Self-Study Plan: Advancing Math and Physics for a College Freshman

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A community college freshman, who previously excelled in AP Calculus, is now pursuing advanced coursework in calculus, differential equations, and linear algebra. With the semester nearing its end and ample free time, the student aims to self-study higher-level math and physics, seeking guidance on the optimal order for learning. Recommendations include starting with freshman-level Electricity and Magnetism (E&M) after mastering calculus, followed by sophomore-level modern physics. For mathematics, suggestions include "Calculus on Manifolds" and real analysis, with further studies in topology and differential geometry recommended for a strong mathematical foundation. While abstract algebra and probability theory are acknowledged as valuable, they are deemed less immediately relevant to the student's physics goals. Caution is advised to avoid burnout before exams.
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Currently a freshman in a community college, second semester. Graduated high school 4 years ago, so when I came to school again it was weird. I had taken ap calc in high school, so I went into calc 2 and calc physics 1 and got A's quite easily.

It boosted my ego and now I think I am some sort of genius haha. I want to challenge myself and see how fast I can learn math and physics. I am in calc 3, differential equations (no partial), and linear algebra right now. I finished learning the course work last month for the semester so now I am waiting for the semester to end (waiting for the time to come for exams).

I have all this free time now, but I want to use it to go ahead and teach myself math and physics as fast and as high as I can, but I am not sure which order I should follow.

In what order should I teach myself math and physics, all the way to the advanced grad work? I know em is next for physics, but I am not sure what math would go with it.
 
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Calc physics 2 is intro E&M as you know. Based on the info in your post, you certainly have covered enough calculus to do freshman E&M. I'd start reading ahead on that material.

When you make it through that, the next topic would be sophomore level modern physics. You should be able to easily figure out what modern physics book your school uses, and read ahead from that.

Be careful not to burn out before your exams!
 
What mathematics goes with each physics course past EM? Math and physics go hand in hand, so I feel like you didn't give me the whole story.
 
Only for mathematics:

I think you may be ready for "Calculus on Manifolds" by Spivak. Or some real analysis.
After this would follow topology and differential geometry.

Other math that you could look at, but which aren't immediately useful are abstract algebra, probability theory and set theory/logic. You can start any of these at any time. But if physics is your goal, then these aren't immediately useful...
 
Thanks, physics is my goal, but i feel I should be strong at math as well even if they aren't directly related. Differential geometry sounds fun.
 

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