Math 30820 Honors Algebra IV (Spring 2017)
Modules, Fields and Galois Theory
| Due | Set | Solutions | Topics |
| 1/25 | Homework 1 | Solutions | Irreducible polynomials |
| 2/1 | Homework 2 | Solutions | Integrality, modules |
| 2/8 | Homework 3 | Solutions | Modules, homomorphisms, torsion, freeness, submodules, quotients. |
| 2/15 | Homework 4 | Solutions | Modules over PIDs, fields and degrees. |
| 2/22 | Homework 5 | Solutions | Fields, degrees, splitting fields, algebraic extensions. |
| 3/1 | Homework 6 | Solutions | Splitting fields, normal extensions, separability. |
| 3/8 | Homework 7 | Solutions | Finite fields, Dirichlet series, cyclotomic polynomials. |
| 3/22 | Homework 8 | Solutions | Cyclotomic polynomials, Galois groups, perfect fields. |
| 3/29 | Homework 9 | Solutions | Galois groups, fixed fields, main theorem of Galois theory, discriminants. |
| 4/5 | Homework 10 | Solutions | Galois groups, fixed fields, main theorem of Galois theory. |
| 4/12 | Homework 11 | Solutions | Explicit Galois groups, fixed fields, main theorem of Galois theory, solvability by radicals. |
| 4/26 | Homework 12 | Solutions | Symmetric polynomials, Galois groups. |
| 5/3 | Homework 13 | Solutions | Galois groups, traces, norms. |
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