Math 81
Galois Theory

Last updated June 23, 2014 15:20:15 EDT

General Information Syllabus HW Assignments

Syllabus

The main focus of the course will be Chapters 13 and 14 on fields and Galois theory, though we shall begin with a rapid review of ring theory from Chapters 8 and 9. While the syllabus below will evolve over time, the weekly syllabus contained on the Homework Assignments page will always be accurate.


Lectures Sections in Text Brief Description
Week 1 7.4, 8.1, 8.2, 8.3, 9.2, 9.3 Review: UFD, PID, Euclidean domains, irreducible and prime elements, prime and maximal ideals, Gauss' lemma and implications
Week 2 9.4, 9.5, 13.6 (part), 13.1 Irreducibility criteria, roots of unity, cyclotomic polynomials, characteristic, constructing fields, finite extensions
Week 3 13.2, 13.6 Algebraic Extensions of fields, Cyclotomic polynomials
Week 4 13.3, 13.4 Constructions with compass and straightedge, splitting fields, algebraic closure
Week 5 13.5, 14.1 Separability, finite fields, fixed fields and automorphism groups
Week 6 14.2 The Fundamental Theorem of Galois Theory
Week 7 14.2, 14.3, start 14.4 FTGT, Finite Fields, Composite Extensions
Week 8 14.4, 14.5 Composite extensions, cyclotomic extensions
Week 9 14.6, 14.7 Solvable and Radical Extensions, Galois groups of polynomials
Week 10    


T. R. Shemanske
Last updated June 23, 2014 15:20:15 EDT