Math 389: Topics in Field Extensions, Fall 2006
Instructor:
Chad Schoen
Time:
T-Th 1:15 - 2:30, August 29-September 26, 2006
Location:
Room 227 Physics Building.
Prerequisites:
Math 251. The course will make free use of basic notions about rings,
ideals, modules, principal ideal domains, algebraic and transcendental
field extensions, separable and inseparable field extensions and Galois theory.
Math 358 (Algebraic Number Theory) or Math 252 (Commutative Algebra).
The course will make free use of basic notions of commutative algebra
such as integral extension of rings, integral closure, finitely generated
modules over Noetherian rings. Basic theorems about Dedekind domains
and discrete valuations will be reviewed very rapidly.
About the course:
The course will treat important topics in the theory of field extensions
beyond those covered in Math 251. This material is considered basic material by algebraists,
algebraic geometers and number theorists. The material does not overlap with
the content of the standard algebraic geometry and number theory courses taught
regularly at Duke. It will complement such courses.
Intended audience:
Graduate students at any level who have completed Math 251 and Math 358 (or Math 252)
especially those who are considering working in algebra, algebraic geometry or number theory.
Any student, undergraduate or graduate, who has the prerequisites and is interested in
expanding his/her general mathematical knowledge in this area.
Level of difficulty:
This course will probably go a little more quickly than Math 358, which
went more quickly than Math 251.
Text:
The course will not follow a text closely. References will be given for
individual topics and theorems. There is no recommended text.