Just curious, how many people here have been taught calculus and never used it? Upvote if you put your hand up.
I find these questions a bit strange, because it sort of misses the point of learning as a whole. Do I use Civil War history every day? No, probably not, but I also don't regret being taught it at school. Am I conducting a lot of chemical experiments? No, but I think it's valid for me to have learned chemistry in high school. Am I performing literary analysis on everything I consume? Well, yes, but that's just something I do for fun, it's not like people are paying me for it.
The reason that they teach calculus is two fold. First, most of this stuff is somewhat additive. Do you use "calculus" every day? Probably not, but having learned calculus might make other aspects of math or programming easier, stuff that you might end up using full time.
Second, the people designing programs for Computer Science degrees (and probably others as well) at some level need to have a "one size fits all" for their students. My professor doesn't know if I'm going to get a job doing video game physics, if I'm going to designing video compression filters, or if I'm going to be a web developer, but they want to make sure that if I graduate with a CS degree, I am more or less qualified for most reasonable software engineering positions, or least given the tools to become qualified.
We could extrapolate this logic further: how many people here are realistically writing low-level C code? I know I'm not, but I don't regret them teaching me how it's done, it informs my high-level code writing.
If you haven't used something from calculus (or other branch of mathematics beyond grade school stuff) in this sector, you've either been avoiding it or had others do the work for you on stackoverflow or something.
You can't even have big O notation without calculus.
- Understanding the ideas behind derivatives / gradients and integrals has let me grasp some basic concepts regarding physical systems and regarding money.
- I've helped some physicists turn their ideas into C++ code, and knowing a little calculus narrowed the communications gap.
- In deep learning systems, if I didn't already know some basic calculus, understanding auto-differentiation and back-propagation would have seemed like an insurmountable challenge.
I'm not qualified to guess how universal my experience is.
[EDIT] Making the later high school math classes and early university math classes focus entirely on practical application might also be a good idea. I have a feeling it would turn off ~0% people who will eventually become mathematicians, and then the other 200 people in that one mathematician's graduating high school class might actually use what they learned every now and then, once out of school.
I mean, I don't recall the exact recipe for most calculus operations, even though I spent hours in college learning them. But I do know that I can build a taylor series* to approximate certain functions, and that it will be pretty quick and have a bounded error.
* Use Wolfram Alpha
I think I've used trig once or twice for house projects, but by "used" I mean "plugged some numbers into the relevant calculator, without needing to actually know the formula", and if that counts I guess I also do advanced cryptography and all kinds of other crazy stuff daily, like when I used GPS or access a web page over SSL.
Far and away the most useful math I was taught in school was the memorization of basic "math facts" (e.g. multiplication tables), including and especially the ability to do mental math with fractions and percentages. This is the stuff (rote memorization) that professional mathematicians seem to hate and want to get rid of or downplay, even calling it "not actually math" et c. Easily the best use of my time in any math class, ever, though I didn't know it at the time.
As far as any utility it had in "shaping my mind", my four semesters of college French were at least as useful for that as my... oh, I dunno, 28 semesters of math? Youtube and reading blogs has been more useful for developing my mind in the way people usually mean when they say that's what learning math's good for, even if you don't use it. I also never use that [edit: the French, I mean] unfortunately, so like math, I've lost almost all of it.
I'd guess 99% of the math I use in a given year could be done by an average 5th grader. Every now and then I take a stab at (re-)learning some math, but it's just so hard to justify the time. What am I going to do with it, really, unless I put in thousands of study-hours to get really good at some niche? Nothing. So I usually end up distracted by some fun-but-not-enlightening recreational math, which is fine, but about as improving as solving Sudoku puzzles.
Paid software developer since age 15, BS degree in computer science, approaching age 40.
I'm not a mathematician, but my understanding of them saying that is because that's more computation than mathematical thinking. You're not getting an understanding of what's actually happening when you've memorized 4x5=20, all you're doing is creating basic word-mapping.
Maybe I just lived a very different life, but even though I'm reasonably good with my times tables, I still almost always use a calculator/spreadsheet/spotlight/phone to do all but the most basic of computations. Why wouldn't I? I always have a supercomputer in my pocket that is substantially more likely to be correct than a twenty year old memory of fourth grade.
> I'd guess 99% of the math I use in a given year could be done by an average 5th grader.
I don't mean to come off as a jerk, but I guess I'm just going to say it; in the 25 years you've been a developer, have you not tried to make a game? Some machine learning? Data science?
I'm not saying you need to be the next Guass or anything, but all of those require more advanced math than what I was taught in fifth grade. To make a platformer game, you have to know enough to do a basic Euler integration. To do machine learning, you have to know enough to at least know what a Sigmoid is [1]. To do data science, you have to understand basic statistical methods (E.g. ANOVA, Chi Squared, Student T Tests). Maybe you were taught all this stuff in fifth grade, but I don't think that the majority of students where.
[1] I don't do machine learning for a living, I know that the Sigmoid has fallen out of favor but I think my point still stands.
