504 -- Algebra II (Spring 2024)
Course Info
Who: Prof Daniel Studenmund
What: Math 504 -- Algebra II (Fields and Galois theory)
When: 1:10-2:10 MWF
Where: Whitney 309
Why: To learn a fundamental and beautiful part of number theory, and in doing so vindicate Évariste Galois
Office: Whitney 114
Office Hours: Tuesdays 1:00-2:30 and Fridays 12:00-1:00, and any time by appointment
Textbooks: Fields and Galois theory, by Milne
Abstract Algebra by Dummit and Foote
Source: https://www.jmilne.org/math/CourseNotes/ft.html
Class schedule and homework
Weeks 11 and 12: Algebraic closure, separable closure, infinite Galois groups
Homework4 (pdf), due May 1
Weeks 9 and 10: Fundamental theorem of algebra, insolvability of the quintic, Galois groups over Q, the general polynomial
Weeks 7 and 8: Cyclotomic extensions, finite fields, Galois groups of polynomials, primitive element theorem
Weeks 5 and 6: Galois groups, Fundamental Theorem of Galois Theory, examples, composites and intersections of Galois extensions
Homework 3 (pdf), due Mar 13
Weeks 3 and 4: Splitting fields, separability, automorphisms of extensions
Homework 2 (pdf), due Feb 23
Weeks 1 and 2: Introduction to fields, construction of algebraic extensions, algebraic and transcendental numbers, application to constructions
Homework 1 (pdf), due Feb 7