Getting Started With Gilbert Strang's Applied Math Material
The MIT course OpenCourseWare has the lecture videos, and the accompanying textbook is available through the MIT Press. I've used both over the years when I needed to brush up on numerical methods or revisit linear algebra foundations for engineering work. The structure is deliberate—Strang builds from basic vector spaces into differential equations and optimization, and he does it with a lot of examples rather than proofs. Here is where most people run into trouble. The textbook is dense in a specific way—it assumes you are comfortable switching between abstract notation and concrete computation, and Strang doesn't hold your hand through that transition. I ran into this back in 2019 when I was trying to use his approach to sparse matrix decomposition for a finite element mesh I was debugging. The book walks through the theory of Cholesky factorization cleanly, but it doesn't explicitly cover what happens when your matrix has structural zeros that cause fill-in during the factorization. I ended up implementing a minimum degree reordering myself in MATLAB before running the factorization, which cut the memory usage from roughly 4 gigabytes down to about 300 megabytes on a 10,000 by 10,000 problem. That kind of gap between the textbook treatment and actual computation is pretty typical across the later chapters. The video lectures are actually more practical than the book in some respects. Each MIT OCW lecture is about an hour long, and Strang tends to work through a concrete problem before stating the general theorem. If you are watching them on 1.5x speed and pausing to actually work the example on paper, one lecture will take you about 40 minutes. Going through the full set of lectures on linear algebra will take roughly 30 hours. The applied mathematics set is longer and jumps around more because it covers multiple subjects.
One thing the material handles poorly is the bridge to modern computational tools. Strang writes from a perspective where hand computation and theoretical understanding come first, and software implementation comes second. That worked fine when the book was written, but today you are going to need to pair his explanations with actual code. His website at mit.edu/ocw has supplementary notes, and there is a companion MATLAB guide that maps directly to the book chapters. Without that pairing, you will find yourself understanding the concept but having no idea how to actually implement it. The exercises are another area where expectations need calibration. They range from straightforward computational drills to problems that require insight most students won't have on the first read. I'd estimate that only about 40 percent of the exercise set is accessible to someone working through the material for the first time without additional guidance. The solutions manual exists but is not freely available online, and the answer keys in the back of the book only cover selected problems. If you hit a wall on a problem set, checking worked examples from the MIT OCW problem solution videos helps more than you might expect. There is also a limitation worth noting upfront. This material is not a modern numerical analysis textbook. If you are looking for coverage of iterative solvers like GMRES, preconditioning strategies, or parallel computing approaches, you will not find it here. Strang focuses on direct methods and classical theory. For a graduate-level complement that covers the computational side more thoroughly, you would need something like Trefethen and Bau or Saad's iterative methods text alongside it.
The download situation is straightforward. The textbook is published by Wellesley-Cambridge Press, and the MIT OpenCourseWare lectures are freely available under a Creative Commons license. The OCW link is ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2023/. The book can be downloaded in PDF form from the Wellesley-Cambridge Press website at wellesleycambridge.com. You do not need to register for anything to access the video lectures, though the problem set solutions are less consistently posted than the lecture videos themselves. I have found that the most effective way to use this material is to pick one chapter, watch the corresponding lecture at normal speed, work through at least five exercises from that chapter before moving on, and then code a small implementation of whatever algorithm the chapter covers. Skipping the coding step is where people usually lose the practical benefit. The mathematical understanding will feel solid after the lectures and exercises, but that understanding is fragile if you never translate it into working code. The book also has some idiosyncrasies that trip people up. Notation changes between chapters without much warning. Boundary value problems get handled differently in different sections. Strang sometimes references results from earlier chapters assuming you remember them, which is reasonable if you are working straight through the book sequentially but frustrating if you are jumping around to fill gaps. I keep a personal reference sheet of his key formulas—the spectral theorem, the four fundamental subspaces relationship, the SVD form—because flipping back through 500 pages to find the exact statement takes too long during problem solving.
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Overall, this is solid foundational material, but it is not self-contained in the way modern online courses often claim to be. You need to supplement it with actual computation and be prepared to work through harder problems than the text makes it seem like you should. It is useful, and it is still one of the better single resources for building intuition, but treating it as a complete curriculum without additional practice will leave you with gaps that show up fast in any real application.
