Selected topics concerning fields, including Galois theory.

Galois theory and related topics.

Introduction to the theory of vector spaces for students of mathematics or physics: Basics, vector spaces, linear transformations, solutions of systems of equations, matrices, determinants, endomorphisms, eigenvalues, eigenvectors.

Eigenvalues and eigenvectors, Jordan normal form, bilinear forms, euclidean and unitary vector spaces, spectral theorem, multilinear algebra, tensor product

This course will give an introduction to various aspects of number theory, both algebraic and analytic.

This course offers an introduction to the representation theory of finite groups. The idea of representation theory is to study groups via their actions on finite-dimensional vector spaces. This is a very powerful idea, since it reduces many group-theoretic problems to problems in linear algebra. Representation theory has far-reaching applications in many different fields.