This is a problem I always had in university. Higher math always seemed to start with "the definition of X is Z etc." and I would never know what's the purpose of doing this. When I attended a talk of Gilbert Strang many years later it was eye opening because it was a totally different approach that always accompanied theoretical concepts with a concrete interpretation.

Actually I now think it might also be a cultural thing. If you take a look at the approaches the English Wikipedia takes vs. the German Wikipedia take explaining a vector space you'll know what I mean:

https://en.wikipedia.org/wiki/Vector_space#Introduction_and_...

https://de.wikipedia.org/wiki/Vektorraum#Definition

I'd second the point on different cultures doing it differently. One of my profs once said he had a book written by two mathematicians, one German and another Italian. It was fairly evident who had worked on which part. He also mentioned that the "old style" German books would almost apologize if they "had" to use just a few pictures to illustrate something.

I had a math professor who told me that advanced math books are like Hoyle's Rules of Games. There are two ways you can use Hoyle's Rules of Games. You can memorize the rules of bridge and stop there, but then you will have a pretty dull experience. Or you can use the book as a tool to start playing bridge, and it will open you up to a rich and engaging activity.

> Unfortunately Coding the Matrix is no longer available on Coursera.

The book itself is still for sale, and the website has course slides and auto-grading software for some of the exercises: https://codingthematrix.com/

The course seems to be still mirrored in the Internet Archive: https://archive.org/details/academictorrents_54cd86f3038dfd4...

Honestly I think we spend way too much teaching students calculus and differential equations and way too little on linear algebra. LA is a lot more useful for most real engineering work, particularly software engineering.

I had to build a somewhat basic SVG editor in React recently and the other devs on the team had to leave a lot of the core to me because I was the only one that remembered enough matrix math to do it.

No, linear algebra is not more useful than calculus or differential equations for any branch of engineering other than computer engineering. Computers engineering is the only discrete engineering discipline.

Calculus is useful roughly to the degree it's able to turn non-linear problems into problems of linear algebra.

In what field?

Every branch of science and engineering. e.g. optimizing distribution networks, predicting the weather, designing structures that won’t fall down, setting the orbits of rockets, controlling robots, simulating materials for 3d animation, designing new pharmaceutical molecules, analyzing data from high-energy physics experiments, ...

If you look at how people solve differential equations in practice, it’s all matrix algebra.

Linear algebra is also pervasive throughout pure mathematics.

Edit: I think everyone should also learn calculus though, and differential equations are the heart of calculus. Here’s an introductory calculus book http://www.math.smith.edu/~callahan/intromine.html and here’s an introductory linear algebra book https://web.stanford.edu/~boyd/vmls/ which try to get students closer to the way these tools get used in practice.

Linear algebra has many uses beyond computers:

http://aix1.uottawa.ca/~jkhoury/app.htm

https://math.stackexchange.com/questions/256682/why-study-li...

Yes, and all of them outside of computer science/engineering are using linear algebra on top of calculus.

Computer software/engineering is the only field of science that can use naive linear algebra directly to solve hard problems in the field.

Ummm, what about say quantum mechanics as the first huge example off the top of my head..

How many school graduates will end up studying quantum mechanics?

>When it was taught to me, both in HS and College

That's so cool that you had access to a linear algebra class in HS!

To be fair, my HS exposure was in honors Math, and it was very limited exposure: matrixes, determinants, and how to represent systems of equations.

Teaching systems of linear equations and using Gauss factorization to solve the equations is quite mundane in HS.

videos from the course are also available here http://cs.brown.edu/courses/cs053/current/lectures.htm