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Current Update:
Problem Set 9 is now available for download, and is due on Thursday, May 8th.  This is the final problem set of the semester.  Remember that the final project is also due on May 15th.

Final Exam:  The take-home final will be handed out on Tuesday, May 13th, and due on Monday, May 19th.

MATH 18.786 - Spring 2008

This is an introductory course in algebraic number theory at the first-year graduate level.  Topics will include number fields and algebraic integers, unique factorization, class numbers, cyclotomic fields, local fields and valuations, decomposition and inertia groups, computer algebra systems, and time allowing, basic class field theory.  Undergraduates who have the appropriate background are welcome in this course, but you must meet the prerequisites, and will need my formal approval in order to register.  In addition, be prepared for the pace, workload, and independence of a graduate course.

Course Information

Scheduled Time
Lectures TR 1:00
Office Hours W 1:30

Textbook (required)
G. Janusz, Algebraic Number Fields (2nd ed.)
Prerequisites (undergraduates only) 18.100 (Analysis), 18.701 (Algebra I),
18.702 (Algebra II), and 18.781 (Elem. Number Theory)
OR approved equivalents...

Contact Information:
Phone: (617) 253-4470

e-mail: mahlburg (at) math (dot) mit (dot) edu.

Office: 2-172 (First floor of Math building, south wing)

Problem Sets

There will be approximately 10 problem sets, due on Thursdays in class.  Please start working on them early, since important results and/or proofs will often appear!



There are several good textbooks on Algebraic Number Theory, and it is a broad enough topic that there is no universal standard.  Please supplement your reading with any of these:

There are also many good online notes and texts available for Algebraic Number Theory:


Past Updates

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