| 2026.01.05 |
Introduction |
|
| 2026.01.06 |
Cubic equations |
notes01 |
| 2026.01.08 |
Over the real numbers |
problems01 |
| 2026.01.12 |
Polynomials in several variables |
|
| 2026.01.13 |
Symmetric polynomials |
notes02 |
| 2026.01.15 |
The discriminant |
problems02 |
| 2026.01.19 |
Existence of roots |
|
| 2026.01.20 |
Fundamental theorem of algebra |
notes03 |
| 2026.01.22 |
Field extensions |
problems03 |
| 2026.01.26 |
Irreducible polynomials |
|
| 2026.01.27 |
Prime radicals |
notes04 |
| 2026.01.29 |
Degree of an extension |
problems04 |
| 2026.02.02 |
Algebraic extensions |
|
| 2026.02.03 |
Splitting fields |
notes05 |
| 2026.02.05 |
Normal extensions |
problems05 |
| 2026.02.09 |
Separable extensions |
|
| 2026.02.10 |
Theorem of the primitive element |
notes06 |
| 2026.02.12 |
Definition of the Galois group |
problems06 |
|
Winter break |
|
| 2026.02.23 |
Galois groups of splitting fields |
|
| 2026.02.24 |
Permutations of roots |
notes07 |
| 2026.02.24 |
Midterm |
|
| 2026.02.26 |
Examples of Galois groups |
problems07 |
| 2026.03.02 |
Galois extensions |
|
| 2026.03.03 |
Conjugate fields |
notes08 |
| 2026.03.05 |
Normal subgroups and normal extensions |
problems08 |
| 2026.03.09 |
Fundamental theorem of Galois theory |
|
| 2026.03.10 |
First applications |
notes09 |
| 2026.03.12 |
Solvable groups |
problems09 |
| 2026.03.16 |
Radical and solvable extensions |
|
| 2026.03.17 |
Solvable extensions and solvable groups |
notes10 |
| 2026.03.19 |
Simple groups |
problems10 |
| 2026.03.23 |
Solving polynomials by radicals |
|
| 2026.03.24 |
Cyclotomic polynomials |
notes11 |
| 2026.03.26 |
Roots of unity |
problems11 |
| 2026.03.30 |
Geometric constructions |
|
| 2026.03.31 |
Constructible numbers |
notes12 |
| 2026.04.02 |
Review |
problems12 |
| 2026.04.?? |
Exam |
TBD |
