I'm about to embark on a PhD in mathematical biology. My major is in computer science.
I would like to acquire a more rigorous understanding of math, which I am going to need to tackle some research problems. My plan is, initially, to go through Linear Algebra Done Right by Axler, and Principles of Mathematical Analysis by Rudin as a refresher.
I was considering to go through a foundations book like Naive Set Theory by Halmos beforehand. But perhaps a category theory-based approach could be more enriching, as it could help me to see connections between many areas and concepts in math. Is this a good idea?
Sets for Mathematics and Conceptual Mathematics, both by Lawvere seem to be popular choices. The former seems to be a nice construction of set theory using categories instead of ZFC, but not much more than that. The latter seems to spend more time addressing the connection between categories and different branches of math, like linear maps. Any suggestions?