About This Course

Why Linear Algebra Matters Now More Than Ever

Welcome to one of the most exciting and relevant mathematics courses you will ever take! Linear algebra is not just another math requirement to check off your list—it is the mathematical language that powers the modern world of artificial intelligence, machine learning, computer graphics, data science, robotics, and so much more.

Every time you interact with a large language model like ChatGPT or Claude, linear algebra is working behind the scenes. When your phone recognizes your face, when Netflix recommends your next favorite show, when autonomous vehicles navigate city streets, and when medical imaging systems detect diseases—linear algebra makes it all possible.

The Foundation of Modern AI

At the heart of every neural network lies matrix multiplication. The attention mechanisms that make transformers so powerful? Matrix operations. The embeddings that capture the meaning of words and images? Vectors in high-dimensional spaces. Principal component analysis for dimensionality reduction? Eigenvalue decomposition. The gradient descent algorithms that train every deep learning model? Linear algebra from start to finish.

Understanding linear algebra gives you the superpower to truly comprehend how AI systems work—not as mysterious black boxes, but as elegant mathematical structures you can reason about, debug, and improve.

Learning Through Interactive Visualization

This course takes a fundamentally different approach to teaching linear algebra. Instead of drowning in abstract notation, you will build deep intuition through over 150 interactive MicroSimulations. These browser-based visualizations let you experiment with vectors, matrices, transformations, and decompositions in real-time.

Watch eigenvectors remain unchanged as transformations stretch space around them. See how SVD decomposes images into fundamental components. Explore how gradient descent navigates loss landscapes. Manipulate quaternions and witness how they elegantly solve the gimbal lock problem. These are not passive animations—they are hands-on laboratories where you control the parameters and discover the concepts yourself.

You Will Have Fun

Yes, you read that right. This course is designed to be genuinely enjoyable. The MicroSims turn abstract concepts into interactive playgrounds. The connections to real-world AI applications give every topic immediate relevance. And the satisfaction of truly understanding how modern technology works is deeply rewarding.

Whether you aspire to build the next breakthrough in AI, create stunning computer graphics, develop autonomous systems, or simply want to understand the mathematical foundations of our increasingly algorithmic world—this course will give you the tools, the intuition, and the confidence to succeed.

Let's explore the beautiful mathematics that shapes our digital future!

Background

In January of 2025, I was invited to lead a group of four students in a senior design project. These were all students in their senior year at the University of Minnesota Department of Electrical Engineering and Computer Design. Each student team member was assigned to create an intelligent textbook for either a class they took or a subject they were interested in. One of these students selected Linear Algebra. This course is a fork of that textbook, but it has been redesigned significantly to focus on the application of linear algebra in machine learning.

Our tools have also matured since January 2025. This version of our intelligent textbook was generated using Claude Code Skills. We also put a much stronger focus on creating high-quality MicroSims that bring abstract concepts to life.

— Dan McCreary, January 2025