Yeah, this is some B.S. here. I have a degree in CS and math. It sounds like parent comment doesn't really know analysis. The exercises in Rudin 1 are way harder than memorizing some rules to evaluate integrals.

That's how I remember it. I know I had to take calculus twice, but passed analysis the first time. To be fair, this is 20+ years ago and my memory sucks at the best of times.

Looking at it now, I think maybe I just found it too boring to remember the tricks, and too tedious to not make mistakes, while I found coming up with proofs more "interesting" and requiring less rote memorization.

Ah, for sure pure math is much more enjoyable to learn. I'm glad you find math interesting. Especially as a writer; that's really cool. Sorry for my previous comment.

I wish the university calculus changed the curriculum. I didn't find it particularly useful to learn how to integrate e.g. inverse trig given that WolframAlpha exists. There are lots of other examples of teaching memorization of silly tricks like that. I guess they probably do it because it's easy to test.

No offense taken, I totally understand that it can come across as odd. I hope my clarification makes more sense. Once I learned more about say, why leibniz and newton came up with their formulations, and what say, the inverse of the square root of the determinant of the jacobian actually allows one to formulate (how a space "dilate" when a continuous distortion is applied to it, for example), calculus (applied calculus) became a much more interesting topic for me.

While I only got so far in proving stuff about a cyber-physical I was working on, but this was really fun to learn: https://github.com/LS-Lab/KeYmaeraX-release

See also: http://lfcps.org/lfcps/

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).

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.

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.

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.