# Algebra - I

- Institution: IMSc
- Department: Mathematics
- Taught by: Prof. S. Viswanath, Prof. Amritanshu Prasad
- Level: Graduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106137)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106137)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

Foundational PG level course in algebra, suitable for M.Sc and first year PhD students in Mathematics.

Intended audience: Any Interested Learners

Prerequisites: BSc-level linear algebra

## Lectures

1. [Permutations](https://invisiblenetwork.ai/learn/nptel/111106137/5aae44ed63b0) (YouTube)
2. [Group Axioms](https://invisiblenetwork.ai/learn/nptel/111106137/7541725ef107) (YouTube)
3. [Order and Conjugacy](https://invisiblenetwork.ai/learn/nptel/111106137/57a0903dc147) (YouTube)
4. [Subgroups](https://invisiblenetwork.ai/learn/nptel/111106137/f33db0828521) (YouTube)
5. [Problem solving](https://invisiblenetwork.ai/learn/nptel/111106137/ec1ce355393e) (YouTube)
6. [Group Actions](https://invisiblenetwork.ai/learn/nptel/111106137/cdeccc91628f) (YouTube)
7. [Cosets](https://invisiblenetwork.ai/learn/nptel/111106137/2e38cfdbe646) (YouTube)
8. [Group Homomorphisms](https://invisiblenetwork.ai/learn/nptel/111106137/1f709a914924) (YouTube)
9. [Normal subgroups](https://invisiblenetwork.ai/learn/nptel/111106137/230227aae0d0) (YouTube)
10. [Quotient Groups](https://invisiblenetwork.ai/learn/nptel/111106137/64b2e5414e38) (YouTube)
11. [Product and Chinese Remainder Theorem](https://invisiblenetwork.ai/learn/nptel/111106137/8c79349ebd62) (YouTube)
12. [Dihedral Groups](https://invisiblenetwork.ai/learn/nptel/111106137/87e8c374d1e2) (YouTube)
13. [Semidirect products](https://invisiblenetwork.ai/learn/nptel/111106137/95e0cf36e56d) (YouTube)
14. [Problem solving](https://invisiblenetwork.ai/learn/nptel/111106137/933cd5da8c2e) (YouTube)
15. [The Orbit Counting Theorem](https://invisiblenetwork.ai/learn/nptel/111106137/cf3bf509404a) (YouTube)
16. [Fixed points of group actions](https://invisiblenetwork.ai/learn/nptel/111106137/b2b5d10e520e) (YouTube)
17. [Second application: Fixed points of group actions](https://invisiblenetwork.ai/learn/nptel/111106137/2d334e4afa3c) (YouTube)
18. [Sylow Theorems - a preliminary proposition](https://invisiblenetwork.ai/learn/nptel/111106137/559d88d608f7) (YouTube)
19. [Sylow Theorem I](https://invisiblenetwork.ai/learn/nptel/111106137/39e037e37d07) (YouTube)
20. [Problem solving I](https://invisiblenetwork.ai/learn/nptel/111106137/c0a435d48fb2) (YouTube)
21. [Problem solving II](https://invisiblenetwork.ai/learn/nptel/111106137/1b531f9fa53d) (YouTube)
22. [Sylow Theorem II](https://invisiblenetwork.ai/learn/nptel/111106137/e39e676a252e) (YouTube)
23. [Sylow Theorem III](https://invisiblenetwork.ai/learn/nptel/111106137/bb5011cf3911) (YouTube)
24. [Problem solving I](https://invisiblenetwork.ai/learn/nptel/111106137/c90a62706315) (YouTube)
25. [Problem solving II](https://invisiblenetwork.ai/learn/nptel/111106137/a83c00f94a81) (YouTube)
26. [Free Groups I](https://invisiblenetwork.ai/learn/nptel/111106137/b110921cc67b) (YouTube)
