To get to PDE, you'll have to take a class in ODE, another semester, plus at least one semester for PDE, and one, more likely two, in advanced algebra, and probably a two-semester course in advanced calculus, so about nine semesters.
Somewhere in there, you'll need to sneak in a class on theoretical statistics, but that should be easy ;. Expect at least ten to fifteen hours per week of course work out of the classroom it could be far more: a chemistry prof I know said his p-chem class required 40 hours of homework per week. In other words, I'd predict at least 2, hours of work for this level of math knowledge. How long, how fast? Colleges have a guideline of 2 to 3 hours of study for every hour in the classroom.
A typical class is 3 credit hours a semester, so for only mathematics you would have Calc plus Diffy Q to make it to an associate degree level of study. Its faster than college programs run, but you are missing the evaluation of a teacher and side classes that you would get in school.
Add in some physics and chemistry or whatever you think you need and that time doubles. Now you are on par with a college program. By way of comparison, and things do vary, my degree in Electrical Engineer Tech associate level , was It turns out I am bad at math and switched to education.
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If you are reading along at home, don't do that. It sucks. The headache is that you can do portions of GR and Astrophysics at certain points during that study. You simply won't know what or when that is appropriate unless you have a mentor. Finding an open course will help with that.
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I would guess that you could obtain a 4 year degree's worth of study in 8 years at home. It doesn't seem right. I have an engineering degree, so I've got about 20 credits in the calculus-ODE-PDE sequence and a few picked up on the side, in advanced calculus and statistics. My eyes glaze over with the math needed for GR and QM. Of course, there is numerical relativity and computational QM. I was going to say that this is high, but it really does depend on how easily it comes to the learner and math is really all about practice.
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A good book to guide one is The Theoretical Minimum. It goes over the basic math you need for physics. Thank you to everyone that responded! Here is what I have put on my Amazon wishlist Elliott Mendelson. How to Calculate Quickly. Henry Sticker.
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