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Ask Slashdot: How Many of You Actually Use Math?
An anonymous reader writes with a question that makes a good follow-on to the claim that mathematics requirements in U.S. schools unnecessarily limit students' educational choices: "I'm a high school student who is interested in a career in a computer science or game development related position. I've been told by teachers and parents that math classes are a must for any technology related career. I've been dabbling around Unity3D and OGRE for about two years now and have been programming for longer than that, but I've never had to use any math beyond trigonometry (which I took as a Freshman). This makes me wonder: will I actually use calculus and above, or is it just a popular idea that you need to be a mathematician in order to program? What are your experiences?"
The bulk of programming jobs have nothing at all to do with math beyond the high school level.
Its mostly counting beans and keeping records. Really, it is.
Gaming, (image rendering and manipulation), statistics, and rocket science are a few of the obvious areas that come to mind where more advanced maths may be necessary. Even these fields have packages available to do the heavy lifting once you figure out what it is that you want to do. Knowing what to do the key. This kind of programming constitutes about 1% of the available jobs and 98% of the chest thumping on slashdot.
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go google quaternions, or rotation matricies
properly understanding these sort of techniques that are used widely in 3D programming applications without having knowledge of linear algebra is damned near impossible
It doesn't matter if you use it in practice. You'll learn to think critically to solve abstract problems. Don't buy into the hype that you don't need math.
Follow-up:
Math is nothing more than a language that allows the speaker to make very precise statements. If you can't see how this is useful in programming then no-one can help you.
Others do what they can, mathematicians do what they want.
You are probably not gonna use what you learned in Huckleberry Finn or History, either.
There's a reason these are taught, and it's not all about pure facts.
(-1: Post disagrees with my already-settled worldview) is not a valid mod option.
Also, if you can't handle the math, you aren't cut out for the job. Even if you don't use it daily. Same reason that premedical students take physics (to keep morons out of medical school).
It's not necessarily the actual math skills that are important - it's the understanding of the concepts behind it that will increase your understanding of any kind of process, job, or task - programming being one of them. Knowing what the area under a curve means is probably more important than knowing how to calculate it.
I don't use calculus or any kind of advanced algebra in my day to day work (in communications, far from programming) but I'm sure glad that I understand the basic concepts, thanks to a first degree in engineering.
Realistic physics requires it. On top of that, the more math you learn before entering the field, the more opportunities will be available to you as a programmer. Don't cripple yourself while you're still young.
Damn_registrars has no butt-hole. Damn_registrars has no use for a butt-hole.
How many of you use the problem solving skills that were developed in math class? I may not use math everyday, but I certainly solve complex problems that I'm sure others with less math education would struggle to solve.
Logic is math, and EVERYONE needs logic.
Even if you never write a proof or solve an integral in your working life, it's important to understand how math works. Life, all of it, is one big word problem. If you don't have a basic understanding for the mathematical nature of the universe, you're simply not going to be able to navigate it as well. If you don't understand how mathematical arguments work, you won't be able to offer useful opinions on the matters of the day.
I'm not sure that everyone needs to know calculus, but everyone needs to know what calculus is and what it's used for. Everyone needs to be numerate.
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Calculus is pretty much a modeling language when it comes to programming, not an implementation language. When it's appropriate, calculus is generally done outside of the program implementation, its output being the algorithmic shortcuts and validations that you can rely on when writing the actual code.
Agreed. Any graphics engine uses a ton of linear algebra under the hood, so you'll need that if you ever want to modify one or write your own. Also, if you want to do any kind of physics simulation (which you probably will, if you're doing games), you may need calculus (but maybe not, since video games fake as much as they can get away with).
I explicitly release the above into the public domain.
Purity
The CB App. What's your 20?
Which is also why there is a lot of high school level code out there.
If you never learn more than you need then you'll never know if you have learned as much as you need.
Learning more math won't always make you a better programmer. But it will show you whether you can do something better than someone who knows less math.
Also, you'll never be able to verify that your algorithm is working by manually processing sample inputs. That's a tremendously useful ability to have. See the following thought process:
>> "See if I give it A, it should give B, but instead it gives C"
>> "Let me try it by hand"
>> "My algorithm is wrong" or "My implementation of the algorithm is wrong" or "I'm using the wrong algorithm to solve this problem" (knowing the difference saves you notable amounts of time)
>> "I now have an understanding of the actual problem and can solve it"
Yeah, you'll notice that a lot of the richest and most successful people never completed college. And that's fine but in my humble opinion, that's a risky bet to take. I've done interviewing for developers for a fortune 500 company and seeing a college degree on the resume doesn't cause me to kick back and say "Oh thank god, they have taken Multivariate and Differential Equations calculus, now all my Spring applications are going to be able to compute the triple integral (by parts) of a toroid in three dimensional space as it passes through a fluctuating field exerting a force on it!" (Yes, I know that makes no sense at all) No, what that tells me is that we're going to be able to throw you in an environment where you have no clue what to do but resources to go out and find what to do. On top of that, you're going to be able to digest the driest and shittiest of documentation (like a calc book) and come back to me and have gleaned some working knowledge from it. Sure, you might have to go to the next cubicle and say "What is up with this stack dump?" And you may have to seek out an authority (like a professor) but you're going to come to some answer for our problems.
