Mathematical Methods for Physics is such a great course. Took the course, and an Advanced version in undergraduate when I was still attempting to be a physicist. The course is at its core a bunch of very important Mathematical concepts that a Physicist or adjacent will need that you won't quite ever come across naturally in mathematics courses unless you go into graduate studies. A "Here is the problem, here is the math and here is why" is just very useful. Legendre Polynomials, Bessel Functions, Lagrangian, Fourier Functions. Just tons of interesting and really useful math that when you hit a problem in their space you have a super power.<p>My professor for the courses always said it was about putting more mathematical tools in your tool box. Which is a perspective I've since carried.
We're in something of an autodidacticism boom. I have yet to see anyone, in years, actually become proficient at college-level math/physics without formal instruction, just by doing self-study with tutorials like pdfs and videos.<p>There will always be major knowledge gaps or roadblocks/impasses of understanding, like notation or clarification needed. This is not to say it cannot be done but I have to see anyone do it.
Reading the numerous lecture notes on mathematical methods used in physics that are available online is like reading stories about love: it never gets old, and each time you learn something new!
Ronald L. Graham, Donald E. Knuth, Oren Patashnik: oncrete Mathematics<p><a href="https://archive.org/details/concrete-mathematics/page/n11/mode/2up" rel="nofollow">https://archive.org/details/concrete-mathematics/page/n11/mo...</a>
Tangential: Has anybody here read <i>Mathematical Methods and Physical Insights: An Integrated Approach by Alec J. Schramm.</i>? Would love to hear your opinion on this.