# Mathematical Tools for Cognitive Science

- Institution: IIT Kanpur
- Department: Multidisciplinary
- Teacher: Prof. Himanshu Yadav
- Level: Undergraduate
- Language: English
- Subjects: Mathematics, Psychology and the brain
- Source: [NPTEL](https://nptel.ac.in/courses/127104003)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/127104003)
- Who can watch: Teens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This is a foundational course on Mathematics intended for students of Cognitive Science, Cognitive Systems, Psychology, and Linguistics. We are going to cover the following topics:. functions, differentiation, Matrix and Vector Algebra, Integration, multivariate calculus, and sets, probability, and random variables.

Intended audience: Cognitive Science students, Psychology students, Linguistics students, Biological and Neuroscience students

## Lectures

1. [Lecture 01: Real numbers and Exponents](https://invisiblenetwork.ai/learn/nptel/127104003/35209abb32f8) (YouTube)
2. [Lecture 02: Equations](https://invisiblenetwork.ai/learn/nptel/127104003/bad598dc405d) (YouTube)
3. [Lecture 03: Graphs](https://invisiblenetwork.ai/learn/nptel/127104003/b5ad23c70271) (YouTube)
4. [Lecture 04: Graphs and Equations](https://invisiblenetwork.ai/learn/nptel/127104003/48a34c0c8360) (YouTube)
5. [Lecture 05: Functions](https://invisiblenetwork.ai/learn/nptel/127104003/d59c090fa429) (YouTube)
6. [Lecture 06: Inverse Functions](https://invisiblenetwork.ai/learn/nptel/127104003/d1d582765c40) (YouTube)
7. [Lecture 07: Graphs of Inverse Functions](https://invisiblenetwork.ai/learn/nptel/127104003/60ce18c3bf06) (YouTube)
8. [Lecture 08: Exponential Functions](https://invisiblenetwork.ai/learn/nptel/127104003/4a52f4d1a232) (YouTube)
9. [Lecture 09: Logarithmic Functions](https://invisiblenetwork.ai/learn/nptel/127104003/e2a57421405d) (YouTube)
10. [Lecture 10: Applications of Logarithmic and Exponential Functions](https://invisiblenetwork.ai/learn/nptel/127104003/e4de2597d5a8) (YouTube)
11. [Lecture 11: Introduction to Trigonometric Functions](https://invisiblenetwork.ai/learn/nptel/127104003/925fc8725851) (YouTube)
12. [Lecture 12: Sine and Cosine Functions](https://invisiblenetwork.ai/learn/nptel/127104003/4bec45e4f978) (YouTube)
13. [Lecture 13: Trigonometric Identities](https://invisiblenetwork.ai/learn/nptel/127104003/c470c38d37b6) (YouTube)
14. [Lecture 14: Trigonometric Identities: Examples](https://invisiblenetwork.ai/learn/nptel/127104003/deb81a02301e) (YouTube)
15. [Lecture 15: Representation of a point in a plane](https://invisiblenetwork.ai/learn/nptel/127104003/0fc9f9df1c06) (YouTube)
16. [Lecture 16: Introduction to Differentiation](https://invisiblenetwork.ai/learn/nptel/127104003/e2f26550ba01) (YouTube)
17. [Lecture 17: Derivative of a Function](https://invisiblenetwork.ai/learn/nptel/127104003/250421c51b29) (YouTube)
18. [Lecture 18: Some Basic Derivatives](https://invisiblenetwork.ai/learn/nptel/127104003/25829a939a76) (YouTube)
19. [Lecture 19: Differentiation Examples](https://invisiblenetwork.ai/learn/nptel/127104003/fdb92541c515) (YouTube)
20. [Lecture 20: Practice Problems on Differentiation](https://invisiblenetwork.ai/learn/nptel/127104003/1587333f1ee9) (YouTube)
21. [Lecture 21: Maxima and Minima of a Function](https://invisiblenetwork.ai/learn/nptel/127104003/f5fd899344ed) (YouTube)
22. [Lecture 22: Maxima and Minima examples](https://invisiblenetwork.ai/learn/nptel/127104003/639d7d1eac87) (YouTube)
23. [Lecture 23: Partial Derivative](https://invisiblenetwork.ai/learn/nptel/127104003/f3c44e2d1a18) (YouTube)
24. [Lecture 24: Least Squares Method](https://invisiblenetwork.ai/learn/nptel/127104003/f7e5adfafec2) (YouTube)
25. [Lecture 25: Differentiation Applications](https://invisiblenetwork.ai/learn/nptel/127104003/a573a9026f21) (YouTube)
26. [Lecture 26: Introduction to Matrices](https://invisiblenetwork.ai/learn/nptel/127104003/d8ab18153b3d) (YouTube)