27. [Free Groups IIa](https://invisiblenetwork.ai/learn/nptel/111106137/ec27aded2808) (YouTube)
28. [Free Groups IIb](https://invisiblenetwork.ai/learn/nptel/111106137/a04f6185bcc6) (YouTube)
29. [Free Groups III](https://invisiblenetwork.ai/learn/nptel/111106137/7787eab1010c) (YouTube)
30. [Free Groups IV](https://invisiblenetwork.ai/learn/nptel/111106137/34bfbb3b3e5b) (YouTube)
31. [Problem Solving/Examples](https://invisiblenetwork.ai/learn/nptel/111106137/768555c6a1a6) (YouTube)
32. [Generators and relations for symmetric groups – I](https://invisiblenetwork.ai/learn/nptel/111106137/4acf58d52bab) (YouTube)
33. [Generators and relations for symmetric groups – II](https://invisiblenetwork.ai/learn/nptel/111106137/d61324d0746b) (YouTube)
34. [Definition of a Ring](https://invisiblenetwork.ai/learn/nptel/111106137/d09af28e4f89) (YouTube)
35. [Euclidean Domains](https://invisiblenetwork.ai/learn/nptel/111106137/fca063677814) (YouTube)
36. [Gaussian Integers](https://invisiblenetwork.ai/learn/nptel/111106137/504452f2d831) (YouTube)
37. [The Fundamental Theorem of Arithmetic](https://invisiblenetwork.ai/learn/nptel/111106137/bb89764b3604) (YouTube)
38. [Divisibility and Ideals](https://invisiblenetwork.ai/learn/nptel/111106137/5d0704be0658) (YouTube)
39. [Factorization and the Noetherian Condition](https://invisiblenetwork.ai/learn/nptel/111106137/49ced2e65763) (YouTube)
40. [Examples of Ideals in Commutative Rings](https://invisiblenetwork.ai/learn/nptel/111106137/b422350d54e6) (YouTube)
41. [Problem Solving/Examples](https://invisiblenetwork.ai/learn/nptel/111106137/1c9dfa440350) (YouTube)
42. [The Ring of Formal Power Series](https://invisiblenetwork.ai/learn/nptel/111106137/d1062792f22b) (YouTube)
43. [Fraction Fields](https://invisiblenetwork.ai/learn/nptel/111106137/3bc41fc36bb5) (YouTube)
44. [Path Algebra of a Quiver](https://invisiblenetwork.ai/learn/nptel/111106137/f455dc9de745) (YouTube)
45. [Ideals In Non-Commutative Rings](https://invisiblenetwork.ai/learn/nptel/111106137/f4412e319b34) (YouTube)
46. [Product of Rings](https://invisiblenetwork.ai/learn/nptel/111106137/b183bae470f1) (YouTube)
47. [Ring Homomorphisms](https://invisiblenetwork.ai/learn/nptel/111106137/1691c662ea9e) (YouTube)
48. [Quotient Rings](https://invisiblenetwork.ai/learn/nptel/111106137/75d315cbb213) (YouTube)
49. [Problem solving](https://invisiblenetwork.ai/learn/nptel/111106137/4f3d6817280d) (YouTube)
50. [Tensor and Exterior Algebras](https://invisiblenetwork.ai/learn/nptel/111106137/0c0ad07ff85a) (YouTube)
51. [Modules : definition](https://invisiblenetwork.ai/learn/nptel/111106137/b2b7248c027d) (YouTube)
52. [Modules over polynomial rings $K\[x\]$](https://invisiblenetwork.ai/learn/nptel/111106137/3e45332968c8) (YouTube)
53. [Modules: alternative definition](https://invisiblenetwork.ai/learn/nptel/111106137/35a0ddc92c1f) (YouTube)
54. [Modules: more examples](https://invisiblenetwork.ai/learn/nptel/111106137/7f7ffa31b7ff) (YouTube)
55. [Submodules](https://invisiblenetwork.ai/learn/nptel/111106137/a81a392d73ff) (YouTube)
