[nextos]

Modern mathematics is built around linear algebra and analysis. It's no coincidence math bootcamps like Harvard Math 55 go this route. If you are into long-term mathematical learning and you can afford the detour, I'd start by learning linear algebra from e.g. Axler and analysis from e.g. Bressoud (both are didactic masterpieces).

Alternatively, you can start by studying any of the alternative foundations to mathematics (set theory, logic, etc). Perhaps from a toned down alternative to Sørensen & Urzyczyn. A beautiful and very modern way to do this for a CS student would be to marry it with a course on automated theorem proving (using Isabelle or Coq). Any book suggestions welcome.