# An Invitation to Mathematics

- Institution: IMSc
- Department: Mathematics
- Teacher: Prof. Sankaran Vishwanath
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111106083)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111106083)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Introduction](https://invisiblenetwork.ai/learn/nptel/111106083/a99f8e2f75bf) (Video)
2. [Long division](https://invisiblenetwork.ai/learn/nptel/111106083/046e76de1822) (Video)
3. [Applications of Long division](https://invisiblenetwork.ai/learn/nptel/111106083/b8daa9422649) (Video)
4. [Lagrange interpolation](https://invisiblenetwork.ai/learn/nptel/111106083/c247ca25e330) (Video)
5. [The 0-1 idea in other contexts - dot and cross product](https://invisiblenetwork.ai/learn/nptel/111106083/2e62aa90068d) (Video)
6. [Taylors formula](https://invisiblenetwork.ai/learn/nptel/111106083/323021ec6175) (Video)
7. [The Chebyshev polynomials](https://invisiblenetwork.ai/learn/nptel/111106083/59e0f4cc6387) (Video)
8. [Counting number of monomials - several variables](https://invisiblenetwork.ai/learn/nptel/111106083/65e71584ce63) (Video)
9. [Permutations, combinations and the binomial theorem.](https://invisiblenetwork.ai/learn/nptel/111106083/d3413cbc3270) (Video)
10. [Combinations with repetition, and counting monomials.](https://invisiblenetwork.ai/learn/nptel/111106083/37ee8279e335) (Video)
11. [Combinations with restrictions, recurrence relations](https://invisiblenetwork.ai/learn/nptel/111106083/2dc3ef86ce81) (Video)
12. [Fibonacci numbers; an identity and a bijective proof.](https://invisiblenetwork.ai/learn/nptel/111106083/23783ef2268a) (Video)
13. [Permutations and cycle type](https://invisiblenetwork.ai/learn/nptel/111106083/09296f5ca9b7) (Video)
14. [The sign of a permutation, composition of permutations](https://invisiblenetwork.ai/learn/nptel/111106083/efd4c78082de) (Video)
15. [Rules for drawing tangle diagrams](https://invisiblenetwork.ai/learn/nptel/111106083/ab300a60f8db) (Video)
16. [Signs and cycle decompositions](https://invisiblenetwork.ai/learn/nptel/111106083/6b0fd99e5dad) (Video)
17. [Sorting lists of numbers, and crossings in tangle diagrams](https://invisiblenetwork.ai/learn/nptel/111106083/cce595629459) (Video)
18. [Real and integer valued polynomials](https://invisiblenetwork.ai/learn/nptel/111106083/4ef22f9f8a58) (Video)
19. [Integer valued polynomials revisited.](https://invisiblenetwork.ai/learn/nptel/111106083/34c29b633162) (Video)
20. [Functions on the real line, continuity](https://invisiblenetwork.ai/learn/nptel/111106083/61c15d64088c) (Video)
21. [The intermediate value property.](https://invisiblenetwork.ai/learn/nptel/111106083/440cb5b67b71) (Video)
22. [Visualizing functions.](https://invisiblenetwork.ai/learn/nptel/111106083/739eb2d063fe) (Video)
23. [Functions on the plane, Rigid motions.](https://invisiblenetwork.ai/learn/nptel/111106083/80f5f91d61d7) (Video)
24. [More examples of functions on the plane, dilations.](https://invisiblenetwork.ai/learn/nptel/111106083/21bac46bb1b1) (Video)
25. [Composition of functions](https://invisiblenetwork.ai/learn/nptel/111106083/aae92a924d4f) (Video)
26. [Affine and Linear transformations](https://invisiblenetwork.ai/learn/nptel/111106083/68d3e8e223e9) (Video)
27. [Length and Area dilation, the derivative](https://invisiblenetwork.ai/learn/nptel/111106083/b3abffa13210) (Video)
28. [Examples-I](https://invisiblenetwork.ai/learn/nptel/111106083/1f6986e9343d) (Video)
29. [Examples-II](https://invisiblenetwork.ai/learn/nptel/111106083/0ac55aaf346b) (Video)
30. [Linear equations, Lagrange interpolation revisited](https://invisiblenetwork.ai/learn/nptel/111106083/8df6cb80bc1d) (Video)
31. [Completed Matrices in combinatorics](https://invisiblenetwork.ai/learn/nptel/111106083/b99752d378d0) (Video)
32. [Polynomials acting on matrices](https://invisiblenetwork.ai/learn/nptel/111106083/ba432db20a19) (Video)
33. [Divisibility, prime numbers](https://invisiblenetwork.ai/learn/nptel/111106083/007f265e1fd3) (Video)
34. [Congruences, Modular arithmetic](https://invisiblenetwork.ai/learn/nptel/111106083/a244752dc0df) (Video)
35. [The Chinese remainder theorem](https://invisiblenetwork.ai/learn/nptel/111106083/830b587cd02f) (Video)
36. [The Euclidean algorithm, the 0-1 idea and the Chinese remainder theorem](https://invisiblenetwork.ai/learn/nptel/111106083/16d19c52c72b) (Video)