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Alright. This is a question about what to learn (next), not a specific topic. Details in next posts.

Mathematics
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I just finished looking at basic calculus concepts, except for partial derivatives and differential equations. I'm looking to where to study next.
Now, I self studied both trig and calculus, and I skipped the so called "pre calc"
I can do most of the differential calculus problems in my textbook, and as for integration, I understand how to integrate by u-sub, and by parts (as well as a little partial fractions)

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However, for most methods, I know how to do the math, but I'm not particularly good at it (I couldn't do a "integrate sec^3 x problem without difficulty").
Since I'm just self studying, I wonder if I should move on (because I will relearn calc in 2 or 3 years), or, if I should go back and make sure I am a boss at the math.
Now, I'm wondering, given that I should move forward, what I should study (linear? Differential equations?). If I should look back, I am still interested in what I should learn next.
And, if you can, it would be extremely helpful if you gave me maybe 3 or 4 things to learn in order, or parallel.
Any particular career or path of study you're interested in?
My gut reaction regardless is to say proofs.
Math. Any and all.
If you want to do a lot of math, proofs is the way to go. It's what I would call the "gateway" to serious math.
Well, I'm also interested in applications...

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