# An Introduction to Number Theory - Institution: IIT Kanpur - Department: Mathematics - Teacher: Prof. Somnath Jha - Level: Undergraduate - Language: English - Subjects: Mathematics - Source: [NPTEL](https://nptel.ac.in/courses/111104900) - Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.) - Syllabus: [at the source](https://nptel.ac.in/courses/111104900) - Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words) ## Lectures 1. [Lecture 1: Abelian Groups - I](https://invisiblenetwork.ai/learn/nptel/111104900/52bd506a5da7) (Video) 2. [Lecture2: Abelian Groups - II](https://invisiblenetwork.ai/learn/nptel/111104900/2f51736743bc) (Video) 3. [Lecture3: Abelian Groups - III](https://invisiblenetwork.ai/learn/nptel/111104900/53ab07699fc8) (Video) 4. [Lecture 4: Abelian Groups - IV](https://invisiblenetwork.ai/learn/nptel/111104900/7d032a451ae4) (Video) 5. [Lecture 5: Abelian Groups - V](https://invisiblenetwork.ai/learn/nptel/111104900/5d9395404609) (Video) 6. [Lecture 6: Abelian Groups - VI](https://invisiblenetwork.ai/learn/nptel/111104900/9e9e151354a1) (Video) 7. [Lecture 7: Commutative Rings - I](https://invisiblenetwork.ai/learn/nptel/111104900/b4c51696f599) (Video) 8. [Lecture 8: Commutative Rings - II](https://invisiblenetwork.ai/learn/nptel/111104900/059edd22efa6) (Video) 9. [Lecture 9: Commutative Rings -III](https://invisiblenetwork.ai/learn/nptel/111104900/1118d4336f41) (Video) 10. [Lecture 10: Chinese Reminder Theorem](https://invisiblenetwork.ai/learn/nptel/111104900/4a92a0ff688b) (Video) 11. [Lecture 11: Fermat's Little Theorem and Wilson's Theorem](https://invisiblenetwork.ai/learn/nptel/111104900/b18fe9407e5e) (Video) 12. [Lecture 12: Prime ideals and maximal ideals](https://invisiblenetwork.ai/learn/nptel/111104900/185760335d56) (Video) 13. [Lecture 13: Ideals in a PID](https://invisiblenetwork.ai/learn/nptel/111104900/fa937926d038) (Video) 14. [Lecture 14: Ideals in a UFD](https://invisiblenetwork.ai/learn/nptel/111104900/327e253794cc) (Video) 15. [Lecture 15: Gauss Lemma](https://invisiblenetwork.ai/learn/nptel/111104900/3c14dd22ac85) (Video) 16. [Lecture 16: Field Extensions](https://invisiblenetwork.ai/learn/nptel/111104900/6d2daa6f390a) (Video) 17. [Lecture 17: Finite Fields](https://invisiblenetwork.ai/learn/nptel/111104900/bf0f663a600e) (Video) 18. [Lecture 18: Multiplicative groups of finite fields](https://invisiblenetwork.ai/learn/nptel/111104900/bc16c5603d7b) (Video) 19. [Lecture 19: Legendre Symbol](https://invisiblenetwork.ai/learn/nptel/111104900/5501484bdca9) (Video) 20. [Lecture 20: Quadratic Reciprocity](https://invisiblenetwork.ai/learn/nptel/111104900/85a33848e454) (Video) 21. [Lecture 21: Zero sets of polynomials](https://invisiblenetwork.ai/learn/nptel/111104900/f18b004bef99) (Video) 22. [Lecture 22 : Ring of quadratic integers - I](https://invisiblenetwork.ai/learn/nptel/111104900/fe560dc28eef) (Video) 23. [Lecture 23 : Ring of quadratic integers - II](https://invisiblenetwork.ai/learn/nptel/111104900/722362f96bcd) (Video) 24. [Lecture 24 : Gaussian integers](https://invisiblenetwork.ai/learn/nptel/111104900/9f0fbff8b81d) (Video) 