Textbook/study plan questions

[jb188397]

I am self studying physics as a hobby with the very broad goals of eventually learning theoretical analytical mechanics, EM, general relativity, etc. I have no specific deadlines. My two questions are:

1. With regards to learning the required math, if there is no particular rush, is it better to work with through dedicated math texts for linear algebra, ODE, differential geometry concurrently with physics texts or just get through the standard methods texts like Boas and Arfken to get the basic techniques down and refer to the individual math texts as needed for enrichment?
2. Regarding learning physics, is it better to work through one text at a time on a particular topic or juggle several to see different perspectives?

Assume that I have studied mechanics, EM, multivariable calculus/linear algebra in college a long time ago, and more recently have studied single variable analysis I.e. Rudin and am comfortable with proofs.

Thanks!

 

[fresh_42]

I am self studying physics as a hobby with the very broad goals of eventually learning theoretical analytical mechanics, EM, general relativity, etc. I have no specific deadlines. My two questions are:

1. With regards to learning the required math, if there is no particular rush, is it better to work with through dedicated math texts for linear algebra, ODE, differential geometry concurrently with physics texts or just get through the standard methods texts like Boas and Arfken to get the basic techniques down and refer to the individual math texts as needed for enrichment?
2. Regarding learning physics, is it better to work through one text at a time on a particular topic or juggle several to see different perspectives?

Assume that I have studied mechanics, EM, multivariable calculus/linear algebra in college a long time ago, and more recently have studied single variable analysis I.e. Rudin and am comfortable with proofs.

Thanks!

I truly believe mathematics used by physicists and mathematics used by mathematicians are two different languages. And I mean language in a literal sense: different vocabulary, foremost different perspectives, and often different formulas. E.g. physics requires measurements, and measurements require coordinates aka frames. Hence you will meet coordinates in physics all the time: linear, affine, even projective, curved, local, in unusual metrics, and so on. The average mathematician hates coordinates. So if you don't want to spend time learning both, I recommend specifically searching for texts, books, pdf that address physicists particularly. E.g. look for "Differential Geometry for Physicists" instead of just "Differential Geometry." Here is a list of tips and tricks https://www.physicsforums.com/threads/how-to-use-the-w-in-www.1062388/ on how to use the internet. Almost all universities publish lecture notes on their servers nowadays so that you can find everything online. And if you want to buy books, try to figure out whether they fit your purposes beforehand. Many editors have reading probes for their textbooks or on Google Books. Or you can download those lecture notes and find a copy shop to make a paperback out of it.