Current
Update: |
5/03/08 |
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. |

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 |
Room |

Lectures | TR 1:00 |
2-102 |

Office Hours | W 1:30 |
2-172 |

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 Set 1 - Due Feb. 14
- Problem Set 2 - Due Feb. 28
- Problem Set 3 - Due Mar. 6

- Problem Set 4 - Due Mar. 13
- Problem Set 5 - Due Apr. 3
- Problem Set 6 - Due Apr. 10
- Problem Set 7 - Due Apr. 17
- Problem Set 8 - Due May 1
- Problem Set 9 - Due May 8

- Possible project ideas

- Course syllabus

- Neukirch, Algebraic Number Theory - more geometric
viewpoint

- Cox, Primes of the Form x
^{2}+ ny^{2}- contains a good review of Class Field Theory, although the title focus of the book is a little out of date - Stewart and Tall, Algebraic
Number Theory and Fermat's Last Theorem - covers some of the
history of the development of algebraic number theory

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

- J. Milne's Algebraic Number Theory Notes
- J. Milne's Class Field Theory Notes
- William Stein's Classical and Adelic ANT Notes
- Robert Ash's Algebraic
Number Theory

- Homepage for SAGE - free,
open-source mathematics computation package

- Homepage for PARI/GP
(and documentation)
- another free, open-source computation package

- Kiran Kedlaya's 18.786 course page
- As taught in the spring of 2006

- 4/19/08: No
class on Tuesday, Apr. 22nd due to Patriot's Day. Problem Set 8 (download) is due on
Thursday, May 1st.

- 4/10/08: The
seventh problem set is now
available for download.

- 4/01/08: Please
review the (updated!) list of possible projects
and start thinking about what you would like to study in more detail.

The sixth problem set is now available for download.

- 3/21/08: The fifth
problem set is now
available for download.

- 3/07/08: The
fourth problem set is available for download.
Reminders: I will be out of town on Thurs., Mar. 13, but class
will be held as usual. Office hours on Wed., Mar. 12 are cancelled. The midterm will be
handed out on Tues, Mar. 18, and due on Thurs.,
Mar. 20. There will be no homework due that week.

- 3/03/08: The
third problem set is available for download.

- 2/16/08: The
second problem set available for download.
There is no class on Tuesday, Feb. 19 due to President's Day, so the
homework is due in two weeks, on Thursday, Feb. 28. Also, I've
added sample solutions in both GP and SAGE (which can
run GP) for the computation problem from PSet 1.

- 2/15/08: The
second problem set will be available for download on Saturday, Feb. 16,
and will be due on Thursday, Feb. 28.

- 2/07/08: The first problem set and the syllabus are now available for
download. Check back soon for an expanded syllabus with a course
topic and reading outline.

- 1/17/08: Watch this space for important course announcements!

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Mahlburg's homepage