Instructor: Mitesh M. Khapra
When: August-November 2022
Lectures: Slot D
Where: CS25
Teaching Assistants: TBD
| Name | Working hours | Days | |
|---|---|---|---|
| Aswanth Kumar M | cs21m010@smail.iitm.ac.in | 2-3 pm | Wednesday |
| Hanumantappa Budihal | cs21m022@smail.iitm.ac.in | 2-3 pm | Wednesday |
| Keyur Raval | cs21m029@smail.iitm.ac.in | 2-3 pm | Wednesday |
| Mohammed Safi Ur Rahman Khan | cs21m035@smail.iitm.ac.in | 2-3 pm | Thursday |
| Nandini Mundra | cs21s041@smail.iitm.ac.in | 2-3 pm | Monday |
| Praveen S V | cs21s006@smail.iitm.ac.in | 2-3 pm | Tuesday |
| Sanjanaa G V | cs21m057@smail.iitm.ac.in | 2-3 pm | Monday |
| Siddesh Hegde | cs21m064@smail.iitm.ac.in | 2-3 pm | Thursday |
| Yash Hareshkumar Madhani | cs20s002@smail.iitm.ac.in | 2-3 pm | Friday |
| Lecture | Contents | Slides | Linear algebra and its applications (Gilbert Strang) Section mapping |
|---|---|---|---|
| Lecture 1 | Introduction to Vectors and Matrices | Slides | 1.1, 1.2 of GS |
| Lecture 2 | Fun with matrix multiplication, System of linear equations | Slides | 1.4, 1.6 of GS |
| Lecture 3 | Lines, planes, solving a system of linear equations | Slides | 1.2 of GS |
| Lecture 4 | Gauss Elimination, LU factorisation | Slides | 1.3, 1.4, 1.5 of GS |
| Lecture 5 | PA = LU, cost of Gaussian Elimination, the practical utility of LU factorisation, computing inverse using Gaussian Elimination | Slides | 1.3, 1.6, 1.5 of GS |
| Lecture 6 | Vector spaces, subspaces, independence, span, basis, dimensions | Slides | 2.1, 2.3 of GS |
| Lecture 7 | Column space of a matrix, null space of a matrix | Slides | 2.1 of GS |
| Lecture 8 | Solving Ax = 0 | Slides | 2.2 of GS |
| Lecture 9 | Solving Ax=b, Rank Nullity Theorem, some unsolved mysteries | Slides | 2.2 of GS |
| Lecture 10 | The four fundamental subspaces | Slides | 2.4 of GS |
| Lecture 11 | A tiny bit of ML, vector norms, orthogonal vectors, orthogonal subspaces | Slides | 3.1 of GS |
| Lecture 12 | Projecting a vector onto another vector, Projecting a vector on to a subspace, Linear Regression (Least Squares) | Slides | 3.2,3.3 of GS |
| Lecture 13 | Orthonormal vectors, orthonormal basis, Gram-Schmidt orthogonalization, QR factorisation | Slides | 3.1, 3.2, 3.3, 3.4 of GS |
| Lecture 14 | Properties of determinants | Slides | 4.2 of GS |
| Lecture 15 | Formula for determinant, co-factors, Finding A inverse, Cramer's rule for solving Ax=b, Determinant=Volume | Slides Essence of Linear Algebra (3Blue1Brown) |
4.3, 4.4 of GS |
| Lecture 16 | The Eigenstory begins, computing eigenvalues and eigenvectors | Slides | 5.1 of GS |
| Lecture 17 | Change of basis | Slides Essence of Linear Algebra (3Blue1Brown) |
- |
| Lecture 18 | Diagonalisation (Eigenvalue Decomposition) of a matrix, Computing powers of A | Slides | 5.2 of GS |
| Lecture 19 | Algebraic and Geometric Multiplicity, Schur's theorem, Spectral theorem for Symmetric matrices, Trace of a matrix | Slides | 5.5 of GS |
| Lecture 20 | Principal Component Analysis (the wishlist) | Slides | 5.5 of GS |
| Lecture 21 | Principal Component Analysis (the math) | Slides | See Lecture 48 in this playlist |
| Lecture 22 | Singular Value Decomposition | Slides | 6.3 of GS |
| Lecture 23 | Counting Principles: Very simple counting, multiplication principle | Slides | 1.6 of B&T |
