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