Exercise sheets

Exercise sheets are also posted on the ADAM page for the course.
Sheet #  Date  Topics  Homework due 
1 

Sept. 23 
Finite fields, Euclidean rings, PID, UFD ... 
Sept. 30 
2 

Sept. 30 
Modules over $\mathbb{Z}$, Quadratic number fields, Traces and norms, ... 
Oct. 7 
3 

Oct. 7 
Discriminant, Noetherian modules, Gaussian integers and a Diophantine equation, ... 
Oct. 14 
4 

Oct. 14 
Eisenstein's criterion, Cyclotomic polynomials, Integers in cyclotomic fields, ... 
Oct. 21 
5 

Oct. 21 
Hermite's theorem, Determination of a ring of integers, Class numbers of some quadratic fields, ... 
Oct. 28 
6 

Oct. 28 
A bound on the class number, Units in real quadratic fields, localisation of ideals, ... 
Nov. 4 
7 

Nov. 4 
DedekindKummer on decomposition of primes, Splitting of primes in quadratic fields, ... 
Nov. 11 
8 

Nov. 11 
Decomposition and inertia groups, Quadratic Reciprocity Law, a FermatPell equation, ... 
Nov. 18 
9 

Nov. 18 
Rabinowitz's theorem, Hyperbola method, Quadratic Gauss sums, ... 
Nov. 25 
10 

Nov. 25 


