Syllabus for 18.787 (Topics in Number Theory, MIT, fall 2007)This document does not include a summary of the course; for that, see my first set of lecture notes. For additional notes and the calendar of lectures, see here.
Lectures: TR 1-2:30, room 4-153.
Instructor info: Kiran Kedlaya, 2-165, x3-2946, kedlaya (at) mit (dot)
Office hours: Wednesday 1-2 or by appointment. (I recommend email for making appointments.)
Textbooks: There is no one source for the material that I will be discussing (some of it will be written down for the first time this semester!), so I will be posting detailed lecture notes. However, I do recommend An Introduction to G-Functions by Dwork, Gerotto, and Sullivan (Princeton University Press, available in softcover), which has a good fraction of the target material, particularly in the earlier parts of the course.
Prerequisites: algebraic number theory (18.786 or equivalent), mainly because you need to be comfortable with dealing with p-adic numbers (there will be a very brief review at the beginning); and undergraduate complex analysis (18.112 or equivalent). There will be one or two places where you may be more comfortable if you have had some exposure to algebraic geometry (e.g., 18.725) and commutative algebra (18.705), but not too many. Also, undergraduates must have my explicit permission to enroll in the course.
Homework: none. I may include exercises in some of my lecture notes, but these will not be required for credit unless perhaps you are an undergraduate; see below.
Grading: grades will be pro forma for graduate students. For undergraduates, see me to negotiate grading criteria.