[ivansavz]

I recommend you start with a review of all the topics from high school math which are not clear to you, e.g. functions, solving equations, geometry, and algebra. This may take some time, but it's totally worth it. Building your math knowledge is like building a house---you want to start from a solid foundation.

Next, the traditional "pillars" of STEM are calculus and mechanics. Calculus will beef-up your skills for understanding and manipulating function. Mechanics is important because it teaches you about modelling real-world phenomena with mathematical equations.

Perhaps of even greater importance are the subjects of probability and linear algebra. Probabilistic reasoning and linear algebra techniques (e.g. eigendecomposition) are used for many applications.

RE problems, I think you should reconsider your stance about that. It is very easy to fall into the "I learned lots of cool stuff today" trap, where you think you're making progress, but actually you haven't integrating the knowledge fully. Solving problems usually will put you outside of your comfort zone and force you to rethink concepts and to form new "paths" between them. That's what you want---ideally the math concepts in your mind to be a fully connected graph. Speaking of graphs, here's a concept map from my book that shows (a subset of) the links between concepts from high school math, physics, calculus, and linear algebra: http://minireference.com/static/tutorials/conceptmap.pdf

Good luck with your studies!

[eru]

All good points. By the way, if you go from first principles, do measure and integration theory before probability theory.