# Mathematical Foundations for Machine Learning

- Institution: IISc Bangalore
- Department: Computer Science and Engineering
- Taught by: Prof. Ashok Rao, Prof. Arulalan Rajan
- Level: Undergraduate
- Language: English
- Subjects: Computer science, Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/106108702)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/106108702)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

This course will provide a holistic approach to the mathematical foundations for Machine Learning. The course is focussed on developing mathematical ideas, necessary for machine learning applications, through intuitions and visualizations.The course primarily focuses on three important mathematical domains, namely

Linear Algebra

Probabilty and Statistics and

Multivariable Calculus,

on which the ML and data science ideas are built.

Intended audience: BE/BTech/ME/MTech//BSc/MSc(Maths)/MCA

Prerequisites: Basic Mathematics at school and undergraduate level

## Lectures

1. [Why this course?](https://invisiblenetwork.ai/learn/nptel/106108702/38ebd13a6b17) (YouTube)
2. [Fields and Their Properties – Algebraic Tools for ML](https://invisiblenetwork.ai/learn/nptel/106108702/98ef84439eba) (YouTube)
3. [Fields, Vector Spaces](https://invisiblenetwork.ai/learn/nptel/106108702/150faad3f67a) (YouTube)
4. [Vector Spaces and Subspaces](https://invisiblenetwork.ai/learn/nptel/106108702/8a59f8a4e50e) (YouTube)
5. [Combining Vectors and Linear Independence](https://invisiblenetwork.ai/learn/nptel/106108702/2c8ab5e33185) (YouTube)
6. [Basis and Dimension](https://invisiblenetwork.ai/learn/nptel/106108702/26cff1c75676) (YouTube)
7. [Linear Transformation - Intuition](https://invisiblenetwork.ai/learn/nptel/106108702/47c05a67282f) (YouTube)
8. [Subspaces associated with Linear Transformations](https://invisiblenetwork.ai/learn/nptel/106108702/63bed58ca444) (YouTube)
9. [Matrix representation of Linear Transformation](https://invisiblenetwork.ai/learn/nptel/106108702/65ee1c294ce5) (YouTube)
10. [Examples of Linear Transformation](https://invisiblenetwork.ai/learn/nptel/106108702/88e04fb31fab) (YouTube)
11. [Eigenvalues and Eigenvectors](https://invisiblenetwork.ai/learn/nptel/106108702/2d43b6f0be90) (YouTube)
12. [Multiplicity of Eigen Values](https://invisiblenetwork.ai/learn/nptel/106108702/83b140fee0bd) (YouTube)
13. [Diagonalization of Matrix](https://invisiblenetwork.ai/learn/nptel/106108702/e1ce5207ea51) (YouTube)
14. [Diagonalizability, Invariant subspaces](https://invisiblenetwork.ai/learn/nptel/106108702/d36260ad546f) (YouTube)
15. [Dot Product on Vector Space](https://invisiblenetwork.ai/learn/nptel/106108702/f9d546b807a5) (YouTube)
16. [Orthogonality on Vector Space](https://invisiblenetwork.ai/learn/nptel/106108702/a12a54d6687f) (YouTube)
17. [Orthonormal Basis](https://invisiblenetwork.ai/learn/nptel/106108702/4372ad64ef90) (YouTube)
18. [Orthogonal Projections](https://invisiblenetwork.ai/learn/nptel/106108702/4ee6b70075b0) (YouTube)
19. [Construction of Orthogonal Basis](https://invisiblenetwork.ai/learn/nptel/106108702/b746f821dade) (YouTube)
20. [Approximating a vector in any given subspace](https://invisiblenetwork.ai/learn/nptel/106108702/29fa32ac47fd) (YouTube)
21. [Real Symmetric Matrices](https://invisiblenetwork.ai/learn/nptel/106108702/c6526653c29d) (YouTube)
22. [Least Square Fitting and Pseudo Inverse - 1](https://invisiblenetwork.ai/learn/nptel/106108702/e1956531c7c3) (YouTube)
23. [Least Square Fitting and Pseudo Inverse - 2](https://invisiblenetwork.ai/learn/nptel/106108702/d9bb651187ae) (YouTube)
24. [Principal Component Analysis (PCA)](https://invisiblenetwork.ai/learn/nptel/106108702/ccbc1945f40d) (YouTube)
25. [Singular Value Decomposition (SVD)](https://invisiblenetwork.ai/learn/nptel/106108702/cd7f218cb402) (YouTube)
26. [Singular Value Decomposition (SVD) Interpretation](https://invisiblenetwork.ai/learn/nptel/106108702/ef6f85bfd6e8) (YouTube)
27. [Support Vector Machine (SVM)](https://invisiblenetwork.ai/learn/nptel/106108702/820dab9b1450) (YouTube)
28. [Consolidating Week1 to Week 4](https://invisiblenetwork.ai/learn/nptel/106108702/9ca3d9c4439a) (YouTube)
29. [Introduction to Probability - 1](https://invisiblenetwork.ai/learn/nptel/106108702/1af7162adfa2) (YouTube)
30. [Introduction to Probability - 2](https://invisiblenetwork.ai/learn/nptel/106108702/39f9481e04bc) (YouTube)
31. [Mutually Exclusive Events, Independent Events and Conditional Probability](https://invisiblenetwork.ai/learn/nptel/106108702/ef5c29384a53) (YouTube)