Yes! But there are lots of kinds of games, and none of my attempts were in 3d or involved physics. Also I've learned that without real users beating down my door for a feature I will not ever finish a project, so I've given up on "fun" coding entirely and haven't written any kind of game whatsoever in probably 15+ years. It's a waste of time for me, as I will not finish it. I need a guaranteed smiling face at the end of the process, or there's no chance I'll get far. If I decided I really wanted to make a game these days, unless unusual physics were vital to it, I'd probably let an existing engine take care of all that for me—why would I code it from scratch, when the point is to have a finished game, not manually write as much of it as possible at the expense of making it take longer?
> Some machine learning?
Never had a reason. I'll learn it if I ever have one. My usual approach to anything a whole bunch of people are doing, but I'm not, is to assume that some of them must be idiots, and they're doing OK, so, since I'm an idiot, I'll pick it up just fine, too—if I ever need to. This approach has yet to fail me. I've yet to try to do something new that lots of other people are doing and found that no, in fact I'm too dumb to pick it up pretty fast.
See above about needing someone who wants the output of my work, before I can reliably finish projects. There's no way I'm going to complete a "learning project" in machine learning, for its own sake, unless I'm just very interested in whatever's being learned—and I just don't really care that much about machine learning. I get the gist, so it's not some big mystery to me how it works, OK, that's neat. I'll dig deeper if I ever have even the slightest reason to. Just haven't yet.
> Data science?
Not done anything interesting, or "real" data science. Fixing up data, yes. Doing very simple math on it, sure. If I ever knew what any of these: "ANOVA, Chi Squared, Student T Tests" are I've long since forgotten. Certainly never used any.
I coded that kind of stuff when I was like 12, in BASIC, with no idea about integration as far as I can remember now. I think I'd read about simulating a bouncing ball in a basic programming book somewhere? This did help with getting the ideas about calculus later.
Added: http://www.vpri.org/pdf/hc_pers_comp_for_children.pdf has a more detailed scenario of kids coding Euler integration without knowing it's called that.
Similar situation as GP and I have never made a game. Simply because it doesn't interest me in the slightest
Velocity = Velocity + changes in velocity
Position = Position + Velocity
Do this on an infinite loop and That’s a numeric Euler integration of velocity to get position.
It’s not gatekeeping, I’m not saying you shouldn’t be allowed to make a game without credentials. I was a college dropout for almost a decade until three months ago. I was just saying that that is more advanced math than what a fifth grader does.
I am sorry that you think that it is absurd.
[edit] Wikipediaing "Euler integration", which redirects to "Euler method", it's not clear to me at all how knowing the stuff on that page (and it's Wikipedia, so nothing on the page looks like 5th grade math, even if it actually is) is particularly helpful with coming up with those two addition formulas.
[edit edit] I don't mean the tone of any of this to be hostile—it's so hard to convey tone in plain text—but I'm just legitimately not following how this is connected, except in a "well you could derive these two very simple things from a very powerful, more complex, general method that's useful for a bunch of other stuff too—there's no particular reason to, but you could" sort of way.
What makes this more complicated (and granted you might not be doing this if your goal is to clone Mario) is when you need to combine forces together. In that case, the change in velocity comes from acceleration, and the change in acceleration comes from the summation of forces in X and Y directions. Obviously the actual calculation is trivial, just simple arithmetic, but the knowledge of what's going on, and how to expand on it is not. If you wanted to make Joust, for example, you need to know all this stuff about forces, or at least I did when I cloned Joust a million years ago. I agree that Wikipedia has a way of complicating things, and it's possible that even without formal training in calculus that you would have rediscovered what I described, and that's totally fair, but that's still calculus! You're still doing calculus, you just didn't realize it at that point.
Of course if you need more accurate physics in your games (unlikely for a basic platformer), you would need to use a more advanced integration method, e.g. RK4 or Adams Bashforth.
I apologize if I came off slightly gatekeepey; I should be clear that I don't particularly care if you know the name of these methods. I'm just saying that these methods are calculus concepts, and as such having an understanding of calculus can help you with that.
> I apologize if I came off slightly gatekeepey; I should be clear that I don't particularly care if you know the name of these methods. I'm just saying that these methods are calculus concepts, and as such having an understanding of calculus can help you with that.
None of your posts bothered me at all. Appreciate the care, though.
It depends on what you do. One will absolutely run into calc doing any sort of scientific computing, simulations, signal processing, machine learning, or graphics programming. But you can absolutely make a good living in software knowing no calculus.
Technically, though, I learned that calculus from a textbook, rather than by being taught.
Imo, they we should be teaching basic linear algebra before calculus. Multiplying vectors and matrices by hand gives a very good feel for how integrals work.
(...that being said, calculus is a lot more than just a way to calculate, it's a whole method of thinking of the world, and that's clearly not outdated quite yet)
That, too, is calculus. However, a closed-form solution will always be preferred—"a second or two" might be acceptable if you're only evaluating the function once, but it's clearly not good enough when you're applying it to a large data set. We may all be carrying around supercomputers in our pockets but we're still well short of the point where that kind of optimization wouldn't lead to a noticeable increase in both performance and (practical) functionality.