MATH 617 -- Number Theory

Fall 2007

Instructor: Katia Consani
Office: 216 Krieger Hall
Phone: (410) 516-5116.
Email: kc@math.jhu.edu

Class Times: MTW, 12:00-12:50 pm.
Room: HOD 311.

References: The official textbook for this course is:

S. Lang, Algebraic Number Theory , Springer-Verlag, 1994.

but the following references may be useful for complementary reading:

G. J. Janusz, Algebraic Number Fields , Providence RI, A.M.S. 1996.

J. Neukirch, Algebraic Number Theory , Springer-Verlag, 1999.

Outline of the course: This course is a semester long, first-year graduate course in algebraic number theory. Topics expected to be covered include number fields, classgroups and units, Dirichlet's units theorem, cyclotomic fields, local fields, valuations, decomposition and inertia groups, ramification, ideles and adeles.

Prerequisites: Abstract algebra: including groups, rings and ideals, fields and Galois theory, e.g. 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. That means I will expect a level of scholarly and mathematical maturity appropriate to a first-year graduate student in mathematics. In particular, material will go somewhat quickly and students will also be expected to pick up some of it on their own. I will try to follow the textbook but I also expect to complement some of the topics with further material. For this reason I warmly suggest ALL STUDENTS ENROLLED to take notes in class. Problem sets may be challenging; students will be expected to cope with this in appropriate ways, such as forming study groups.

Grading: Homework will be assigned periodically during lectures. The exercises will be collected by the instructor and graded by a grader who will assign an overall grade. The final grade will be determined from two components: 1) homework performance, and 2) a final oral exam where students will be tested on the material explained in the course as well as on some background material (cfr. Prerequisites).

Homework: 1st Homework (due in class on October 10), [Sol]; 2nd Homework (due on October 31), [Sol]; 3rd Homework (due on December 5).

Important Note: Class will be cancelled during the week of October 22-26, as the instructor expects to be away.