4 February 2015

Best Time to Learn Linear Algebra is Now!

Linear Algebra is a crucial prerequisite for many things, including Statistics, Data Mining, Machine Learning, Computer Vision, Image Processing and many many others, so it's very important to know the basics of Linear Algebra to understand more advanced concepts. For example, it's really helpful for our IT4BI studies, especially for the specialization at TU Berlin.

And the best time to learn Linear Algebra or refresh your knowledge about it is right now! At this moment there are a couple of nice MOOCs that have just started and a few more are about to start in the nearest future.

Even if you don't join right now, they should be available in the future for learning as self-paced versions. Additionally I would like to include my favorite video courses on Linear Algebra, they are also for learning at your own speed with no deadlines.

Just started

So I'll begin with the courses that have just started and you still have time to jump in.


LAFF stands for "Linear Algebra - Foundations to Frontiers", and the course page is here. This is the second run of the course, and the first one was quite successful: many students participated and most of them enjoyed the course.

This offering started on 28 Jan 2015, but the first deadline is on 16 Feb 2015, so there's still plenty of time to enroll. The estimated effort is 8 hours a week, and the duration is 15 weeks.

The course includes theoretical videos but all the theory is reinforced with programming exercises. Last time it involved exercises in Python, but this time they switched to Matlab. What is more, MathWorks offered to give free licenses of Matlab to all the participants. This alone is already a good reason to enroll in the course! But, as the teachers say, it's still possible to use python for this, if you wish, because all the coding exercise only require clicking on a "pass" button and it's not actually checked how the exercises are implemented, so it can be any programming environment.

Additionally, you may download all the lecture notes at ulaff.net. The notes themselves are a very good source of information, even without the videos.

Coding the Matrix, Coursera

The full name of the course is "Coding the Matrix: Linear Algebra through Computer Science Applications", it's offered at Coursera. The course webpage is here. The workload is up to 10 hours per week, and it lasts for 10 weeks.

This is also a second time when the course is offered, and it follows the same philosophy as LAFF: learning through coding. While the theoretical part is somewhat similar to LAFF, the exercises are different. They also different in a way that there's an automatic checker that verifies your the solutions that you have to submit to the server. The programming environment for this course if Python 3, and it's not possible to use anything else.

The book that is used for this course has the same title as the course (check the amazon page and the book's page). The author, Philip Klein, promises to offer a more advanced version of this class in the future, so you might want to subscribe for the updates on his website.

Linear Algebra, Coursera (Russian only)

If you speak Russian, there's another MOOC that has just stared at coursera. The course website is here. I'm not sure if there're many readers who know Russian, but I still would like to mention it, because I think it's nice that Coursera goes very international. It's a first run of this course, so I can't comment on the course content, but you can go check yourself.

Start soon

Applications of Linear Algebra, edX

This is a series of two courses
  • Part 1, starts on 23 Feb 2015 (5 weeks)
  • Part 2, starts on 6 Apr 2015 (4 weeks)
The syllabus looks pretty promising: they put the emphasis on applications and focus on Computer Graphics and Data Mining. The estimated effort for each course is up to 20 hours in total. They unfortunately don't provide a detailed syllabus with all the topics, but it seems complimentary to the basic ones like LAFF or Coding the Matrix.

Introduction to Linear Models and Matrix Algebra, edX

This is another course at edX, this time offered by Harvard. The course page is here, it starts on 16 Feb 2015 and takes 2 week.

This course is a part of a "Life Sciences" series of courses by Harward:


If you don't like deadlines, you can take all of the courses above at your own pace, so you don't have to follow the schedule and do all the homework. However there are many other good Linear Algebra video lectures that are self-paced from the very beginning, and I'd like to recommend a couple of them.

Linear Algebra at OpenCourseWare (MIT)

In my opinion, these are the best Linear Algebra lectures ever recorded. While LAFF and Coding the Matrix are quite good, the way G. Strang presents the material is excellent. It's a live recording of the MIT class, probably quite old, because it often feels like it was digitized from video tapes. You'll find the recordings at OpenCourseWare. Alternatively you can just google and find in on YouTube, iTunes university or in many other places. However, while the videos are amazing, you have to do the exercises to strengthen the theory, and this is where other courses come in. So, other courses are complimentary.

Also, G. Strang has written a nice paper "The Fundamental Theorem of Linear Algebra" (or, a fresher one, "The Four Fundamental Subspaces: 4 Lines") which I recommend to everybody who want to refresh the Linear Algebra knowledge. It's essential for understanding the concepts of Linear Algebra to think in terms of spaces and subspaces, and this article helps a lot to do it with nice pictures which are very helpful for grasping the main ideas. You may also want to check our post about this paper: The Fundamental Theorem of Linear Algebra by G. Strang

Linear Algebra, Khan academy

Every time I go to google to look for some basic Linear Algebra things, there's always a result from the Khan Academy course. And the content is very nice: many things are explained in a very nice and understandable way. The videos are nicely categorized and it's very easy to jump over some parts you already know without being lost. It's in some sense also complimentary to Strang's course, because some things are explained differently, although it doesn't have so nice visualization of the subspaces.


  1. Thank you, I'm russian, so "Linear Algebra, Coursera (Russian only)" is pretty useful = )