**Instructor**: Mitesh M. Khapra**When**: September-December 2020**Lectures**: Slot D**Where**: Online-
**Teaching Assistants**Name Email Working hours Days Ananya B. Sai ananya.b.sai@gmail.com 2-4 pm Monday Madhura Pande madhurapande2011@gmail.com 3-5 pm Thursday Aakriti Budhraja aakriti.budhraja@gmail.com 12-2 pm Wednesday Preksha Nema preksha.nema9@gmail.com 2-4 pm Friday Rajat Soni cs19m052@smail.iitm.ac.in 2-3 pm Wed,Thu Himasagar Mallepalli cs19m036@smail.iitm.ac.in 3-5 pm Thursday Janakiram Yellapu cs19m028@smail.iitm.ac.in 3-5 pm Thursday Bikash Kumar Behra cs19m019@smail.iitm.ac.in 2-3 pm Thu, Fri Bethu Sai Sampath cs19m018@smail.iitm.ac.in 12-2 pm Wednesday

Assignments (best N-1 out of N assignments) : 70 %, Quizzes : 30 %

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

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 | |

Lecture 40 | Markov inequality, Chebychev inequality, Weak law of large numbers | Slides | 5.1, 5.2, 5.3 of B&T |

Lecture 41 | Central Limit Theorem | Slides | 5.4 of B&T |

Lecture 42 | Information Content, Entropy, Cross Entropy, KL Divergence | Slides |

Quiz/Assignment | Topics | Resources | Release Date | Solution |
---|---|---|---|---|

Homework 1 | Introduction to Vectors and Matrices | Homework 1 | 10 September, 2020 | - |

Homework 2 | Linear Combination, Elementary matrices, Inverse, Transpose, LU Factorization, Lines and Planes | Homework 2 | 21 September, 2020 | - |

Homework 3 | System of Linear Equations, Rank, Nullspace and Column Space, Free variables, Reduced Echelon Form | Homework 3 | 4, October, 2020 | - |

Homework 4 | Projection, Vector norms, Dot products, Orthogonal/Orthonormal vectors and matrices, Determinants | Homework 4 | 16, October, 2020 | - |

Homework 5 | The Eigenstory | Homework 5 | 01, November, 2020 | - |

Homework 6 | Counting, Events, Multiplication rule, Bayes' Theorem | Homework 6 | 11, November, 2020 | - |

Homework 7 | Discrete random variables, expectation and variance | Homework 7 | 26, November, 2020 | - |

Tutorial 1 | - | Tutorial 1 | 13 September, 2020 | - |

Tutorial 2 | - | Tutorial 2 | 26 September, 2020 | - |

Tutorial 3 | - | Tutorial 3 | 10 October, 2020 | - |

Tutorial 4 | - | Tutorial 4 | 20 October, 2020 | - |

Tutorial 5 | - | Tutorial 5 | 21 October, 2020 | - |

Tutorial 6 | - | Not released | - | |

Tutorial 7 | - | Tutorial 7 | 11 November, 2020 | - |

Tutorial 8 | - | Tutorial 8 | 26 November, 2020 | - |

Tutorial 9 | - | Tutorial 9 | 26 November, 2020 | - |