Courses taught

Probability, a dynamic and crucial field in mathematics, influences various sciences such as quantum mechanics, statistics, genetics, epidemiology, economics, engineering, and computer science. This beginner-friendly course builds essential concepts from the ground up, focusing on intuitive understanding, rigorous proofs, and practical applications. Topics include combinatorial analysis, probability axioms, independence, conditional probability, distributions, functions of random variables, laws of large numbers, and central limit theorems. We also explore diverse applications to highlight the relevance of probabilistic concepts.

Ordinary differential equations (ODEs) are fundamental in mathematics, natural sciences, and social sciences, modeling dynamic phenomena like motion, growth, and decay. Widely applied in physics, biology, economics, chemistry, and engineering, they bridge theory and practice. This course covers first-order scalar equations, nth-order linear equations, and n-dimensional linear systems. Additional topics may include regular singular points, Laplace transforms, phase plane analysis, existence and uniqueness theorems, and numerical methods. Students will develop skills to formulate, solve, and interpret ODEs in diverse scientific and engineering contexts. 

This course introduces fundamental concepts of linear algebra, including systems of linear equations, vector spaces, linear independence, dimension, linear transformations, matrices, determinants, eigenvalues, eigenvectors, diagonalization, inner products, orthogonality, and least squares. Tailored for non-Mathematics majors, it highlights practical applications in computer graphics, optimization, machine learning, data analysis, network theory, and engineering, offering a robust foundation for a wide range of disciplines.