# Algebraic Number Theory

- Institution: IISc Bangalore
- Department: Mathematics
- Teacher: Prof. Mahesh Kakde
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111108609)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111108609)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lec 01 Overview and Motivation](https://invisiblenetwork.ai/learn/nptel/111108609/33fce6c20340) (Video)
2. [Lec 02 Algebraic Numbers](https://invisiblenetwork.ai/learn/nptel/111108609/2ab51033d7a6) (Video)
3. [Lec 03 The ring of integers](https://invisiblenetwork.ai/learn/nptel/111108609/951d5f041c17) (Video)
4. [Lec 04 Lattices](https://invisiblenetwork.ai/learn/nptel/111108609/6221654a313c) (Video)
5. [Lec 05 Properties of ring of integers](https://invisiblenetwork.ai/learn/nptel/111108609/e546408a6a25) (Video)
6. [Lec 06 Discriminant](https://invisiblenetwork.ai/learn/nptel/111108609/21065f9a22c9) (Video)
7. [Lec 07 Dedekind Domains (DD)](https://invisiblenetwork.ai/learn/nptel/111108609/d1dcfb694780) (Video)
8. [Lec 08 Algebraic properties of DD](https://invisiblenetwork.ai/learn/nptel/111108609/fd7d205157b5) (Video)
9. [Lec 09 Unique Factorization of Ideals-1](https://invisiblenetwork.ai/learn/nptel/111108609/6ec38bb3ff0f) (Video)
10. [Lec 10 Unique Factorization of Ideals-2](https://invisiblenetwork.ai/learn/nptel/111108609/88ecd991c8e7) (Video)
11. [Lec 11 Ring of Integers is a DD](https://invisiblenetwork.ai/learn/nptel/111108609/c8922a15a5d0) (Video)
12. [Lec 12 Ideal Class Group](https://invisiblenetwork.ai/learn/nptel/111108609/40d08bbb7f05) (Video)
13. [Lec 13 Integral Ideal in an ideal class](https://invisiblenetwork.ai/learn/nptel/111108609/b26c4f9f6f26) (Video)
14. [Lec 14 Finiteness of ideal class group](https://invisiblenetwork.ai/learn/nptel/111108609/3de3b5f1f701) (Video)
15. [Lec 15 Geometry of numbers-1](https://invisiblenetwork.ai/learn/nptel/111108609/326aeeec0127) (Video)
16. [Lec 16 Geometry of numbers-2](https://invisiblenetwork.ai/learn/nptel/111108609/b557c1709880) (Video)
17. [Lec 17 Dirichlet's Unit Theorem-1](https://invisiblenetwork.ai/learn/nptel/111108609/12cb7a3468d5) (Video)
18. [Lec 18 Dirichlet's Unit Theorem-2](https://invisiblenetwork.ai/learn/nptel/111108609/41f278ee5dee) (Video)
19. [Lec 19 Relative extension-1](https://invisiblenetwork.ai/learn/nptel/111108609/3362cce4fc09) (Video)
20. [Lec 20 Relative extension-2](https://invisiblenetwork.ai/learn/nptel/111108609/7a8b16a46a17) (Video)
21. [Lec 21 Decomposition Group](https://invisiblenetwork.ai/learn/nptel/111108609/ddf3e9c84698) (Video)
22. [Lec 22 Inertia Group](https://invisiblenetwork.ai/learn/nptel/111108609/b1b1a456bfc4) (Video)
23. [Lec 23 The Artin map](https://invisiblenetwork.ai/learn/nptel/111108609/b7b8722b082a) (Video)
24. [Lec 24 Valuations](https://invisiblenetwork.ai/learn/nptel/111108609/630a50815d6f) (Video)
25. [Lec 25 Archimedean valuations](https://invisiblenetwork.ai/learn/nptel/111108609/c759612beebe) (Video)
26. [Lec 26 Non-archimedean valuations](https://invisiblenetwork.ai/learn/nptel/111108609/7b6c7506e566) (Video)
27. [Lec 27 p-adic numbers](https://invisiblenetwork.ai/learn/nptel/111108609/7856273caa35) (Video)
28. [Lec 28 p-adic completion of a Number field](https://invisiblenetwork.ai/learn/nptel/111108609/852ddb2ea8ae) (Video)
29. [Lec 29 Product formula](https://invisiblenetwork.ai/learn/nptel/111108609/b5b06235fbc3) (Video)
30. [Lec 30 Hensel's lemma](https://invisiblenetwork.ai/learn/nptel/111108609/9b86f5717472) (Video)