25. [Lecture 25: Ring of quadratic integers - III](https://invisiblenetwork.ai/learn/nptel/111104900/f0fee2497507) (Video) 26. [Lecture 26 : Ring of quadratic integers - IV](https://invisiblenetwork.ai/learn/nptel/111104900/fb87058198be) (Video) 27. [Lecture 27: Ideal class group of quadratic fields](https://invisiblenetwork.ai/learn/nptel/111104900/89eae496850b) (Video) 28. [Lecture 28: Binary quadratic forms](https://invisiblenetwork.ai/learn/nptel/111104900/45fe21b950ee) (Video) 29. [Lecture 29: Binary quadratic forms and ideal class group of imaginary quadratic fields – I](https://invisiblenetwork.ai/learn/nptel/111104900/ec4ad9500bd5) (Video) 30. [Lecture 30: Binary quadratic forms and ideal class group of imaginary quadratic fields – II](https://invisiblenetwork.ai/learn/nptel/111104900/a28c89a1e3ad) (Video) 31. [Lecture 31: Binary quadratic forms and ideal class group of imaginary quadratic fields – III](https://invisiblenetwork.ai/learn/nptel/111104900/02adf74cb852) (Video) 32. [Lecture 32: Binary quadratic forms and ideal class group of imaginary quadratic fields – IV](https://invisiblenetwork.ai/learn/nptel/111104900/9225f7d64e87) (Video) 33. [Lecture 33: Units in the rings of quadratic integers](https://invisiblenetwork.ai/learn/nptel/111104900/762d83af80ea) (Video) 34. [Lecture 34: Integral solutions of the equation 𝑥 2 − 2𝑦 2 = 1](https://invisiblenetwork.ai/learn/nptel/111104900/e2d488d675b2) (Video) 35. [Lecture 35: Dirichlet's approximation theorem](https://invisiblenetwork.ai/learn/nptel/111104900/4bdd2da97aee) (Video) 36. [Lecture 36: Brahmagupta - Pell's equation](https://invisiblenetwork.ai/learn/nptel/111104900/e8bb7696c8b0) (Video) 37. [Lecture 37: Congruent Numbers - I](https://invisiblenetwork.ai/learn/nptel/111104900/0552e7a21bbf) (Video) 38. [Lecture 38: Congruent Numbers - II](https://invisiblenetwork.ai/learn/nptel/111104900/419b213facad) (Video) 39. [Lecture 39: The n = 4 case of the Fermat's Last Theorem](https://invisiblenetwork.ai/learn/nptel/111104900/9b6cc083dd5c) (Video) 40. [Lecture 40: Congruent Numbers and Elliptic Curves](https://invisiblenetwork.ai/learn/nptel/111104900/2692f8854ad0) (Video) 41. [Lecture 41: Sum of two squares theorem](https://invisiblenetwork.ai/learn/nptel/111104900/62d087ed8af2) (Video) 42. [Lecture 42: Sum of four squares theorem](https://invisiblenetwork.ai/learn/nptel/111104900/49a40cfac662) (Video) 43. [Lecture 43: Sum of integer cubes](https://invisiblenetwork.ai/learn/nptel/111104900/c9c80a4e3cec) (Video) 44. [Lecture 44: Rational cube sum problem](https://invisiblenetwork.ai/learn/nptel/111104900/f8b2436c82e2) (Video) 45. [Lecture 45: Affine and Projective Spaces- I](https://invisiblenetwork.ai/learn/nptel/111104900/7d70c2172e61) (Video) 46. [Lecture 46: Affine and Projective Spaces- II](https://invisiblenetwork.ai/learn/nptel/111104900/dd5f6e14bb4f) (Video) 47. [Lecture 47: Elliptic Curves - I](https://invisiblenetwork.ai/learn/nptel/111104900/758919424ba8) (Video) 48. [Lecture 48: Elliptic Curves - II](https://invisiblenetwork.ai/learn/nptel/111104900/91fb45b6e24d) (Video)