Target audience: This is a basic, introductory course in commutative algebra and algebraic geometry suitable for anyone who has taken math 251.
Course Description : The course will introduce algebraic geometry which is a core subject in mathematics. Very loosely speaking algebraic geometry is that branch of mathematics which studies the geometry of figures defined by polynomial equations in several variables. The simplest examples of such figures are familiar from high school (lines, planes, conic sections, caustics, cardoid, four leaved rose,...). We will quickly see that this list barely scratchs the surface. Furthermore, we will quickly find that algebraic geometry is based on commutative algebra and that progress in geometry requires us to develope basic themes in commutative algebra including extension and contraction of ideals, finite and integral extensions of rings, localization, completion, and dimension theory. Commutative algebra is also the basis for much of algebraic number theory. However this course will be strongly biased towards algebraic geometry. To keep things from getting too complicated we will focus on affine algebraic varieties. The course should prepare participants for Math 273 in which quasi-projective algebraic varieties are defined and studied. Math 252 is an essential course for students considering working in algebraic geometry or a related algebraic field. It is a prerequisite for all subsequent courses in algebraic geometry and for some courses in several complex variables and algebraic number theory.
Text: The course will not follow a text as closely as Math 251 did. A larger fraction of the homework will come from handouts. An excellent reference for commutative algebra is: Introduction to Commutative Algebra, by Atiyah and Macdonald
Homework: Weekly homework assignments.
Grading : Grading will be based on homework and any projects and exams. A final exam is possible. A mid-term is unlikely.