31. [Lec 31 Finite extensions of local fields](https://invisiblenetwork.ai/learn/nptel/111108609/380c4d30f256) (Video)
32. [Lec 32 Factorisation of conorm of a prime ideal in a finite extension-I](https://invisiblenetwork.ai/learn/nptel/111108609/6feda51370e9) (Video)
33. [Lec 33 Factorisation of conorm of a prime ideal in a finite extension-II](https://invisiblenetwork.ai/learn/nptel/111108609/f80e74135bfa) (Video)
34. [Lec 34 Different-I](https://invisiblenetwork.ai/learn/nptel/111108609/3091038658ec) (Video)
35. [Lec 35 Different-II](https://invisiblenetwork.ai/learn/nptel/111108609/6e6a317a82cb) (Video)
36. [Lec 36 Different-III](https://invisiblenetwork.ai/learn/nptel/111108609/9ae4674dff56) (Video)
37. [Lec 37 Ramification and different ideal](https://invisiblenetwork.ai/learn/nptel/111108609/a410b4fd6509) (Video)
38. [Lec 38 Quadratic Fields](https://invisiblenetwork.ai/learn/nptel/111108609/e1a2df5df488) (Video)
39. [Lec 39 Binary quadratic forms-I](https://invisiblenetwork.ai/learn/nptel/111108609/1d17c3df72e3) (Video)
40. [Lec 40 Binary quadratic forms-II](https://invisiblenetwork.ai/learn/nptel/111108609/7968f605841a) (Video)
41. [Lec 41 Reduced binary quadratic forms](https://invisiblenetwork.ai/learn/nptel/111108609/399bec848bb1) (Video)
42. [Lec 42 Class group of imaginary quadratic fields and binary quadratic forms-1](https://invisiblenetwork.ai/learn/nptel/111108609/eea70da8d0ab) (Video)
43. [Lec 43 Class group of imaginary quadratic fields and binary quadratic forms-2](https://invisiblenetwork.ai/learn/nptel/111108609/d43613c7ac20) (Video)
44. [Lec 44 Computation of Class group of imaginary quadratic fields using binary quadratic forms](https://invisiblenetwork.ai/learn/nptel/111108609/976bde2e5446) (Video)
45. [Lec 45 Order two elements in Class group of imaginary quadratic fields](https://invisiblenetwork.ai/learn/nptel/111108609/1870091f683a) (Video)
46. [Lec 46 Pure cubic fields-1](https://invisiblenetwork.ai/learn/nptel/111108609/51aed37e0bef) (Video)
47. [Lec 47 Pure cubic fields-2](https://invisiblenetwork.ai/learn/nptel/111108609/a88ef9185c2f) (Video)
48. [Lec 48 Pell's equation-1](https://invisiblenetwork.ai/learn/nptel/111108609/7d25bec4143f) (Video)
49. [Lec 49 Pell's equation-2](https://invisiblenetwork.ai/learn/nptel/111108609/5939945306cf) (Video)
50. [Lec 50 Biquadratic fields-1](https://invisiblenetwork.ai/learn/nptel/111108609/b12118643fd3) (Video)
51. [Lec 51 Biquadratic fields-2](https://invisiblenetwork.ai/learn/nptel/111108609/2b90f1238265) (Video)
52. [Lec 52 Cyclotomic fields-1](https://invisiblenetwork.ai/learn/nptel/111108609/c5f03bcbf651) (Video)
53. [Lec 53 Cyclotomic fields-2](https://invisiblenetwork.ai/learn/nptel/111108609/8d8b9f90a7b2) (Video)
54. [Lec 54 Compuation of class groups-1](https://invisiblenetwork.ai/learn/nptel/111108609/4ec09aee1108) (Video)
55. [Lec 55 Compuation of class groups-2](https://invisiblenetwork.ai/learn/nptel/111108609/73686c172014) (Video)
56. [Lec 56 Compuation of class groups-3](https://invisiblenetwork.ai/learn/nptel/111108609/5770d5894960) (Video)
57. [Lec 57 Compuation of class groups-4](https://invisiblenetwork.ai/learn/nptel/111108609/8d1f153f1642) (Video)
58. [Live Session 28-03-2025](https://invisiblenetwork.ai/learn/nptel/111108609/33fce6c20340-2) (Video)
59. [Live Session 04-04-2025](https://invisiblenetwork.ai/learn/nptel/111108609/2ab51033d7a6-2) (Video)
60. [Live Session 15-04-2025](https://invisiblenetwork.ai/learn/nptel/111108609/951d5f041c17-2) (Video)