FUNDAMENTALS OF ADVANCED ALGEBRA
- Overview
- Assessment methods
- Learning objectives
- Contents
- Full programme
- Teaching methods
- Contacts/Info
Linear Algebra; Algebra 1 and Algebra 2 (basics of group theory and ring theory).
Tests with exercises; final oral exam.
To provide the students an introduction to Galois Theory, and the ability of solving easy exercises on extensions of fields.
The course is an introduction of Galois Theorem. First, we will introduce algebraic extensions of fields, and then we will focus on Galois extensions and associated Galois groups. After proving the fundamental theorem of Galois Theory, we will aim at the characterization of those algebraic equations which are solvable via radicals. Finally, we will introduce the ring of algebraic integers of a number field.
- Fields and extensions of fields
- Algebraic closure of a field
- Galois extensions and the Galois group
- Fundamental Theorem of Galois Theory
- Cyclotomic extensions and cyclic extensions
- Solvable groups
- Solvability of algebraic equations
- Rings of algebraic integers
Lectures and exercises.
Reception with the teacher is by appointment: contact at claudio.quadrelli@uninsubria.it