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Calculus (at least our exams and lecture) were so much about "calculating" and applying rules and clever tricks on complex functions and multiple dimensions whi

by larve 4y ago

Calculus (at least our exams and lecture) were so much about "calculating" and applying rules and clever tricks on complex functions and multiple dimensions which just... didn't work for me. I had a lot of other things going on, so this recollection is probably off. Calculus and diff eqs started making sense to me when I started working in mathematica and systemmodeler, and realizing that it was a brilliant tool. It probably also came from the way it was taught, which was completely devoid of any historical or practical context. It was just a lot of "compute the laplacian of e^i_sin(phi) or whatever. I found groups, limits, continuity, fields to be much more amenable to my thinking. It felt way more similar to the things I really enjoyed (building software in scheme and C and writing exploits in assembly).

bmitc 4y ago
Oh, I see. So it seems it was more about the presentation and interest rather than the concepts. You may like Calculus by Michael Spivak if you're interested in it again. It is much more analytical than computational.
- larve 4y ago
  That's one of the books I used when I got back into it. These days, there is so much great material on youtube and edx and coursera (plus maths stackexchange and discords) that it's absolutely fantastic to learn maths, as fantastic instructors are immediately available. For me, I realized thst I need to write the code to accompany the maths, because it helps me disambiguate mathematical notation and put "types" on things. It helped me a lot to work alongside real maths PhDs and realize that they have a very "intuitive" approach to maths, and don't necessarily yeet lemmas and proofs around all day, instead spending a lot of time brainstorming on the whiteboard and discussing things out, very similarly to software design. It was one of them telling me that my thinking was very mathematical that helped me "deconstruct" the fear of maths that I had built up.
  - bmitc 4y ago
    I agree that using programming to understand a domain is very useful, as it’s something I’m trying to do a lot of these days. Although sometimes, there needs to be some simplification to do that that maybe skirts around the meat of the matter. But as always, a diverse approach is more powerful than a singular one.

by larve 4y ago

bmitc 4y ago

Oh, I see. So it seems it was more about the presentation and interest rather than the concepts. You may like Calculus by Michael Spivak if you're interested in it again. It is much more analytical than computational.

larve 4y ago
That's one of the books I used when I got back into it. These days, there is so much great material on youtube and edx and coursera (plus maths stackexchange and discords) that it's absolutely fantastic to learn maths, as fantastic instructors are immediately available. For me, I realized thst I need to write the code to accompany the maths, because it helps me disambiguate mathematical notation and put "types" on things. It helped me a lot to work alongside real maths PhDs and realize that they have a very "intuitive" approach to maths, and don't necessarily yeet lemmas and proofs around all day, instead spending a lot of time brainstorming on the whiteboard and discussing things out, very similarly to software design. It was one of them telling me that my thinking was very mathematical that helped me "deconstruct" the fear of maths that I had built up.
- bmitc 4y ago
  I agree that using programming to understand a domain is very useful, as it’s something I’m trying to do a lot of these days. Although sometimes, there needs to be some simplification to do that that maybe skirts around the meat of the matter. But as always, a diverse approach is more powerful than a singular one.