In early 2013, I was looking for online courses for BigData Analytics. My friends advised me that a strong foundation in linear algebra would make it easy to grasp techniques in machine learning and statistics. Luckily, MIT has made classroom videos by Gilbert Strang available for free :)

Who is Gilbert Strang? A respected and much loved professor who has taught linear algebra for over 30 years at MIT. He has a gift for making complicated material look easy through visualization and intuition.

Lectures

Course Website — YouTube Playlist for Fall 2005 Lectures. There are 35 videos consisting of 31 lectures and 4 exam reviews (video numbers 13, 24b, 32 and 34). Each video is 50 minutes long. Gilbert Strang speaks slowly. So even when videos are played back at 1.5x the normal speed, he is completely understandable. High speed playback reduces the time commitment for watching the 31 lectures to about 17 hours.

High speed playback in Chrome: Sign up for HTML5 player in Chrome by visiting http://youtube.com/testtube. Then click on the gear icon in the bottom right corner of the YouTube video player. A drop down menu for playback speed should appear. Choose 1.5x.

Lectures 1 thru 11 build the beautiful theory of the four spaces of a matrix (column space, null space, row space and left null space). Lecture 12 puts it all together for the special case of electrical networks, leading to Euler's formula for nodes, edges and loops in graphs. Lectures 14 thru 17 develop projection matrices, least squares and orthogonal bases. These were the first lectures where formulae became important. Lectures 18 thru 20 develop the theory of determinants in a beautiful way. Lectures 21 thru 24 teach power series, eigenvalues and eigenvectors, with applications to ODEs and Markov matrices. The remaining lectures are about positive definite matrices, SVD and pseudo inverses.

Recitations

These are problem solving sessions conducted by teaching assistants: YouTube Playlist for 2008 — YouTube Playlist for 2011.

Textbook

Linear Algebra (4th Ed) (584 pages, 2009). An international edition of this book is available for $20 at AbeBooks (International Edition Books). For residents of USA, choosing a seller in USA may result in speedier delivery.

The textbook is a great complement to the video lectures. It helps understand the material better. In order to really absorb the material for long term, problem solving is important. There are hundreds of problems in the book, chosen carefully by Strang. The textbook is quite verbose though. It reminds me of Introduction to Algorithms by Cormen, Leiserson and Rivest.

For a long list of (dry but useful) linear algebra formulae, see Matrix Cookbook, a handy reference.

Teaching Style

Gilbert Strang emphasizes applications and computability over pure mathematics. For example, he talks about determinants but he does not dwell on them because no linear solver actually computes determinants.

If you aspire to be a wonderful math or computer science professor, I would encourage you to watch the YouTube Playlist for Fall 2005 Lectures in its entirety. Gilbert Strang chooses illustrative examples in two or three dimensions to teach ideas that generalize to higher dimensions. Watching the entire series will be helpful in appreciating how much material is covered (quite a lot), and how different concepts like pivots, determinants and eigenvalues are brought together in a beautiful way towards the end of the course.

Other Resources by Gilbert Strang

A research paper that tersely summarizes the linear algebra course: The Fundamental Theorem of Linear Algebra by Gilbert Strang, The American Mathematical Monthly, Vol 100, No 9, Nov 1993, pages 848-855.

Gilbert Strang also teaches Computation Science and Engineering (MIT 18.085): YouTube Playlist for 2008 Videos. Textbook: Computational Science and Engineering (725 pages, 2007).

© Copyright 2008—2017, Gurmeet Manku.