I would say that properly learning new maths takes a long time and it might not be worth trying to seriously study areas that aren’t clearly related to the kind of research you want to do (like category theory).
Like, being a maths undergrad is a full time job and maths undergrads typically learn the equivalent of a few slim textbooks worth of content every few months.
Probably you work more hours and are more driven than your average maths undergrad, but then again you’ll be studying alone and trying to do other kinds of work too. Unless you’re exceptionally driven (or skip all the excercises) then it will be enough of an achievement to study a couple of textbooks a year. So spend them wisely!
I am graduating with a math minor, so like to believe I am aware of how painfully slowly you can move through a textbook with full understanding. I fully agree with you about spending your math points wisely and thanks for the reminder. I do tend to get overly ambitious. If you have a background in math (and AIA) or can point me to others who might be willing to have a zoom call or just a text exchange about how to better focus my math studies I would be very grateful.
Having said that, I do enjoy the study of math intrinsically, so some of the math I look at may be purely for my own enjoyment and I’m ok with that, but it would be good if when I am learning math it can be both enjoyable AND helpful for my future work on AIA. : )
I’m certainly no expert on self-studying maths. I’ve generally found it easy to pick up a conceptual understanding from skimming textbooks, and for some subjects (e.g. statistics, Bayesian probability, maybe logic) I think that’s where most of the value lies. I’ve never had the drive or made the time to work through a lot of exercises on my own, and I’d guess that for subjects like linear algebra being able to actually work through problems is probably the important part.
So if you have a subject where both (i) it’s not clearly relevant, and (ii) getting a useful understanding requires working through a lot of exercises, then I’d probably hold off.
Good luck!
I would say that properly learning new maths takes a long time and it might not be worth trying to seriously study areas that aren’t clearly related to the kind of research you want to do (like category theory).
Like, being a maths undergrad is a full time job and maths undergrads typically learn the equivalent of a few slim textbooks worth of content every few months.
Probably you work more hours and are more driven than your average maths undergrad, but then again you’ll be studying alone and trying to do other kinds of work too. Unless you’re exceptionally driven (or skip all the excercises) then it will be enough of an achievement to study a couple of textbooks a year. So spend them wisely!
Thank you!
I am graduating with a math minor, so like to believe I am aware of how painfully slowly you can move through a textbook with full understanding. I fully agree with you about spending your math points wisely and thanks for the reminder. I do tend to get overly ambitious. If you have a background in math (and AIA) or can point me to others who might be willing to have a zoom call or just a text exchange about how to better focus my math studies I would be very grateful.
Having said that, I do enjoy the study of math intrinsically, so some of the math I look at may be purely for my own enjoyment and I’m ok with that, but it would be good if when I am learning math it can be both enjoyable AND helpful for my future work on AIA. : )
I’m certainly no expert on self-studying maths. I’ve generally found it easy to pick up a conceptual understanding from skimming textbooks, and for some subjects (e.g. statistics, Bayesian probability, maybe logic) I think that’s where most of the value lies. I’ve never had the drive or made the time to work through a lot of exercises on my own, and I’d guess that for subjects like linear algebra being able to actually work through problems is probably the important part.
So if you have a subject where both (i) it’s not clearly relevant, and (ii) getting a useful understanding requires working through a lot of exercises, then I’d probably hold off.