Learning objectives
The students will learn the basic definitions, problems, and techniques in modules and Galois theory.
Prerequisites
Algebra (groups, rings, fields) and Linear Algebra.
Course unit content
Building on the courses of Algebra and Linear Algebra, the course covers the theory of modules over rings; algebraic extensions and Galois theory; algebraic spaces.
Full programme
Bibliography
S. Lang, Algebra, Graduate Text in Mathematics, Springer.
Teaching methods
The topics of the course will be discussed during the lectures, together with examples, applications, and exercises.
Assessment methods and criteria
At the end of the course there will be an exam in two parts. The first one will be a one-hour long written exam. The second one will be at the board, where the student will be asked to discuss, explain, and prove the main results of the course.
Other information