For those of you who don't know: this is a companion to the Princeton Companion to Mathematics, which is excellent but focuses mainly on pure math. Also, the editor of this new volume was a highly respected applied mathematician named Nick Higham, who sadly died a few months ago.

I’m an encyclopedia lover who works on a variety of applied math problems as part of $dayjob at a national lab.

I thought the book might be fun to browse around in, so I purchased it. I knew the companion book (…to Mathematics) had a very good reputation.

It didn’t work for me…long story short is, the articles were written at too high a level of sophistication to serve as an introduction for a curious outsider. It was more of what someone in a nearby field might want to get up to speed on what is known, when their background in “that kind of thing” is already quite strong.

I was surprised for various reasons - I know Higham’s technical work, enjoy his blog, and I have a decent math background. (Of course, he’s the editor, not the author - it’s an enormous book.)

Ah, well. Not every shoe has to fit.

How should one use a book like this? Is it to get an overview of a topic before diving in? I don’t think I’ve ever learnt any mathematics from reference works, so I’m curious as to their intended audience.

The most advanced math I had were the 1st and 2nd year multivariable calculus and linear algebra courses in college.

I am interested in visualizations/simulations of physical systems as a way to learn advanced math. Is there any books or resources that take that approach?

Also relevant : Foundations of Applied Mathematics - https://foundations-of-applied-mathematics.github.io/