Glibert Strang’s 18.06 Linear Algebra course at MIT OpenCourseWare is exquisite! Jeannie and I went through it about a year ago. Strang’s approach to the material and engaging teaching style make the course a joy. Unlike other OER (Open Educational Resources) courses that we have taken, I cannot recommend just watching the videos. Instead one needs to really think about the concepts which is greatly facilitated by doing the exercises: this is typical for mathematics. It took significant effort to master the content. The material builds quickly and it was essential for us to work hard on each lecture. On several occasions we re-watched the videos and had to read the text carefully and collate with other on-line resources (some provided or referenced in the wonderful OpenCourseWare materials but some found by web searching, Wikipedia, etc.). We also used resources from our library (personal and public).

Jeannie and I were able to enjoy the whole course but it definitely took significant effort. This is the only video course that we have thoroughly studied and it was worth it!

Are there any other OER video courses on linear algebra? I have not found any which is a shame for such important material.

Linear algebra is one of the most useful branches of mathematics beyond introductory (high school) algebra and geometry. It is the algebraic study of intersections of complexes of lines, planes and hyperplanes and therefore has a strong geometrical component. Since each coordinate in the Cartesian representation of a line can be thought of as a variable, linear algebra provides a first order or “linear” approximation to multivariable systems. It is therefore a widespread and fundamental tool. Linear algebra has found applications in business, economics, engineering, genetics, computer graphics, social sciences, graph theory and much more. It is essential for anyone wanting to understand advanced mathematics. The matrix or an array of numbers is the basic object of study in linear algebra. So it is sometimes called matrix theory. Vector spaces are the abstract form of linear algebra.

Is that a good characterization of linear algebra? How would you improve it?

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