Unit 1

Direct methods for convex functions – sparsity inducing penalty functions- Constrained Convex Optimization problems – Krylov subspace -Conjugate gradient method – formulating problems as LP and QP – Lagrangian multiplier method-KKT conditions – support vector machines- solving by packages (CVXOPT) – Introduction to RKS – Introduction to DMD-Tensor and HoSVD- Linear algebra for AI.

Unit 2

Introduction to PDEs – Formulation and numerical solution methods (Finite difference and Fourier) for PDEs in Physics and Engineering- Computational experiments using Matlab/Excel/Simulink.

Unit 3

Multivariate Gaussian and weighted least squares – Markov chains – Markov decision Process

Unit 4

Introduction to quantum computing-Bells inequality-Quantum gates

Course Objectives:

• To provide students with advanced knowledge and skills in optimization, PDEs, probability and statistics, and quantum computing.
• To develop students proficiency in solving real-world problems in various domains, including physics, engineering, and computer science using the concepts of optimization, PDEs, and probability.
• To apply the concepts and techniques learned in the course to solve complex problems and communicate their solutions effectively to both technical and non-technical audiences.
• To equip students with advanced mathematical knowledge and problem-solving skills highly valued in various industries and research fields.

Course Outcomes:

After completing this course, students should be able to:
CO 1: Apply the fundamental techniques of optimization theory to solve data science problems.
CO 2: Analyse and solve computationally, physical systems using the formalism of partial differential
Equations.
CO 3: Apply Markovian concepts in stochastic sequential systems.
CO 4: Explain Bells Inequality and Quantum gates.

1. Gilbert Strang, Linear Algebra and Learning from Data, Wellesley, Cambridge press, 2019.
2. Gilbert Strang, “Differential Equations and Linear Algebra Wellesley”, Cambridge press, 2018.
3. Stephen Boyd and Lieven Vandenberghe, Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares, 2018.
4. Bernhardt, Chris. Quantum computing for everyone. Mit Press, 2019. (From pages 71 to 140).