Mathematical Foundations of AI

Overview

The “Mathematical Foundations of AI” course provides a rigorous introduction to the fundamental mathematical concepts behind many algorithms in machine learning and artificial intelligence, including linear algebra, calculus, and optimization theory. Starting with vectors and matrices, the course covers basic operations and geometric interpretations, matrix transformation and inversion, solving systems of linear equations, matrix factorizations such as diagonalization, singular value decomposition (SVD), and Cholesky decomposition.

The course then introduces calculus-based optimization to identify and classify extrema in both univariate and multivariate functions before handling constrained optimization using Lagrange multipliers and the Karush-Kuhn-Tucker (KKT) conditions. Finally, attention turns to iterative optimization methods, which form the computational basis of many modern machine learning models.

By the end of the course, students will be equipped with the mathematical knowledge needed to understand the foundations of machine learning and AI techniques, providing a solid basis for further study in AI-related fields. Enroll now to build the mathematical foundations you need for a career in AI!

Syllabus

• To understand and apply vector and matrix operations
• To use matrix transformations (e.g., Gauss elimination) and to compute matrix inverses to solve systems of linear equations
• To apply diagonalization, singular value decomposition, and the Cholesky decomposition for dimension reduction and matrix factorization
• To apply basic calculus concepts to perform unconstrained optimization on univariate and multivariate functions
• To formulate and solve constrained optimization problems using Lagrange multipliers and the Karush-Kuhn-Tucker (KKT) conditions
• To understand and implement iterative optimization algorithms

---

Subjects

Artificial Intelligence