I’m biased towards some versions of graph / network theory , dynamical systems and multiobjective optimization theory. Since you are into neural nets and multivariable calculus it sounds like you are already doing a version of these. (I was in an interdisplinary field and took a fair amount of applied math and physics, many of the details of which i never used or really remember—i can look them up—my applied interests were in between very technical and ‘fermi’ (back of the envelope) problems and i usually tried to phrase them both ways—one solvable. and the other intractable.
I never had a class in statistics but i studied it a bit on my own (partly because one area i did use a bit was statistical physics, though alot of that does not like what you see in a statistics text thoughn they overlap, and also newer texts sometimes sort of have both fields—neural nets to an extent can be viewed as analogous or closely related to statistical physics (sometimes almost the same formalism). .
since i was into applications (and usually not the ones i was assigned to do which were more in biochemsitry and biotech—fields that don’t really interest me even though formally they can be phrased in analogy to ones i was interested in, i never could really get into the research (felt they were not problems of high priority to solve, or at least were ‘aesthetically’ inintersting—just alot of tecnique. its like music—i’m more into forms of modern pop/underground ‘Fermi’ music, rather than (tecnical) classical, thogh they can overlap. ).
It may not be especially useful if you want to get a job or even a math degree The applications of that field are few and far between , only other way you can get a job in that is if you have a degree at PhD level. Or if you can write software you can be slightly involved in that field.
Many if not most or all modern fields of science use some variant of that formalism.
I’m biased towards some versions of graph / network theory , dynamical systems and multiobjective optimization theory. Since you are into neural nets and multivariable calculus it sounds like you are already doing a version of these. (I was in an interdisplinary field and took a fair amount of applied math and physics, many of the details of which i never used or really remember—i can look them up—my applied interests were in between very technical and ‘fermi’ (back of the envelope) problems and i usually tried to phrase them both ways—one solvable. and the other intractable.
I never had a class in statistics but i studied it a bit on my own (partly because one area i did use a bit was statistical physics, though alot of that does not like what you see in a statistics text thoughn they overlap, and also newer texts sometimes sort of have both fields—neural nets to an extent can be viewed as analogous or closely related to statistical physics (sometimes almost the same formalism). .
since i was into applications (and usually not the ones i was assigned to do which were more in biochemsitry and biotech—fields that don’t really interest me even though formally they can be phrased in analogy to ones i was interested in, i never could really get into the research (felt they were not problems of high priority to solve, or at least were ‘aesthetically’ inintersting—just alot of tecnique. its like music—i’m more into forms of modern pop/underground ‘Fermi’ music, rather than (tecnical) classical, thogh they can overlap. ).
Can you say something about why you feel this is especially useful?
It may not be especially useful if you want to get a job or even a math degree The applications of that field are few and far between , only other way you can get a job in that is if you have a degree at PhD level. Or if you can write software you can be slightly involved in that field.
Many if not most or all modern fields of science use some variant of that formalism.