Suggestions on a particular arXiv publication on math needed for theoretical physicists I'm going to start my PhD in a year and I'll be taking a gap year doing other stuff. But I also wanted to fill in the gaps in my math knowledge and I came across an arXiv publication called "Mathematics for Theoretical Physicists." This is the link. 
I was wondering if anyone has read it/skimmed through it and if so, do you suggest that it's a good book? 
Thanks!
 A: No, don't spend your gap year reading that unless you are really inclined to out of interest in the mathematics.  If you want to be well-prepared, read Zee's QFT in a nutshell or something else that is pedagogical and helpful for the kinds of subjects that grad students are really likely to struggle with.
The problem with reading that book is that it will be too slow.  You might want to read it later, but since grad school is coming, you really want to focus your attention on something that will get to the physics faster, even if it means sacrificing completeness (pun intended har har) or the material.
If you want to learn differential geometry, read Wald's GR and learn GR at the same time.  If you want to learn something about Lie groups, read Georgi's Lie Algebras in Particle Physics.  etc.  If you want to learn more about math relevant to classical mechanics, read Dirac's Lectures on Quantum Mechanics (not principles of quantum mechanics) or maybe wald's qft in curved spacetime.
A: If you are majoring in theoretical physics, I think that it is not a good choice. The book provides a comprehensive collection of mathematical notions, but it does not mention their applications in physics.   
