Linear algebra: basic knowledge of vector spaces and linear maps over arbitrary fields;
Algebra: everything what is needed will be included in the lecture notes, so students don't really have to be familiar with this, but it would be helpful to have some basic knowledge of field extensions and Galois theory, only for fields of characteristic 0.
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 , linear forms in logarithms)
approximation of algebraic numbers by rationals (Roth's theorem, higher dimensional generalizations by Schmidt)