This common course with Haluk Şengün is dedicated to the cohomology of arithmetic groups in low rank (e.g. Bianchi groups), their associated geometric models (hyperbolic geometry) and connections to number theory.

This course is a survey of mathematical algorithms, with a focus on number theory. There were exercise sessions with Pari/GP, available here.

This course is a survey of Galois theory and its connections with algebraic number theory, without proofs.

- Lecture notes. [ notes ]
- Number fields. [ questions | solutions ]
- Algebraic integers. [ questions | solutions ]
- Ideal factorisation. [ questions | solutions ]
- The class group. [ questions ]

- Number fields. [ questions | solutions ]
- Algebraic integers. [ questions | solutions ]
- Ideal factorisation. [ questions | solutions ]
- The class group. [ questions | solutions ]
- Units. [ questions | solutions ]
- Revision. [ questions | solutions ]

I have written these solutions with Samuel Le Fourn.

- Logical operations. [ solutions (french) ]
- Quantifiers. [ solutions (french) ]
*Reduction ad absurdum*. [ solutions (french) ]- Contraposition. [ solutions (french) ]
- Induction. [ solutions (french) ]
- Sets. [ solutions (french) ]
- Image, inverse image, composition. [ solutions (french) ]
- Injections, surjections, bijections. [ solutions (french) ]
- Finite sets, counting. [ solutions (french) ]
- Counting, handling sums. [ solutions (french) ]