Syllabus

Linear Algebra
Vector spaces: Column and row spaces, Solving Ax=0 and Ax=b, Independence, basis, dimension, linear transformations.
Orthogonality: Orthogonal vectors and subspaces, projection and least squares, Gram-Schmidt orthogonalization
Determinants: Determinant formula, cofactors, inverses and volume
Eigenvalues and Eigenvectors: Characteristic polynomial, Diagonalization, Hermitian and Unitary matrices, Spectral theorem, Change of basis.
Positive definite matrices and singular value decomposition
Random processes
Preliminaries: Events, probability, conditional probability, independence, product spaces
Random Variables: Distributions, law of averages, discrete and continuous RV, random vectors, Monte Carlo simulation
Discrete Random Variables: Probability mass functions, independence, expectation, conditional expectation.
Continuous Random Variables: Probability density functions, independence, expectation, conditional expectation, functions of RV, sum of RV, multivariate normal distribution, sampling from a distribution.
Convergence of Random Variables: Modes of convergence, Borel-Cantelli lemmas, laws of large numbers, central limit theorem, tail inequalities

To present the central methods and ideas of linear algebra and random process with a unified approach.

To understand the linear operators on finite-dimensional vector spaces.

To comprehend the complexity of describing random, time-varying functions.

(1) Students would get a better perspective of AI/ML instead of thinking of it as magic.
(2) Students would be able to abstract the data and model.
(3) Equip the students with uncertainty and stochasticity.

Gilbert Strang, Linear Algebra and its Applications, Cengage , 2014

Geoffrey Grimmett, Probability and Random Processes, Oxford University Press , 2006

Athanasios Papoulis and S. Unnikrishna Pillai, Probability, Random Variables and Stochastic Processes, McGraw Hill , 2002

Peter J. Olver, Applied Linear Algebra, Pearson Education , 2006