General Information | Syllabus | HW Assignments |
---|
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