Algebraic number fields are finite extensions of the field of the rational numbers. They contain a ring of integers, which is a Dedekind domain, a slightly more general type of ring than a principal ideal domain. Non-zero ideals of the ring of integers up to isomorphism form a finite abelian group, the ideal class group of the number field. The ring of integers is a principal ideal domain iff this group is trivial. A theorem of Dirichlet describes the structure of the group of units of a ring of integers. The behavior of these concepts under field extensions will be treated, especially for Galois extensions. Special attention will be given to abelian number fields.

The following courses will be taught during the Fall 2015 semester.

More information on these courses can be found on www.mastermath.nl. Registration for these courses can be done through the registration form on the before mentioned website. Only ANT will have a course-site here, as it will be given in Nijmegen, and the videos of the lectures will be posted here. Registration for this course is, for now, still through the regular mastermath site.

More information on these courses can be found on www.mastermath.nl. Registration for these courses can be done through the registration form on the before mentioned website. Only ANT will have a course-site here, as it will be given in Nijmegen, and the videos of the lectures will be posted here. Registration for this course is, for now, still through the regular mastermath site.

- Algebraic Number Theory (see below)
- Asymptotic Statistics
- Continuous Optimization
- Differential Geometry
- Discrete Optimization
- Dynamical Systems
- Elliptic Curves
- Functional Analysis
- Heuristic Methods in Operations Research
- Intensive Course Categories and Modules
- Introduction to Stochastic Processes
- Mathematical Biology
- Numerical Linear Algebra
- Operator Algebras
- Parallel Algorithms
- Probabilistic and Extremal Combinatorics
- Systems and Control