2018/2019
Introduction to Galois Theory
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
1, 2 module
Instructors:
Christopher Ira Brav
Language:
English
ECTS credits:
5
Contact hours:
60
Course Syllabus
Abstract
Galois theory is the study of roots of polynomials and their symmetries in terms of Galois groups. As the algebraic counterpart of the fundamental group of topology, the Galois group is an essential object in algebraic geometry and number theory. This course is optional. Pre-requisites : Basic algebra: groups, rings, linear algebra over a field.
Learning Objectives
- Introduce the subject area to the students, and to offer them an opportunity to prepare and give a talk
Expected Learning Outcomes
- Improve their presentation skills and prepare for participation in research projects in the subject area
- Can solve tasks in Galois Theory
Course Contents
- Review of polynomial rings and more general principal ideal domains
- Extensions of fields, algebraic and transcendental
- Splitting fields of polynomials and Galois groups
- The fundamental theorem of Galois theory
- Computing Galois groups
- Applications
Bibliography
Recommended Core Bibliography
- Ash, R. B. (2007). Basic Abstract Algebra : For Graduate Students and Advanced Undergraduates. Mineola, N.Y.: Dover Publications. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1152113
Recommended Additional Bibliography
- Emil Artin. (2007). Algebra with Galois Theory. [N.p.]: AMS. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1495050