Re:Ask HN: High-Quality Online Degree for Mathematics?
by llamaz on Tuesday January 08, 2019 @05:33AM
(#18854621)
I've read parts of Halmos + Rudin, and I think that they would be a fast track to higher level pure math, but I've known people who've gone down such path and end up being able to prove Fubini's theorem using measure theory without understanding what it means.
The ideal approach for a self learner, which would simulate the university experience, would be doing as many problems in Schaum's outlines for math subjects and supplementing the info with textbooks/online resources.
However, being a computer scientist I think a different approach to mathematics can be more enjoyable and also much more useful for many theoretical and practical developments that are yet to come. The downside is that materials are a lot less cohesive (any other references appreciated!). I'm talking about an approach with a focus on the foundations of mathematics, emphasizing logic, category theory and type theory.
Some links:
http://www.paultaylor.eu/~pt/prafm/
https://ncatlab.org/nlab/show/computational+trinitarianism
https://softwarefoundations.cis.upenn.edu/
http://adam.chlipala.net/frap/
http://concrete-semantics.org/