NOC:Introduction to Galois Theory

Lecture 1 - Motivation and overview of the course

Lecture 2 - Review of group theory

Lecture 3 - Review of ring theory - I

Lecture 4 - Review of ring theory - II

Lecture 5 - Review of field theory - I

Lecture 6 - Review of field theory - II

Lecture 7 - Review of field theory - III

Lecture 8 - Problem Session - Part 1

Lecture 9 - Problem Session - Part 2

Lecture 10 - Beginning of Galois theory

Lecture 11 - Fixed fields

Lecture 12 - Theorem I on fixed fields

Lecture 13 - Theorem II on fixed fields

Lecture 14 - Galois extensions, Galois groups

Lecture 15 - Normal extensions

Lecture 16 - Problem Session - Part 3

Lecture 17 - Problem Session - Part 4

Lecture 18 - Separable extension - Part 1

Lecture 19 - Separable extension - Part 2

Lecture 20 - Characterization of Galois extensions - Part 1

Lecture 21 - Characterization of Galois extensions - Part 2

Lecture 22 - Examples of Galois extensions

Lecture 23 - Motivating the main theorem of Galois theory

Lecture 24 - Main theorem of Galois theory - Part 1

Lecture 25 - Main theorem of Galois theory - Part 2

Lecture 26 - Fundamental theorem of algebra

Lecture 27 - Problem Session - Part 5

Lecture 28 - Problem Session - Part 6

Lecture 29 - Problem Session - Part 7

Lecture 30 - Problem Session - Part 8

Lecture 31 - Problem Session - Part 9

Lecture 32 - Kummer extensions - Part 1

Lecture 33 - Kummer extensions - Part 2

Lecture 34 - Kummer extensions - Part 3

Lecture 35 - Cyclotomic extensions - Part 1

Lecture 36 - Cyclotomic extensions - Part 2

Lecture 37 - Solvability by radicals

Lecture 38 - Characterizations of solvability - Part 1

Lecture 39 - Characterizations of solvability - Part 2

Lecture 40 - Discriminants, Galois groups of polynomials

Lecture 41 - Quartics are solvable

Lecture 42 - Solvable groups - Part 1

Lecture 43 - Solvable groups - Part 2

Lecture 44 - Solvable groups - Part 3

Lecture 45 - Insolvability of quintics

Lecture 46 - Problem Session - Part 10

Lecture 47 - Problem Session - Part 11

Lecture 48 - Problem Session - Part 12

Lecture 49 - Problem Session - Part 13