In short, it tells employers that you know how to play ball and high order concepts don't frighten you. I'm not going to throw integration by parts at you on the job but it is good to know that you stepped up to that challenge -- even if it was just to get to a final, pass it and move on. In short, I went to a liberal arts college, I took classes on music theory, calculus, physics, Native American studies, advanced literature, etc and in those classes I created four part inventions, mounds of calculations, papers, powerpoints, etc and I have used little if any of that in my day to day job post college. But in mastering those processes I learned how to play ball. Now, I'm not saying you need to go take music theory and Native American studies. But the thing with Calculus is that all software development is logic and math. So don't you think you'd want to get all your i's dotted and t's crossed so that any employer that looks at you knows you have studied beyond the requirements of math for writing software into a realm so lofty they won't even be able to use it? I'm sure glad I did.
My work here is dung.
This is completely backwards.
Calculus is used to describe nature in the most fundamental way. Computers simply work with approximations to nature that are reasonable for most types of predictions.
So computers are the ones using a shortcut that is faster. Finding analytic solutions to differential equations is the most fundamental way of understanding nature that we have in science, but this is often much more difficult than using a numerical approach with a computer.
In any case, most people need to learn the full way of doing things (ie the typical calculus way) before they can move on to shortcuts that may be faster.
Hear, hear.
You don't necessarily do a lot of math as a programmer, but being able to think like a mathematician will be a great help. General problem solving involves logic and inference, in much the same way as proving theorems does. Some concepts from Discrete Math become so commonplace (decimal to bin,oct,hex,etc) that you hardly even notice them anymore, but will glaze the eyes of a non-programmer. I have also had to explain floating point evilness to more than one accountant.
The most hard-math thing I have done recently in programming was double linear regression to project the time required for a file copy operation to complete. Some quality time with Wikipedia, a couple of pages of algebra, and a couple of days of debugging later, and I had a "time remaining" display that counts down like a clock. Take that, Windows Explorer.
I am not your blowing wind, I am the lightning.
You need calculus to actually understand statistics for continuous random variables.
Students who do well in the more advanced undergraduate math courses (real analysis, abstract algebra, etc.) may never specifically use those precise topics, but good performance in those courses serves as a strong testament about being able to deal with abstraction, work precisely, and construct correct arguments. Those skills will serve students well and may impress employers/managers that the student actually is pretty good at thinking and problem-solving.
Linear algebra as mentioned above is probably more likely to be specifically useful in applications: modeling, graphics, science and engineering settings, as typically relationships are too complicated to be understood effectively by anything besides a linear approximation. But many linear algebra courses are technique-based and rather cookbook, missing an opportunity to take advantage of good more abstract approaches.
It's psychosomatic. You need a lobotomy. I'll get a saw.
Not everybody needs to use a nondeterministic finite state machine every day, and not everybody needs to calculate the transitive closure of a sparse connectivity matrix every day, but these are (simple) examples of reasonably commonplace algorithms that you can't really understand without being able to do the maths.
As an even simpler example, you can't really use SQL effectively without understanding the maths behind a relational database. I know this for sure, because I keep coming across SQL applications that were clearly written by people with no understanding of the maths, and I get paid lots of money to fix them up properly.
Wouldn't you also say, that having heavy math chops allows you to see clearly when the line from problem to solution is non-optimal? Wouldn't you say that because you've grown your mathematical mind you can clearly see natural symmetry to problems and their data sets? Wouldn't you agree that the rigor of mathematical thinking is precisely the kind of mental ecology in which to couch programming problems? A football player might spend thousands of hours running through obstacle courses lined with tires... I've never seen a single tire on a football field, and yet they keep running them in training. Because those tires exercise the precise muscles those football players will need in the competition in the real world. Grow you math chops. Its worth it.
In undergrad (CS) I did more math than was required, and honours math at that. When I started grad school I was introduced to a transform we were using to analyze medical images. There's an article somewhere where I'm quoted as saying that some smart grad student is going to come along some day and improve the algorithm for calculating that transform so that it's actually practical. It turns out the smart grad student didn't come along, so I had to do it. That involved a lot of calculus, both continuous and discrete. Now I mostly develop new medical image processing techniques and analyze data, which involves fairly high level statistics. Statistics is all calculus and, when you get further on, calculus and linear algebra.
You say you want to be a game programmer? Here are some of the papers from SIGGRAPH this year. Take a read through some of them. This one might be a good place to start... most of the authors are from Pixar. How much math do you see? How much math do you understand? These are the algorithms you'll be working with by the time you graduate. Note that there isn't a lot of continuous calculus in these (but a lot of discrete!). Somebody has already done much of the hard work of discretizing it for you. That's not always the case.
You can probably get away with not learning any math and being a run of the mill code monkey. If you want to be good at what you do though, learn the math.
No, the point of a challenging degree program is to maintain academic standards. To be awarded a degree you need to have achieved a certain standard. If the sole aim was to limit the number of graduates in a program you would simply limit the enrolment. When we have been hiring IT staff one of the things we have looked for is a degree because this shows that they have some depth of knowledge beyond the basics. Sometimes the confidence that this brings can be very important for adapting to new situations.
The point of high-level math and physics classes is not because you "need" them in your job as a programmer. It's a way to limit how many CSE degrees are granted. I was told this straight-up by my college advisor ...
Then like some advisors he is a dumb-a**. I've been offered some pretty crappy advice and insight from advisors, don't take what they say too seriously.
You are basically getting into the trade school vs university argument. A trade school can produce as good a programmer as a university. The point of the university is to provide a more well rounded education so that a person has more options.
I too had some chemistry, physics and years of math that appeared to serve no purpose other than to "weed out" people from the program. However to my surprise I once had the opportunity to participate in a project that would port some chemistry software from mainframes to PCs. I would be interacting with world class polymer chemists. They did not expect me to be a chemist but they did expect me to be scientifically and mathematically literate. The general ed chemistry and physics and the years of math for computer science actually turned out to be useful.