Evaluation | Logistics | Schedule | Quizzes/Assignments

Logistics


Evaluation


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

Textbooks


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

Schedule


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)
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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

Quizzes/Assigments


Quiz/Assignment Topics Resources Release Date Solution
Homework 1 Introduction to Vectors and Matrices 8 August, 2021 -
Homework 2 Linear Combination, Elementary matrices, Inverse, Transpose, LU Factorization, Lines and Planes 18 August, 2021 -
Homework 3 System of Linear Equations, Rank, Nullspace and Column Space, Free variables, Reduced Echelon Form 31 August, 2021 -
Homework 4 Projection, Vector norms, Dot products, Orthogonal/Orthonormal vectors and matrices, Determinants 12 September, 2021 -
Homework 5 The Eigenstory 26 September. 2021 -
Homework 6 Counting, Events, Multiplication rule, Bayes' Theorem 10 October, 2021 -
Homework 7 Discrete random variables, expectation and variance 27 October, 2021 -
Quiz 1 - 8 September, 2021 -
Quiz 2 - 13 October, 2021 -
End Sem - 23 November, 2021 -
Tutorial 1 - Tutorial 1 8 August, 2021 -
Tutorial 2 - Tutorial 2 22 August, 2021 -
Tutorial 3 - Tutorial 3 5 September, 2021 -
Tutorial 4 - Tutorial 4 19 September, 2021 -
Tutorial 5 - Tutorial 5 3 October, 2021 -
Tutorial 6 - 17 October, 2021 -
Tutorial 7 - Tutorial 7 31 October, 2021 -
Tutorial 8 - Tutorial 8 6 November, 2021 -
Tutorial 9 - Tutorial 9 7 November, 2021 -