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The University of Texas at Austin

Linear Algebra - Foundations to Frontiers

The University of Texas at Austin via edX


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!


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

Taught by

Robert van de Geijn and Maggie Myers


4.3 rating, based on 14 Class Central reviews

5 rating at edX based on 6 ratings

Start your review of Linear Algebra - Foundations to Frontiers

  • Life Is Study
    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.
  • Venu
    This is an excellent introductory course in Linear Algebra (LA). If you are taking this course as a lifelong learner - this will be an excellent start. Everything is explained well in an easy to understand manner. The course focuses on computationa…
  • Anonymous
    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 uniq…
  • Anonymous
    Hesitated between 4 and 5 stars, ended up putting 5 because I think the 2-stars given by some people are a bit of a stretch. The course covers enough basics of linear algebra to be used as prerequisites by other courses who need some "basic" LA. It…
  • Anonymous
    Instructors are nice. However.. So far, I have been quite disappointed in this course. There seems to be a substantial reliance on matlab, and FLAME notation, which comes up a lot during the course. While they emphasize that this is useful for unde…
  • Anonymous
    Great course. I found it challenging but rewarding. You can always find help in the discussion section or an informative video explaining the answer. You can tell a lot of dedication went into creating this course.
  • Stojan Karlusic
  • Charles Starbuck

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