Math 252: Commutative Algebra and Algebraic Geometry (Spring
2004)
Instructor
Leslie Saper
Description
This is a basic introductory course in commutative
algebra for first year mathematics graduate students. Commutative algebra
forms the foundation on which algebraic geometry and algebraic number
theory are built, however it is an important course for all students
interested in studying geometry, topology, and mathematical physics. The
text will be Atiyah and MacDonald's classic book, however students may also
wish to consult the optional text by Eisenbud which expounds on the
geometry more fully.
Topics: Affine algebraic varieties, extension and contraction of ideals,
modules of fractions (localization), primary decomposition, integral
dependence, chain conditions, Noetherian rings, Dedekind domains,
completions, and (if time) dimension theory.
Text
- (required) Introduction to Commutative
Algebra, by M. F. Atiyah and I. G. MacDonald
- (optional) Commutative algebra with a view
toward algebraic geometry, by David Eisenbud, Graduate Texts in Math.,
vol. 150, Springer-Verlag, Berlin and New York, 1995
Homework
Weekly homework assignments. During the second half of
the semester each student will take over the teaching responsibilities for
one lecture.
Prerequisites
Math 251 (basic algebra) is a prerequisite.
Course Website
For more information see http://www.math.duke.edu/faculty/saper/Instruction/math252.S04.
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