[Todd]

I came here to suggest the same thing. I started with real analysis but realized that I was lacking the mathematical maturity to understand things back to first principles. My suggestion is to start with learning how the foundations of mathematics were rebuilt starting from axiomatic principles in the last part of the 19th century and early 20th century.

The book How to Prove It helped me tremendously. Get a good book on abstract algebra. Maybe start with Herstein, then progress to Dummit and Foote and, maybe eventually, to Hungerford. This is the kind of math that will help you reason about data sets. It's foundational in mathematics and it also happens to be very applicable to computer science.

After that, you will have a strong basis for branching out to more specialized branches of mathematics that may have more relevance to the types of problems that you're solving.

[nicklaf]

That is excellent advice. If the student is struggling to write proofs in her or his real analysis text, s/eh should definitely seek out "How to Prove It".