References: There is NO official textbook, the instructor will try to develop a self-contained course; however possible references include (but are not limited to):
D.A Marcus, Number Fields, Springer 1977.
J.S. Milne, Algebraic Number Theory, Lecture Notes downloadable from the web.
J. Neukirch, Algebraic Number Theory , Springer-Verlag, 1999.
S. Lang, Algebraic Number Theory, Springer-Verlag, 1994.
Outline of the course: This is a semester long,
first-year graduate course in algebraic number theory. Topics expected to be covered include: number fields, class groups and units, Dirichlet's units theorem, cyclotomic fields, local fields, valuations, decomposition and inertia groups, ramification.
Prerequisites: Abstract algebra: including groups,
rings and ideals, fields and Galois theory, as in 110.401-402 (or equivalent).
Special Notice: This course is listed as a
graduate-level course and will be taught as such even in the presence
of undergraduate students or graduate students in other subjects (i.e.
without a full undergraduate math major). This means that the instructor will
expect a level of scholarly and mathematical maturity appropriate to a
first-year graduate student in mathematics. Material will
go somewhat quickly at times and students will be expected to
pick up some of it on their own. For these reasons the instructor warmly suggest
ALL STUDENTS ENROLLED to take notes in class.
Grading: Homework will be assigned periodically
during lectures. The exercises will be collected by the instructor who
will assign an overall grade. The final grade will
be determined from two components: 1) homework performance and 2) class presence and participation.
Important Note: Classes will be cancelled during the weeks of September 9-13 and October 14-18, as the instructor expects to be away.