About This Course

The MIT course “Matrix Calculus for Machine Learning and Beyond” provides a comprehensive introduction to advanced differentiation techniques essential for modern engineering, scientific computing, and artificial intelligence applications. Moving beyond the boundaries of classical calculus, the course intuitively and practically demonstrates how to perform differentiation on matrices and multidimensional vector spaces.

This approach shows that derivatives are not limited to scalar functions; it covers advanced topics such as derivatives of matrix factorizations, inverses, determinants, and differential equation solutions. The mathematical foundations behind algorithms are explored in depth through techniques such as automatic differentiation, forward and reverse mode differentiation, and Jacobian–vector products. Supported by Python and other computational tools, the course offers a strong foundation for machine learning, optimization, and scientific modeling.

In this regard, the course aims not only to teach computation but also to transform the way students think. It serves as a fundamental building block for learners who wish to deepen their understanding in data science, artificial intelligence, and computational engineering.

Instructors

Prof. Alan Edelman
Professor Alan Edelman is a faculty member in the MIT Department of Mathematics. He is renowned for his pioneering work in numerical linear algebra, high-performance computing, and the Julia programming language. His intuitive approach to computational mathematics and his ability to effectively integrate research and teaching make him a highly influential figure within the MIT community.

Prof. Steven G. Johnson
Professor Steven G. Johnson teaches in the MIT Department of Electrical Engineering and Computer Science. With expertise spanning Fourier analysis, differential equations, photonic computation, and optimization, Johnson brings a strong applied mathematics perspective to the course. He is highly regarded by students for both his technical depth and his clear, instructive teaching style.