Since last year, I've been interested in higher mathematics and don't really know where to start and don't know what knowledge I still need to obtain, before being able to understand the concepts. Currently, I'm in a trigonometry class (I understand it well), but I have studied other subjects by reading textbooks and taking free courses, when possible. If I were to sum up my knowledge, up until trigonometry, I have a good understanding of the topics. I'm also good with symbollic logic. After that point, I have a fragmented knowledge of the topic. I want to study logic, set theoy, abstract algebra, etc. and topology (the most seemingly interesting subject to me). Where do I start? What subject should I start with? What lower mathematics should I learn first?
[Math] study higher mathematics. Where do I start
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Best Answer
There can't be more said to make sure you have the fundamentals down very well. Do your best to understand the topics well.
Having said that, if you're ready for more, there's plenty of places to go. It depends on your interest and your background.
One way to go would be to try to accelerate yourself through the standard Trigonometry, Geometry, Pre-Calculus, Calculus curriculum. This is a good way to go, but won't be the most direct way to the more abstract topics you've listed. If this is of interest, perhaps "A Hitchhiker's Guide to Calculus" by Spivak would be a good place to start.
A good place to start might be number theory. You already have some feelings for numbers, and it'll be a great way to introduce yourself to proving things rigorously. For number theory, this link might be of interest: Best book ever on Number Theory.
Alternatively, you can never start learning to prove things rigorously (essentially thinking clearly) too early. The text "Foundations of Higher Mathematics" by Fletcher and Patty might be a good place to start.
Best of luck!