I personally covered the relevant parts of measure theory and a lot of stochastic processes in math finance, which I think is a good way to do it. I did take an OR class which spent about half the time on Markov chains, but I consider that stuff pretty straightforward if you have a good grounding in linear algebra.
Analysis/abstract/topology are exactly the sort of prereqs I recommend skipping. The intro classes usually spend a bunch of time on fairly boring stuff; intermediate-level classes will usually review the actually-useful parts as-needed.
The crypto recommendation makes sense. For logic, I don’t think there’s much value in diving into the full rigor; it’s mostly the concepts that matter, and proving it all carefully is extremely tedious. Definitely important to get the core concepts, though.
You recommend the basic math courses: linear algebra, probability, a standard calculus sequence. You just don’t recommend the more pure math type courses. In your view, pure math courses spend too much time digging into boring tedious details, and you advise more applied courses instead. That’s an entirely valid perspective. And it may be the most productive tactic.
Real analysis, abstract algebra, and topology are often the hardest and most advanced courses in the undergraduate math catalog. Those are considered the capstone courses of an undergraduate degree in pure mathematics. You reference them as introductory classes or prereqs which seems not correct. At almost any university, Real Analysis is the more advanced, theoretical, and difficult version of calculus.
Did you study martingales or stopped brownian motion? Are those useful or recommended? Those seem relevant to finance and applied probability?
I really enjoyed this post, and thank you for the awesome reply.
Real analysis, abstract algebra, and topology are often the hardest and most advanced courses in the undergraduate math catalog. Those are considered the capstone courses of an undergraduate degree in pure mathematics. You reference them as introductory classes or prereqs which seems not correct.
Yeah, fair. Harvey Mudd is probably unusual in this regard—it’s a very-top-tier exclusively-STEM school, so analysis and abstract algebra were typically late-sophomore-year/early-junior-year courses for the math majors (IIRC). I guess my corresponding advice for someone at a typical not-exclusively-undergrad university would be to jump straight into grad-level math courses.
(As with the post, this advice is obviously not for everyone.)
Did you study martingales or stopped brownian motion? Are those useful or recommended? Those seem relevant to finance and applied probability?
Yup, that comes up in math finance. I haven’t seen them come up much outside of finance, they’re kind of niche in the broader picture.
I personally covered the relevant parts of measure theory and a lot of stochastic processes in math finance, which I think is a good way to do it. I did take an OR class which spent about half the time on Markov chains, but I consider that stuff pretty straightforward if you have a good grounding in linear algebra.
Analysis/abstract/topology are exactly the sort of prereqs I recommend skipping. The intro classes usually spend a bunch of time on fairly boring stuff; intermediate-level classes will usually review the actually-useful parts as-needed.
The crypto recommendation makes sense. For logic, I don’t think there’s much value in diving into the full rigor; it’s mostly the concepts that matter, and proving it all carefully is extremely tedious. Definitely important to get the core concepts, though.
You recommend the basic math courses: linear algebra, probability, a standard calculus sequence. You just don’t recommend the more pure math type courses. In your view, pure math courses spend too much time digging into boring tedious details, and you advise more applied courses instead. That’s an entirely valid perspective. And it may be the most productive tactic.
Real analysis, abstract algebra, and topology are often the hardest and most advanced courses in the undergraduate math catalog. Those are considered the capstone courses of an undergraduate degree in pure mathematics. You reference them as introductory classes or prereqs which seems not correct. At almost any university, Real Analysis is the more advanced, theoretical, and difficult version of calculus.
Did you study martingales or stopped brownian motion? Are those useful or recommended? Those seem relevant to finance and applied probability?
I really enjoyed this post, and thank you for the awesome reply.
Yeah, fair. Harvey Mudd is probably unusual in this regard—it’s a very-top-tier exclusively-STEM school, so analysis and abstract algebra were typically late-sophomore-year/early-junior-year courses for the math majors (IIRC). I guess my corresponding advice for someone at a typical not-exclusively-undergrad university would be to jump straight into grad-level math courses.
(As with the post, this advice is obviously not for everyone.)
Yup, that comes up in math finance. I haven’t seen them come up much outside of finance, they’re kind of niche in the broader picture.