**Prerequisites**

Linear algebra: basic knowledge of vector spaces and linear maps over arbitrary fields of characteristic 0.

Algebra: basic knowledge of rings and fields (only of characteristic 0). Everything else that is needed will be included in the lecture notes. Basic knowledge of Galois theory will be helpful, but not really necessary since what is needed is in the lecture notes.

**Aim of the course**

to give the students some basic knowledge about the following topics:

geometry of numbers (study of lattice points in convex bodies, Minkowski's theorems)

transcendence (transcendence results, e.g., e and \(\pi \), linear forms in logarithms)

approximation of algebraic numbers by rationals (Roth's theorem, higher dimensional generalizations by Schmidt)

More information is available on the course website https://pub.math.leidenuniv.nl/~evertsejh/dio.shtml

**Teachers**

Jan-Hendrik Evertse (UL), evertse@math.leidenuniv.nl

Lola Thompson (UU), l.thompson@uu.nl

**Teaching assistants **(responsible for the exercise classes and grading the homework)

Sebastian Carrillo Santana (UU), s.carrillosantana@uu.nl

Mike Daas (UL), m.a.daas@math.leidenuniv.nl

- Docent: Sebastian Carrillo
- Docent: Mike Daas
- Docent: Jan-Hendrik Evertse
- Docent: Lola Thompson