3 credits
Spring 2025 Lecture HonorsUpper Division
This course will give a thorough introduction to Galois theory. Galois theory is a fundamental tool in many areas of mathematics, including number theory and algebraic geometry. This course will increase students' mathematical maturity and prepare them for graduate school. Topics include finite extension fields and their symmetries, ruler and compass constructions, complex roots of unity, solvable groups, and the solvability of polynomial equations by arithmetic and radical operations. This course is intended for third- or fourth-year students who have taken MA 45000 (Algebra Honors) or MA 45300 (Elements of Algebra I).
Learning Outcomes1Know the historical background of Galois theory.
2Know the classical version which addresses questions about roots of polynomials and the modern formulation in terms of abstract algebra.
3Know about finite extension fields and their symmetries.
4Know how Galois theory answers ancient questions about ruler and compass constructions.
5Know about cyclotomic fields generated by complex roots of unity.
6Know how Galois theory answers questions about the solvability of polynomial equations by arithmetic and radical operations.
Prerequisites
made by Purdue students.