Introduction to Galois Theory 5A82AHAYAF

URI	`m2://res/5A82AHAYAF`
Kind	course
Creators	Krishna Hanumanthu (instructor)
Date	2021-01-13
Scope	in

Expressions

e1: edition

Language	en
Date	2021-01-13

m1: page, Chennai Mathematical Institute (record). nptel 111106145
m2: page, 2021-01-13 (record). nptel 111106145

Contents

part 1: Week 1
session 1: Motivation and overview of the course
session 2: Review of group theory
session 3: Review of ring theory I
session 4: Review of ring theory II
session 5: Review of field theory I
session 6: Review of field theory II
session 7: Review of field theory III
part 2: Week 2
session 8: Problem Session 1
session 9: Problem Session 2
session 10: Beginning of Galois theory
session 11: Fixed fields
session 12: Theorem I on fixed fields
session 13: Theorem II on fixed fields
part 3: Week 3
session 14: Galois extensions, Galois groups
session 15: Normal extensions
session 16: Problem Session - Part 3
session 17: Problem Session - Part 4
session 18: Separable extension - Part 1
session 19: Separable extension - Part 2
part 4: Week 4
session 20: Characterization of Galois extensions - Part 1
session 21: Characterization of Galois extensions - Part 2
session 22: Examples of Galois extensions
session 23: Motivating the main theorem of Galois theory
session 24: Main theorem of Galois theory - Part 1
session 25: Main theorem of Galois theory - Part 2
session 26: Fundamental theorem of algebra
part 5: Week 5
session 27: Problem Session - Part 5
session 28: Problem Session - Part 6
session 29: Problem Session - Part 7
session 30: Problem Session - Part 8
session 31: Problem Session - Part 9
session 32: Kummer extensions - Part 1
part 6: Week 6
session 33: Kummer extensions - Part 2
session 34: Kummer extensions - Part 3
session 35: Cyclotomic extensions - Part 1
session 36: Cyclotomic extensions - Part 2
session 37: Solvability by radicals
session 38: Characterizations of solvability - Part 1
part 7: Week 7
session 39: Characterizations of solvability - Part 2
session 40: Discriminants, Galois groups of polynomials
session 41: Quartics are solvable
session 42: Solvable groups - Part 1
session 43: Solvable groups - Part 2
session 44: Solvable groups - Part 3
part 8: Week 8
session 45: Insolvability of quintics
session 46: Problem Session - Part 10
session 47: Problem Session - Part 11
session 48: Problem Session - Part 12
session 49: Problem Session - Part 13

Catalogue records

nptel: 111106145 (manifestation)
nptel_video: 111106145 (manifestation)