Linear Algebra: Foundations to Frontiers (LAFF) is packed full of challenging, rewarding material that is essential for mathematicians, engineers, scientists, and anyone working with large datasets. Students appreciate our unique approach to teaching linear algebra because:

It’s visual.

It connects hand calculations, mathematical abstractions, and computer programming.

It illustrates the development of mathematical theory.

It’s applicable.

In this course, you will learn all the standard topics that are taught in typical undergraduate linear algebra courses all over the world, but using our unique method, you'll also get more! LAFF was developed following the syllabus of an introductory linear algebra course at The University of Texas at Austin taught by Professor Robert van de Geijn, an expert on high performance linear algebra libraries. Through short videos, exercises, visualizations, and programming assignments, you will study Vector and Matrix Operations, Linear Transformations, Solving Systems of Equations, Vector Spaces, Linear Least-Squares, and Eigenvalues and Eigenvectors. In addition, you will get a glimpse of cutting edge research on the development of linear algebra libraries, which are used throughout computational science.

MATLAB licenses will be made available to the participants free of charge for the duration of the course.

To see what former learners have to say about the course, read reviews on coursetalk.

We invite you to LAFF with us!

Syllabus

Week 0 Get ready, set, go! Week 1 Vectors in Linear Algebra Week 2 Linear Transformations and Matrices Week 3 Matrix-Vector Operations Week 4 From Matrix-Vector Multiplication to Matrix-Matrix Multiplication Exam 1 Week 5 Matrix-Matrix Multiplication Week 6 Gaussian Elimination Week 7 More Gaussian Elimination and Matrix Inversion Week 8 More on Matrix Inversion Exam 2 Week 9 Vector Spaces Week 10 Vector Spaces, Orthogonality, and Linear Least Squares Week 11 Orthogonal Projection and Low Rank Approximation Week 12 Eigenvalues and Eigenvectors Final

Lifecompleted this course, spending 7 hours a week on it.

LAFF requires a major time commitment. Unless you are already familiar with some of the topics, you'll probably spend 5-8 hours a week. It is clear that a tremendous amount of effort went into producing the materials for this course. There are multiple homework exercises after almost every video and most weeks have one or more programming exercises where you implement and visualize linear algebra functions using tools the instructors have created. The instructors were also active on the forums, which was nice to see.

I was expecting a course that would make linear algebra interesting, one where I would understand what it it is used for and why it is useful. Instead, I found a course hugely dependent on Matlab and some weird "Flame" notation that seems to be unique to them. You will never use this anywhere else, and it is not free like Octave.

There were occasional huge leaps with no real preparation. e.g. the beginning of chapter 5 where the law of cosines is "assumed" (but in a totally different form from what most people have probably learned). Since the instructor blows past that part, you are bound to be lost for the rest of the chapter.

For intuitions on how and why matrices work, I found other online materials far far more helpful. This class actually turned me off of a subject I was excited to learn.