I have the CLRS algorithms book as well as Computer Systems: A Programmer’s Perspective, which I’ve done some self-study from. Both are practical and interesting, but I tend to get bogged down in the proofs as some of the math is just not anything I remember seeing (again, 10+ years since I took a math course). Barring that, I’ve not had much if any trouble with the content of either text, so self-study of this material is something I’d be comfortable with going forward. However, I worry that the lack of these classes on a CV/resume is a barrier to entry for some jobs.
My main goal is to improve my ability to model computational problems mathematically. I find this activity tremendously satisfying and challenging. It seems to me that part of being able to do this is not just knowledge, but intuition, experience, and breadth of exposure to mathematics. I definitely do not feel strong enough mathematically to self-study anything beyond basic calculus.
I tend to keep leaning towards Applied Math http://catalog.uoregon.edu/arts_sciences/mathematics/#bsappliedmathematics for various reasons I’ve expressed. My questions 1-4 from the original post still gnaw at me, however.