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I am not doing a physics degree but an engineering degree but i am planning using my free time to self study all the math in preparing myself to self study subjects in theoretical physics. (I've always wanted to do theoretical physics but there are no scholarships offered in my country for the subject and my family is not rich so I had no choice but to self study)

By "self studying" I mean buying books and reading online materials on my own and try to understand everything I can. So far this is my plan,

Analytic geometry -> Single Variable Calculus -> Advanced Calculus (basic Linear algebra + multivariable and vector calculus) -> Linear Algebra -> ODEs -> but here I am stuck as to where do I go from here?

Well first of all is this plan okay?
If it is : how do I continue? Should I continue to real and complex analysis and do more things from pure math? Or should I just stick to the more computational part of math and learn more advanced techniques in solving differential equations or learn more algebraic techniques? How about geometry? Topology? Group theory and more things from pure Math?

If its not : what is the better way of doing it? Should I learn all the basic math first before reading Goldstein's classical mechanics ? Or should I just start with the physics and just pick up the math along the way?

And I also have the time issues to worry about how I wish I can just do a physics degree but unfortunately things don't always go your way. Due to imminent time constriants (engineering has lots of projects im sure) i would like my self study and learning to be as efficient as possible. Hence good advice from all experienced physicists would be very much helpful. Thanks in advance.

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