Is it possible to just learn the mathematics first (i.e. multivariable and vector calculus, linear algebra, etc.) and only then start learning physics? (i.e. from a graduate textbook like Classical Mechanics by Golstein)? Would there be any pitfalls? I am studying on my spare time as a hobby and it seemed the fastest way to learn the math first. I have a highschool physics background and I looked at MIT's OCW syllabus and they have University Physics by Hugh D. Young; Roger A. Freedman as their main book throughout their undergraduate program (more or less). I looked through that book online and it didn't seem like a type of book that would suit my preferences (too many colored pictures, over-explaining, etc.) -- I deeply apologize if this book is held in high regard, but that was just the first impression it gave me and wanted to know if I am mistaken. I also use "Gerard t'Hooft's Theoretical Physics as a challenge" as a guide. Oddly he doesn't recommend any textbooks of that sort, and he just recommends the math and then straight up Classical Mechanics graduate textbooks. There is actually a link to some textbooks that are similar to Young and Freedman's to which he says "(most of these are rather for amusement than being essential for understanding the World)," As for mathematics i use "How to Become a Pure Mathematician (or Statistician)" as a guide, and I was wondering: 2. If the ultimate goal is to learn physics, how is it best to approach the learning of mathematics beforehand - learning math in a pure/analytical way, or learning applied math, i.e. here is the formula, plug in, solve this integral, etc.? Or both? If so how much to focus on one or the other? Or does learning mathematics in a pure math way already imply you will know how to do the apply-math part? Or is pure math just a waste of time if the ultimate goal is to study/understand/do physics? (I am guessing it depends on what type of physics you ultimately want to focus on, but from what I've gathered I understand that the best path is to be a good mathematician in the first place no matter the type of physics.) And last question. Are Feynman's Lectures on Physics worth getting? I glanced through the books and they don't seem to have exercises. If money is a problem would it be better spent on books that have exercises (like the ones in Gerard t'Hooft's list)? Thank you in advance and sorry if it's a long read. As many perspectives and opinions I can get would be much appreciated.