56. [General constructions of submodules](https://invisiblenetwork.ai/learn/nptel/111106137/b9c337e1eb37) (YouTube)
57. [Problem solving](https://invisiblenetwork.ai/learn/nptel/111106137/b9ad130446a1) (YouTube)
58. [Quotient modules](https://invisiblenetwork.ai/learn/nptel/111106137/0b09ac66a519) (YouTube)
59. [Homomorphisms](https://invisiblenetwork.ai/learn/nptel/111106137/3d513339c15f) (YouTube)
60. [More examples of homomorphisms](https://invisiblenetwork.ai/learn/nptel/111106137/2d000d798652) (YouTube)
61. [First isomorphism theorem](https://invisiblenetwork.ai/learn/nptel/111106137/df4a5561cd9f) (YouTube)
62. [Direct sums of modules](https://invisiblenetwork.ai/learn/nptel/111106137/7973253fb820) (YouTube)
63. [Complementary submodules](https://invisiblenetwork.ai/learn/nptel/111106137/fd3ada30bd1d) (YouTube)
64. [Change of ring](https://invisiblenetwork.ai/learn/nptel/111106137/80af51f25159) (YouTube)
65. [Problem solving](https://invisiblenetwork.ai/learn/nptel/111106137/d522d1b5a701) (YouTube)
66. [Free Modules (finitely generated)](https://invisiblenetwork.ai/learn/nptel/111106137/32eebe297070) (YouTube)
67. [Determinants](https://invisiblenetwork.ai/learn/nptel/111106137/e4761a28b984) (YouTube)
68. [Primary Decomposition](https://invisiblenetwork.ai/learn/nptel/111106137/20bad8980acd) (YouTube)
69. [Problem solving](https://invisiblenetwork.ai/learn/nptel/111106137/2531b1145f15) (YouTube)
70. [Finitely generated modules and the Noetherian condition](https://invisiblenetwork.ai/learn/nptel/111106137/7c8c996b5c43) (YouTube)
71. [Counterexamples to the Noetherian condition](https://invisiblenetwork.ai/learn/nptel/111106137/26d019dc87d5) (YouTube)
72. [Generators and relations for Finitely Generated Modules](https://invisiblenetwork.ai/learn/nptel/111106137/27affee97eb4) (YouTube)
73. [General Linear Group over a Commutative Ring](https://invisiblenetwork.ai/learn/nptel/111106137/e212ea85d537) (YouTube)
74. [Equivalence of Matrices](https://invisiblenetwork.ai/learn/nptel/111106137/1d4e6608bc35) (YouTube)
75. [Smith Canonical Form for a Euclidean domain](https://invisiblenetwork.ai/learn/nptel/111106137/e91c8c9be971) (YouTube)
76. [solved_problems1](https://invisiblenetwork.ai/learn/nptel/111106137/0b3afd21c48d) (YouTube)
77. [Smith Canonical Form for PID](https://invisiblenetwork.ai/learn/nptel/111106137/b3cc335768c0) (YouTube)
78. [Structure of finitely generated modules over a PID](https://invisiblenetwork.ai/learn/nptel/111106137/892546fa1853) (YouTube)
79. [Structure of a finitely generated abelian group](https://invisiblenetwork.ai/learn/nptel/111106137/b0f4b2109c1f) (YouTube)
80. [Similarity of Matrices](https://invisiblenetwork.ai/learn/nptel/111106137/bd0802c2266c) (YouTube)
81. [Deciding Similarity](https://invisiblenetwork.ai/learn/nptel/111106137/d0af44cfda83) (YouTube)
82. [Rational Canonical Form](https://invisiblenetwork.ai/learn/nptel/111106137/09549246c407) (YouTube)
83. [Jordan Canonical Form](https://invisiblenetwork.ai/learn/nptel/111106137/fb544a290409) (YouTube)