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

Abstract Algebra, by Dummit and Foote

Infinite Galois Theory, notes by Keith Conrad

Source: https://www.jmilne.org/math/CourseNotes/ft.html

Weeks 11 and 12: Algebraic closure, separable closure, infinite Galois groups

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

Weeks 3 and 4: Splitting fields, separability, automorphisms of extensions

Weeks 1 and 2: Introduction to fields, construction of algebraic extensions, algebraic and transcendental numbers, application to constructions

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