32. [Total Probability Theorem and Bayes' Theorem](https://invisiblenetwork.ai/learn/nptel/106108702/8a0801e2a27b) (YouTube)
33. [Probability - A Measure Theoretic Insight](https://invisiblenetwork.ai/learn/nptel/106108702/9a7178dd6f9e) (YouTube)
34. [Random Experiment and Random Variables](https://invisiblenetwork.ai/learn/nptel/106108702/a3b90689664e) (YouTube)
35. [Discrete Random Variables and Probability Mass Function (PMF)](https://invisiblenetwork.ai/learn/nptel/106108702/9eb8c6b0b66a) (YouTube)
36. [Types of Discrete Random Variables and Their Probability Distributions](https://invisiblenetwork.ai/learn/nptel/106108702/8d3b3779a489) (YouTube)
37. [Continuous Random Variables](https://invisiblenetwork.ai/learn/nptel/106108702/214fcefc3531) (YouTube)
38. [Expected Value of Random Variable](https://invisiblenetwork.ai/learn/nptel/106108702/c4275b4a4732) (YouTube)
39. [Moments and Variance](https://invisiblenetwork.ai/learn/nptel/106108702/24fc73dbdcea) (YouTube)
40. [Joint Distributions and Marginals](https://invisiblenetwork.ai/learn/nptel/106108702/eb8e1c84fb1d) (YouTube)
41. [Joint Moments of Random Variables](https://invisiblenetwork.ai/learn/nptel/106108702/a4220df1bc77) (YouTube)
42. [Independence and Correlation](https://invisiblenetwork.ai/learn/nptel/106108702/28c01642dd6c) (YouTube)
43. [Correlation and Covariance](https://invisiblenetwork.ai/learn/nptel/106108702/2f5dc5db33d8) (YouTube)
44. [Joint Moments of Continuous random Variables and Conditioning of Random Variables](https://invisiblenetwork.ai/learn/nptel/106108702/bc4511029f03) (YouTube)
45. [Markov Inequality](https://invisiblenetwork.ai/learn/nptel/106108702/9ca5349df848) (YouTube)
46. [Chebychev Inequality](https://invisiblenetwork.ai/learn/nptel/106108702/cae7b2044733) (YouTube)
47. [Central Limit Theorem](https://invisiblenetwork.ai/learn/nptel/106108702/3fe86c88f8a2) (YouTube)
48. [Sample Geometry](https://invisiblenetwork.ai/learn/nptel/106108702/8ef1be11faa1) (YouTube)
49. [Covariance Matrix & its properties](https://invisiblenetwork.ai/learn/nptel/106108702/70504a57e17d) (YouTube)
50. [Functions, Derivatives, Infinite Series](https://invisiblenetwork.ai/learn/nptel/106108702/9c9f3272a50c) (YouTube)
51. [Differentiation Rules](https://invisiblenetwork.ai/learn/nptel/106108702/28fc2edc5d55) (YouTube)
52. [Multivariate functions](https://invisiblenetwork.ai/learn/nptel/106108702/74b8d29f109f) (YouTube)
53. [Gradient and Directional Derivatives](https://invisiblenetwork.ai/learn/nptel/106108702/484a46e94796) (YouTube)
54. [Rules for Partial Derivatives, Jacobian and Hessian](https://invisiblenetwork.ai/learn/nptel/106108702/161850237ed6) (YouTube)
55. [Matrix derivatives](https://invisiblenetwork.ai/learn/nptel/106108702/31f8fd03b5ae) (YouTube)
56. [Optimization Overview](https://invisiblenetwork.ai/learn/nptel/106108702/3edf1d3b93b7) (YouTube)
57. [Constrained Optimization, Optimal solutions, Saddle point](https://invisiblenetwork.ai/learn/nptel/106108702/b560e1e09779) (YouTube)
58. [Constrained optimization, Lagrange Multiplier](https://invisiblenetwork.ai/learn/nptel/106108702/a7619f660d82) (YouTube)
59. [Revisiting Least squares, Principal Component Analysis](https://invisiblenetwork.ai/learn/nptel/106108702/bdca432a1567) (YouTube)
60. [Minimizing the Cost Function: Gradent Descent Algorithm](https://invisiblenetwork.ai/learn/nptel/106108702/096bd9a72aca) (YouTube)
61. [Variants of the Gradient Descent Algorithm](https://invisiblenetwork.ai/learn/nptel/106108702/162c76e2b5c4) (YouTube)
62. [Neural Networks , Perceptron](https://invisiblenetwork.ai/learn/nptel/106108702/b92d66beb6ac) (YouTube)
63. [Multilayer Layer Perceptron](https://invisiblenetwork.ai/learn/nptel/106108702/5d0fb00ed100) (YouTube)
64. [Back Propogation Algorithm](https://invisiblenetwork.ai/learn/nptel/106108702/1c8207c2410b) (YouTube)
65. [Data and Patterns](https://invisiblenetwork.ai/learn/nptel/106108702/34134a60fc86) (YouTube)
66. [Classification and a simple binary classifier](https://invisiblenetwork.ai/learn/nptel/106108702/cb129efced8b) (YouTube)
67. [Classification, Clustering Techniques](https://invisiblenetwork.ai/learn/nptel/106108702/a8472b548292) (YouTube)
68. [Linear Regression : Line of best fit](https://invisiblenetwork.ai/learn/nptel/106108702/ead6d92ecbaa) (YouTube)
69. [Logistic Regression](https://invisiblenetwork.ai/learn/nptel/106108702/486afccb37fa) (YouTube)
70. [Course Summary, Credits & Acknowledgments](https://invisiblenetwork.ai/learn/nptel/106108702/d151ce1c34d5) (YouTube)