Mathematical Foundations of Data Science

A graduate-level course that builds the mathematical machinery behind modern machine learning, treating linear algebra, probability, and optimization as the three pillars that actually explain why methods like SVD, regression, and neural nets work rather than just how to run them. You'll work through homework sets, quizzes, and a project, moving from matrix factorizations and the Eckart-Young theorem through concentration inequalities and VC theory to gradient-based training of deep networks. It's the theoretical backbone for anyone heading into statistics or ML research at Bilkent, turning the black-box algorithms from applied courses into objects you can reason about and prove things about.