Somehow discrete math was the only math I understood in CS. Calculus, on the other hand, completely eluded me.

For what it’s worth, I had the damndest time with Calculus until I got a good professor. When he explained it, everything clicked. A good teacher makes a massive difference. It might be worth giving it another go.

If the whole of math were represented by the surface of the planet, "discrete math" would be more than half of it. Calculus (i.e. differentiation/integration on the reals) on the other hand, would be a city. Perhaps a very populated city, but just one.

It's a shame that match curriculum for non-math-majors is an all-roads-lead-to-calculus affair. I think we scare a lot of potentially talented people away from math with that approach.

I'm not sure why you think that? Basically all of physics, chemistry, and other physical sciences is calculus. Calculus is the mathematics of rates of change, and basically all physical science is the study of change.

Discrete math is very important to computer science. But in the rest of the world, calculus (and differential equations) dominate.

Maybe we're having a definition difference. My understanding of the term "discrete math" is that it refers to any math whose characters aren't part of a continuum.

Anything to do with numbers besides the reals. Anything to to with finite sets. Anything to do with groups, rings, polynomials, trees, graphs, ordinals, lattices, compass-straightedge-constructions, polygons, knots, categories, sheaves, topological spaces, vector spaces, and anything to do with oddities like map coloring or plane tiling, and a lot else too.

It's a course in "everything else" for students that are being pigeonholed into a mathematical specialization by the fact that it's been fashionable to use real numbers to describe the world since Newton.

Have you studied math? No mathematician would call algebraic topology discrete math, nor for that matter almost anything else on that list.

Yes, I have a degree in it.

I'd have to ask around but I know a few algebraic topologists and I'd bet that if pressed to describe their work as more-continuous or more-discrete they'd first tell you that this is a silly way to classify subfields in math and then they'd says it's probably more on the discrete side since it's all about categorizing topological spaces based on whether they have certain discrete properties:

- separable - countable - metric - compact

Sure the spaces themselves might be continuous, but topology is for telling those spaces apart based on where and how continuity fails. It's a discretization of things formerly suspected to be the the same.

I mean the notion of compactness is inspired pretty clearly from the continuum. I also have a degree in pure math and disagree strongly with your characterization of topology, which is literally defined up to homeomorphism which is itself defined by it's continuity. Arguably the whole point of topology is characterized by that which is preserved by continuous deformation, which clearly is inspired by more continuous math. I think you are using incredibly strong language and in a misguided way.

Yeah, I think you're right.

There's something about real analysis that makes me uncomfortable. I've been struggling for years to put my finger on it. Whatever it is, topology doesn't have it.

I had mistakenly decided that it was an overappreciation of continuity, but I think it must be something else.

Maybe it's the differential structure itself? Or an (over?)emphasis on the study of functions from space to space instead of the study of the space itself? Or the specificity of calculus (the study of one specific space) instead of the generality of topology (thinking about a lot of spaces and comparing them to each other)

Hmm, I'll have to ponder those. Specificity seems closest. Whatever it is, it's not a rational critique. Despite the discomfort, I'm also fascinated by it because one should not have an emotional response to specific types of math, but I very much do.

Something about the homework in Real Analysis left me feeling angry. Not because it was difficult or presented poorly, but because it was somehow... untrustworthy? As if my betters had decided which ideas were the good ones and the only thing left for me to do was optimize along the one dimension that they had assigned me. I realize that this is nonsense, but I can't seem to shake it.

I think it's totally good and human to have preferences for one sort of math over another :)

Double integration - brings not very nice memories back of my hand aching from writing upto 5 pages of workings out

It was especially bad in quantum mechanics where they made us do it the hard way (using calculus) before showing us the easy way (using noncommutative algebra).

"Calculus" is just the most accessible corner of the broader field of Analysis. And a lot of "discrete" mathematics ends up drawing upon analysis (especially complex analysis) as you delve deeper.

Well this isn't true at all. I'm shocked anyone would upvote this nonsense.

How about we play a game where you make a list of mathematical objects which are continuous, and I make a list of ones that aren't.

I'll start with sets and you can start with the real numbers, and we'll see whose list is longer.

To a certain degree the whole game is nonsense, there's a countable infinity of axioms and a countable infinity of theorems that follow therefrom, so we're never going to get anywhere rigorous with this, but just like it's not unreasonable to say that there are more multiples of 2 than there are of 2000, I think it's fair to say that continuity games on the reals represents a relatively small share when compared to mathematics in general.

All of the advanced technology you use on a daily basis depends on calculus for it to be designed and fabricated.

I didn't say it wasn't useful, just that it's not representative of mathematics as a whole.

How did you graduate with a CS degree?

In my school, to get the CS degree you only need as much calculus as needed to get to the second Physics course, which covers electromagnetism. You don't need a deep understanding of calculus. A lot of applications of calculus in the course can be handled by rote memorization.

I took extra calculus classes from the math department. Those are way harder than what you need for introductory physics.

Not op but for fwiw, in my university you only needed about as much calculus for ComSci as you would learn in IB/AP High school courses with a good prof anyway. Maybe a bit more but it was mostly a repeat.

(I recall one day in 3rd year calculus course realizing "wait a second... I don't need to be here!". I just kept signing up for calculus every year since 11th grade and suddenly realized I don't need, don't want, and don't like the class nor the prof I was in, and that was one pain less I could instill upon myself :)

As others have mentioned 'calculus' can mean one of five or six classes (I, II, III, advanced, diffyQ, probably more), basic differentiation is not hard, most of calc is some tricks a computer can learn or do better.

At least to my knowledge there is no 'theory of calculus' which allows one to solve generic integrals or differentials, calc is as much an unrelated art to comp sci as learning to play chess will help with accounting.

Depends on which country you are in. Not sure eg in Germany you have to do that much calculus for a CS degree.

(Though, what do you mean by calculus? I assume you mean integration and differentiation and real numbers and stuff? Or something else?)

Persistence.

My book recommendation for learning calculus would be Calculus Basic Concepts For High School by Tarasov.

I learned so much math when I looked into RLWE based lattice crypto. Some times it just takes a distinct use case to have something click

Is there a good text book/resource to (re) learn 'discrete math combinatorics' ?