Johns Hopkins

Algebraic Number Theory

Here is a link to the syllabus (also available on Blackboard) and here is a link to the course notes (last updated October 14, 2021 at 12:07pm). Weekly exercises from the course notes are posted below.

Week Exercises
1 1.1.3, 1.3.1, 1.4.2, 1.4.5, 1.4.10, 1.5.1
2 2.1.3, 2.1.5, 2.1.6, 2.1.8, 2.2.2, 2.2.5, 2.2.7, 2.2.9, 2.2.12, 2.2.14, 2.3.4, 2.3.5, 2.3.7, 2.3.9, 2.3.12
3 2.4.3, 2.4.10, 2.4.12, 2.4.13, 3.1.2, 3.2.2, 3.2.4, 3.2.6, 3.3.3, 3.3.7
4 3.3.13, 3.3.14, 3.3.15, 3.3.20, 4.1.2, 4.1.5, 4.1.7
5 4.3.3, 4.3.5, 4.3.7, 4.3.8, 4.3.10, 4.3.14
6 4.4.2, 4.4.6, 5.1.1, 5.1.3, 5.1.6, 5.1.8
7 5.2.3, 5.2.9, 5.2.10

King's College London

Representation Theory of Finite Groups, Spring 2020

TA: Ashwin Iyengar

Course information can be found on Keats.

On this page I will be posting some extra exercises for the course, starting week 3. This is if you want some extra practice with the definitions and theorems from the course, but these are not mandatory, so don't feel like you need to do them. If, however, you decide to turn in the exercises, I will happily grade them for you as though they were on the tutorial sheets for the course.

References to Dummit and Foote (DF) refer to this textbook, which is an enormous source of exercises for all sorts of different topics (if you click the links to the book below they will automatically take you to the correct page in the PDF where the exercise is).

Week Exercises
1 N/A
2 N/A
3 Exercises 3, 6, 8, 10, and 11-13 here, or see DF Section 1.7 (page 44) for more (Ex. 12 is nice)
4 Exercise 12, 13, 20 in here (also Exercise 21, 22, 24 and 25 if you're comfortable with tensor products/alternating products). Exercise 3, 16 in DF page 853 is good, and if you're willing to read the definition of a module over a group ring, try Exercise 14 on the same page.
5 Exercise 10, 12, 13 in DF Section 18.3. If you're comfortable with some Galois theory (or maybe you don't need to be for all of them) try 14-18 on the same page.
6 Exercises 27-33 in here.
7 Exercises 7-13 in DF Section 19.1 are good practice computing character tables. Try Exercise 14, 15, and 1-3 here as well, or any others you think look interesting. Related: find a list of finite groups. Pick one at random. Compute its conjugacy classes. Compute its character table.
8 Try Exercises 2,3,4,5,8 here. If you know about modules over rings you can try reading Section 10.4 of DF (or any source you find on tensor products of modules over commutative rings).

Elementary number theory, Fall 2018

TA: Ashwin Iyengar

Course information can be found on Keats.