Algebraic Number Theory

Master's course, autumn semester 2009/10

Lecturer: B.J.J. Moonen

KdV Institute for Mathematics
office: Science Park 904, C4.160
phone: 525 7006
e-mail: bmoonen (at) uva.nl

Important note:

From 30 October on the course will be taught in a different room. Other than what was announced earlier this will NOT be at the Mauritskade number 57. Instead we shall be in: Roeterseiland, Building D, room D.028 . (Click for route description.)

Registration:

Students from the University of Amsterdam (UvA) or the Free University Amsterdam (VU) have to register following the normal procedures at their own university. Students from one of the other Dutch universities need to register as a visiting student for this course. For Dutch-speaking students this can be done via the following website: inschrijving als bijvakstudent aan de UvA. For the students from other universities who do not speak Dutch, further instructions will follow.

The course will be taught in English. We shall use the lecture notes Algebraic Number Theory by R. Schoof.

Suggestions for further reading:

I.N. Stewart and D.O. Tall: Algebraic Number Theory
S. Lang: Algebraic Number Theory
J. Neukirch: Algebraic Number Theory

(Note that especially the second and third book contain much more than what we intend to discuss.)

Schedule:

4 Sept, 15:00-17:00, Plantage Muidergracht 24, room P.015a. General introduction, Chapter 1 of the lecture notes.
11 Sept, 15:00-17:00, Plantage Muidergracht 24, room P.015a. Chapter 2.
18 Sept, 15:00-17:00, Plantage Muidergracht 24, room P.015a. Parts of chapters 3 and 4.
25 Sept, 15:00-17:00, Plantage Muidergracht 24, room P.015a. Chapters 3 and 4 finished.
2 Oct, 15:00-17:00, Plantage Muidergracht 24, room P.015a. Most of Chapter 5.
9 Oct, 15:00-17:00, Plantage Muidergracht 24, room P.015a. Chapter 5 finished; Chapter 6 until Example 6.5.
16 Oct, 15:00-17:00, Plantage Muidergracht 24, room P.015a. Rest of Chapter 6; Chapter 7 (without proofs)
23 Oct, Autumn break, no lecture.
30 Oct, 15:00-17:00, Roeterseiland, Building D, room D.028. Chapter 9.
6 Nov, 15:00-17:00, Roeterseiland, Building D, room D.028. Chapter 8 + most of Chapter 10.
13 Nov, 15:00-17:00, Roeterseiland, Building D, room D.028.
20 Nov, 15:00-17:00, Roeterseiland, Building D, room D.028.
27 Nov, 15:00-17:00, Roeterseiland, Building D, room D.028.
4 Dec, 15:00-17:00, Roeterseiland, Building D, room D.028.
11 Dec, 15:00-17:00, Roeterseiland, Building D, room D.028.

Exercises:

4 Sept: Algebra test: in Dutch or in English. Additional exercises: Exercises for 4 September.
11 Sept: Here are the answers of last week's Algebra test: Answers (in English). Recommended exercises from the lecture notes: 1.E, 1.F, 1.H, 2.A, 2.B. 2.K.
18 Sept, recommended exercises from the lecture notes: 3.A, 3.C, 3.F, 4.B, 4.F, 4.H.
25 Sept, recommended exercises from the lecture notes: 3.E, 3.K, 4.E, 4.G, 4.I. Note: In exercise 3.K part (iv) the text should read: 'Using parts (i) and (iii), design ...'.
2 Oct: First homework assignment. Your solutions are due on 16 Oct.
9 Oct, recommended exercises from the lecture notes: 5.G, 5.I, 5.M, 5.N, 6.F.
16 Oct, recommended exercises from the lecture notes: 6.A, 6.B, 6.E, 6.G, 6.I.
30 Oct, recommended exercises from the lecture notes: 9.B, 9.C, 9.D, try 9.F.

Assignments:

During the semester there will be two homework assignments. At the end of the course there will be one further assignment. There is no written exam.

Here is the first homework assignment. And here are my solutions.

Here is the second homework assignment. Important note: The second assigment comes in four different versions (A-D) and you are supposed to do only one version, according to which version I have assigned to you. You should ask me which version you should do, in case you do not yet know this. Make sure that you print the correct page of the pdf file that is available here. (There are four pages, one for each version.)

And here is the third and final homework assignment. Important note: This assigment again comes in different versions. Make sure that you do the correct version, and read the instructions very carefully.

To the home page of Ben Moonen