**Instructor**: Mitesh M. Khapra**When**: August-November 2022**Lectures**: Slot D**Where**: CS25-
**Teaching Assistants: TBD**Name Email 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

Quizzes (best n-2) : 70 %, End-sem : 30 %

GS: Linear Algebra and its applications, fourth edition, Gilbert Strang

B&T: Introduction To Probability, 2nd eidtion, by Dimitri P. Bertsekas and John N. Tsitsiklis

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 | - |