27. [Lecture 27: Matrix Operations](https://invisiblenetwork.ai/learn/nptel/127104003/fea4af07ad72) (YouTube)
28. [Lecture 28: Inverse Matrix](https://invisiblenetwork.ai/learn/nptel/127104003/38dfae2e4d7e) (YouTube)
29. [Lecture 29: Introduction to Vectors](https://invisiblenetwork.ai/learn/nptel/127104003/ca018b459d57) (YouTube)
30. [Lecture 30: Dot Product and Cross Product](https://invisiblenetwork.ai/learn/nptel/127104003/a51824459333) (YouTube)
31. [Lecture 31: Introduction to Integration](https://invisiblenetwork.ai/learn/nptel/127104003/59b522bab265) (YouTube)
32. [Lecture 32: Some Basic Integrals](https://invisiblenetwork.ai/learn/nptel/127104003/bc24b2fc8258) (YouTube)
33. [Lecture 33: Integration Examples](https://invisiblenetwork.ai/learn/nptel/127104003/5a39db50cb5a) (YouTube)
34. [Lecture 34: Substitution Method of Integration](https://invisiblenetwork.ai/learn/nptel/127104003/ec906949b7fa) (YouTube)
35. [Lecture 35: Integration by Parts](https://invisiblenetwork.ai/learn/nptel/127104003/2bd41497b11f) (YouTube)
36. [Lecture 36: Introduction to Sets](https://invisiblenetwork.ai/learn/nptel/127104003/585c264218b5) (YouTube)
37. [Lecture 37: Operations on Sets](https://invisiblenetwork.ai/learn/nptel/127104003/7e641bde4a91) (YouTube)
38. [Lecture 38: Properties of Sets](https://invisiblenetwork.ai/learn/nptel/127104003/0cb130ccc052) (YouTube)
39. [Lecture 39: Algebra of Sets](https://invisiblenetwork.ai/learn/nptel/127104003/71a503c3f8f8) (YouTube)
40. [Lecture 40: Sets and Probability](https://invisiblenetwork.ai/learn/nptel/127104003/6348edaf28d9) (YouTube)
41. [Lecture 41: Introduction to Probability](https://invisiblenetwork.ai/learn/nptel/127104003/773c307b9e57) (YouTube)
42. [Lecture 42: Probability Axioms](https://invisiblenetwork.ai/learn/nptel/127104003/8be772e3a87c) (YouTube)
43. [Lecture 43: Probability Corollaries](https://invisiblenetwork.ai/learn/nptel/127104003/0870fdc7bf74) (YouTube)
44. [Lecture 44: Conditional Probability](https://invisiblenetwork.ai/learn/nptel/127104003/9fdabb661313) (YouTube)
45. [Lecture 45: Probability Examples](https://invisiblenetwork.ai/learn/nptel/127104003/bf972dcf73c8) (YouTube)
46. [Lecture 46: Introduction to Random Variables](https://invisiblenetwork.ai/learn/nptel/127104003/a0cba23d5347) (YouTube)
47. [Lecture 47: Discrete and Continuous Random Variables](https://invisiblenetwork.ai/learn/nptel/127104003/64e9e8e2d54b) (YouTube)
48. [Lecture 48: Binomial and Poisson Distributions](https://invisiblenetwork.ai/learn/nptel/127104003/ba446b3cd5f1) (YouTube)
49. [Lecture 49: Normal and Lognormal Distributions](https://invisiblenetwork.ai/learn/nptel/127104003/a7bc6b2f2f32) (YouTube)
50. [Lecture 50: Other Continuous Random Variables](https://invisiblenetwork.ai/learn/nptel/127104003/c404f619eb65) (YouTube)
51. [Lecture 51: Probability Distributions in R](https://invisiblenetwork.ai/learn/nptel/127104003/a0a679b6edea) (YouTube)
52. [Lecture 52: Continuous Random Variables in R](https://invisiblenetwork.ai/learn/nptel/127104003/caf466583183) (YouTube)
53. [Lecture 53: Random Variables Examples in R](https://invisiblenetwork.ai/learn/nptel/127104003/d0bc8f8a910e) (YouTube)
54. [Lecture 54: Likelihood Function](https://invisiblenetwork.ai/learn/nptel/127104003/abe7975b63c5) (YouTube)
55. [Lecture 55: Likelihood Function in R](https://invisiblenetwork.ai/learn/nptel/127104003/c882ee4194aa) (YouTube)
56. [Lecture 56: Joint Likelihood Function](https://invisiblenetwork.ai/learn/nptel/127104003/0be3330c6670) (YouTube)
57. [Lecture 57: Joint Likelihood in R](https://invisiblenetwork.ai/learn/nptel/127104003/8fb5d3177fe8) (YouTube)
58. [Lecture 58: Parameter Estimation](https://invisiblenetwork.ai/learn/nptel/127104003/c653462c3943) (YouTube)
59. [Lecture 59: Statistical Inference](https://invisiblenetwork.ai/learn/nptel/127104003/4e7e6092fb43) (YouTube)
60. [Lecture 60: Statistical Inference in the Bayesian Framework](https://invisiblenetwork.ai/learn/nptel/127104003/19296c4e86e1) (YouTube)