# Introduction to Galois Theory

- Institution: Chennai Mathematical Institute
- Department: Mathematics
- Teacher: Prof. Krishna Hanumanthu
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106145)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106145)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Motivation and overview of the course](https://invisiblenetwork.ai/learn/nptel/111106145/e31e5136b5a2) (Video)
2. [Review of group theory](https://invisiblenetwork.ai/learn/nptel/111106145/f70a6092a968) (Video)
3. [Review of ring theory I](https://invisiblenetwork.ai/learn/nptel/111106145/b1938b5671f5) (Video)
4. [Review of ring theory II](https://invisiblenetwork.ai/learn/nptel/111106145/b838f46fddb3) (Video)
5. [Review of field theory I](https://invisiblenetwork.ai/learn/nptel/111106145/7d2c2d50f982) (Video)
6. [Review of field theory II](https://invisiblenetwork.ai/learn/nptel/111106145/2128cea06665) (Video)
7. [Review of field theory III](https://invisiblenetwork.ai/learn/nptel/111106145/1c9afef37e17) (Video)
8. [Problem Session 1](https://invisiblenetwork.ai/learn/nptel/111106145/7fa389793455) (Video)
9. [Problem Session 2](https://invisiblenetwork.ai/learn/nptel/111106145/6d1558575c72) (Video)
10. [Beginning of Galois theory](https://invisiblenetwork.ai/learn/nptel/111106145/a818fb0f6bf0) (Video)
11. [Fixed fields](https://invisiblenetwork.ai/learn/nptel/111106145/72ec44606fa9) (Video)
12. [Theorem I on fixed fields](https://invisiblenetwork.ai/learn/nptel/111106145/6deeb280ff7b) (Video)
13. [Theorem II on fixed fields](https://invisiblenetwork.ai/learn/nptel/111106145/ce621cb5e91f) (Video)
14. [Galois extensions, Galois groups](https://invisiblenetwork.ai/learn/nptel/111106145/734af6f1d7a5) (Video)
15. [Normal extensions](https://invisiblenetwork.ai/learn/nptel/111106145/7d5f51b78a28) (Video)
16. [Problem Session - Part 3](https://invisiblenetwork.ai/learn/nptel/111106145/7050d506a3f3) (Video)
17. [Problem Session - Part 4](https://invisiblenetwork.ai/learn/nptel/111106145/46d41088c3e5) (Video)
18. [Separable extension - Part 1](https://invisiblenetwork.ai/learn/nptel/111106145/aa5211055a88) (Video)
19. [Separable extension - Part 2](https://invisiblenetwork.ai/learn/nptel/111106145/746e08548e31) (Video)
20. [Characterization of Galois extensions - Part 1](https://invisiblenetwork.ai/learn/nptel/111106145/74e4a542891e) (Video)
21. [Characterization of Galois extensions - Part 2](https://invisiblenetwork.ai/learn/nptel/111106145/8dd97e31338d) (Video)
22. [Examples of Galois extensions](https://invisiblenetwork.ai/learn/nptel/111106145/2c881e44a7ca) (Video)
23. [Motivating the main theorem of Galois theory](https://invisiblenetwork.ai/learn/nptel/111106145/e55dff9bf6e2) (Video)
24. [Main theorem of Galois theory - Part 1](https://invisiblenetwork.ai/learn/nptel/111106145/28825a17c13e) (Video)
25. [Main theorem of Galois theory - Part 2](https://invisiblenetwork.ai/learn/nptel/111106145/7e7bd6a890d5) (Video)
26. [Fundamental theorem of algebra](https://invisiblenetwork.ai/learn/nptel/111106145/cb5e5da2934f) (Video)
27. [Problem Session - Part 5](https://invisiblenetwork.ai/learn/nptel/111106145/7859badc26fc) (Video)
28. [Problem Session - Part 6](https://invisiblenetwork.ai/learn/nptel/111106145/279e4b923feb) (Video)
29. [Problem Session - Part 7](https://invisiblenetwork.ai/learn/nptel/111106145/5363ff381a3d) (Video)
30. [Problem Session - Part 8](https://invisiblenetwork.ai/learn/nptel/111106145/432de508e26d) (Video)
31. [Problem Session - Part 9](https://invisiblenetwork.ai/learn/nptel/111106145/5637958ac95d) (Video)
32. [Kummer extensions - Part 1](https://invisiblenetwork.ai/learn/nptel/111106145/01fcef8bcb4a) (Video)
33. [Kummer extensions - Part 2](https://invisiblenetwork.ai/learn/nptel/111106145/d70d3fd7c18e) (Video)
34. [Kummer extensions - Part 3](https://invisiblenetwork.ai/learn/nptel/111106145/55eadaef9b7f) (Video)
35. [Cyclotomic extensions - Part 1](https://invisiblenetwork.ai/learn/nptel/111106145/be30dbfb36a5) (Video)
36. [Cyclotomic extensions - Part 2](https://invisiblenetwork.ai/learn/nptel/111106145/c19ee7d213ae) (Video)
37. [Solvability by radicals](https://invisiblenetwork.ai/learn/nptel/111106145/f823837c0279) (Video)
38. [Characterizations of solvability - Part 1](https://invisiblenetwork.ai/learn/nptel/111106145/f22ccb47723f) (Video)
39. [Characterizations of solvability - Part 2](https://invisiblenetwork.ai/learn/nptel/111106145/4386bfc03c3a) (Video)
40. [Discriminants, Galois groups of polynomials](https://invisiblenetwork.ai/learn/nptel/111106145/badcfa29cc4d) (Video)
41. [Quartics are solvable](https://invisiblenetwork.ai/learn/nptel/111106145/3db9b150e97c) (Video)
42. [Solvable groups - Part 1](https://invisiblenetwork.ai/learn/nptel/111106145/d76cc6fd8333) (Video)
43. [Solvable groups - Part 2](https://invisiblenetwork.ai/learn/nptel/111106145/50bd7eb526d0) (Video)
44. [Solvable groups - Part 3](https://invisiblenetwork.ai/learn/nptel/111106145/b595145c0a6e) (Video)
45. [Insolvability of quintics](https://invisiblenetwork.ai/learn/nptel/111106145/b9669c2cfd7d) (Video)
46. [Problem Session - Part 10](https://invisiblenetwork.ai/learn/nptel/111106145/35275d933ec4) (Video)
47. [Problem Session - Part 11](https://invisiblenetwork.ai/learn/nptel/111106145/49d76f967987) (Video)
48. [Problem Session - Part 12](https://invisiblenetwork.ai/learn/nptel/111106145/4b1fac55a322) (Video)
49. [Problem Session - Part 13](https://invisiblenetwork.ai/learn/nptel/111106145/e3c7e1cb08a0) (Video)