# MA3A6 Algebraic Number Theory

### 2019-20, Term 1

Lecture notes (complete)

Example sheets

• Example sheet 1
Correction (16/10): Question 11 should say L = Q(beta) where it originally said L=Q(sqrt(beta)). The original question was much harder than it was supposed to be - if you have already solved it, you can still hand in that solution instead of the solution to the corrected question.
Correction (22/10): Question 13(i) should say x sqrt(d) in K where it originally said xd in K.
• Example sheet 2
• Example sheet 3
Correction (11/11): Q2 should say "theta in OK" where it originally said "theta in K".
• Example sheet 4
• Example sheet 5

Lectures: Mon 17.00 (OC0.02), Tue 9.00 (L4), Thu 14.00 (L5)
Support classes: Thu 15.00 (MB2.22)
Office hours: Mon 2-3 (Zeeman C2.11)
Assignment deadlines: Monday noon in weeks 4, 6, 8, 10

Course description

### Assessment

There will be four example sheets. On each sheet, a subset of the questions will be designated as assessed questions and you should submit these for marking. The final mark will be calculated as follows:
15% assignments (best 3 of 4), 85% exam

Deadlines: Monda 12 noon in weeks 4, 6, 8, 10

Exam format: one compulsory question worth 40% of the marks, and four optional questions each worth 20% of the marks

### Books and notes

The content of the course will be similar but not identical to last year. I will again provide lecture notes here a day or two after each lecture, matching exactly what we cover in the lectures this year. Example sheets may change a little from last year.

Prof Siksek's notes also cover similar material, with many worked examples.

The most useful books are:

• Stewart and Tall, Algebraic Number Theory or Algebraic Number Theory and Fermat's Last Theorem.
• Jarvis, Algebraic Number Theory.
Some more advanced books are listed at the beginning of Prof Siksek's notes.