MAA303 - Algebra and Galois Theory (2023-2024)

Prerequisites: MAA101, MAA103, MAA201, MAA206

MAA303 focuses on groups, rings and fields.

The first part of the course will be dedicated to group theory, and we will cover all the basic notions and tools that one uses to study groups: normal subgroups, quotient groups, simple groups, group actions...

The second part of the course will focus on rings. We will introduce the basic notions related to them, such as ideals, principal ideal domains, prime and maximal ideals, ring quotients..., with a particular emphasis on polynomial rings.

In the last part of the course, we will focus on fields. We will introduce field extensions and study their basic properties. At the very end of the course, we will see how groups, rings and fields are deeply related through the study of algebraic equations and Galois theory.

Prerequisites: MAA101, MAA103, MAA201, MAA206

MAA303 focuses on groups, rings and fields.

The first part of the course will be dedicated to group theory, and we will cover all the basic notions and tools that one uses to study groups: normal subgroups, quotient groups, simple groups, group actions...

The second part of the course will focus on rings. We will introduce the basic notions related to them, such as ideals, principal ideal domains, prime and maximal ideals, ring quotients..., with a particular emphasis on polynomial rings.

In the last part of the course, we will focus on fields. We will introduce field extensions and study their basic properties. At the very end of the course, we will see how groups, rings and fields are deeply related through the study of algebraic equations and Galois theory.