| Lecture 24 | Counting sequences, subtraction principle | Slides | 1.6 of B&T |
| Lecture 25 | Counting collections | Slides | 1.6 of B&T |
| Lecture 26 | More fun with counting | Slides | Not covered this year |
| Lecture 27 | Sets, Experiments, Outcomes and Events | Slides | 1.1,1.2 of B&T |
| Lecture 28 | Probability Space, Axioms of Probability, Designing Probability Functions | Slides | 1.2 of B&T |
| Lecture 29 | Conditional probabilities, multiplication rule, total probability theorem, Bayes' theorem, independent events | Slides | 1.3, 1.4 & 1.5 of B&T |
| Lecture 30 | Random Variables, Types of Random Variables (discrete and continuous), Probability Mass Function (PMF), Properties of PMF | Slides | 2.1 & 2.2 of B&T |
| Lecture 31 | Describing distributions compactly, Bernoulli distribution, Binomial distribution | Slides | 2.2 of B&T |
| Lecture 32 | Geometric distribution, Negative Binomial distribution, Hypergeometricdistribution, Poisson distribution, Uniform distribution | Slides | |
| Lecture 33 | Expectation, Variance and their properties, Computing expectation and variance of some known distributions | Slides | 2.4 of B&T |
| Lecture 34 | Joint distribution, conditional distribution and marginal distribution of multiple random variables | Slides | 2.5 of B&T |
| Lecture 35 | Continuous random variables, probability mass function v/s probability density function, cumulative distribution function | Slides | 3.1 & 3.2 of B&T |
| Lecture 36 | Uniform distribution, normal distribution | Slides | 3.3 of B&T |
| Lecture 37 | Exponential families of distributions | Slides | |
| Lecture 38 | Multiple continuous random variables, Bayes' theorem for continuous random variables | Slides | 3.5, 3.6 of B&T |
| Lecture 39 | Moments and moment generating functions: What are they and why do we care about them? | Slides |
| Quiz/Assignment | Topics | Resources | Release Date | Solution |
|---|---|---|---|---|
| Homework 1 | Introduction to Vectors and Matrices | Questions | -- | |
| Homework 2 | Linear Combination, Elementary matrices, Inverse, Transpose, LU Factorization, Lines and Planes | Questions | -- | |
| Homework 3 | System of Linear Equations, Rank, Nullspace and Column Space, Free variables, Reduced Echelon Form | Questions | -- | |
| Homework 4 | Projection, Vector norms, Dot products, Orthogonal/Orthonormal vectors and matrices, Determinants | Questions | -- | |
| Homework 5 | The Eigenstory | Questions | -- | |
| Homework 6 | Counting, Events, Multiplication rule, Bayes' Theorem | Questions | -- | |
| Homework 7 | Discrete random variables, expectation and variance | Questions | -- | |
| Quiz 1 | - | 4 August, 2022 | - | |
| Quiz 2 | - | 18 August, 2022 | - | |
| Quiz 3 | - | 01 September, 2022 | - | |
| Quiz 4 | - | 15 September, 2022 | - | |
| Quiz 5 | - | 29 September, 2022 | - | |
| Quiz 6 | - | 13 October, 2022 | - | |
| Quiz 7 | - | 27 October, 2022 | - | |
| End-Sem | - | 16 November, 2022 | - | |
| Tutorial 1 | - | Tutorial 1 | - | |
| Tutorial 2 | - | Tutorial 2 | - | |
| Tutorial 3 | - | Tutorial 3 | - | |
| Tutorial 4 | - | Tutorial 4 | - | |
| Tutorial 5 | - | Tutorial 5 | - | |
| Tutorial 6 | - | - | ||
| Tutorial 7 | - | Tutorial 7 | - | |
| Tutorial 8 | - | Tutorial 8 | - | |
| Tutorial 9 | - | Tutorial 9 | - |