Math topics useful for computer science/programming
matheducators.stackexchange.com
Math topics useful for computer science/programming
1–10 of 69 posts
Re: Math topics useful for computer science/programming
#2I never liked these kinds of lists. The people who ask the question always seem to be under- or overwhelmed by the answer (programmers don't need any math?! theoretical computer scientists need all math?!). And the people who answer are almost always skewed toward whatever it is they do.
Even the top-voted response to the OP is obviously biased toward the logic flavor of computer science, with awkwardly scattered recommendations for non-logicish topics that are far more useful for all flavors of computer science ("perhaps even eigenvalues," seriously?!).
These lists even ignore the deeper question being asked: how do you figure out what sort of mathematics you need for the things you're interested in? Not all computer scientists (and programmers) like the same things in computer science and programming. It's much more advisable to figure out what you like before you go around trying to learn all the math there is to learn related to CS, and then ask about what math topics are related to that.
Re: Math topics useful for computer science/programming
#3This does not seem very informed, starting from the false premise in the question up to the random concepts listed in the answers.
Calculus is actually important for Computer Science, it's actually important for everything, it's where you learn how to handle the exponential function and the natural logarithm, how to do approximations and bounds, how to handle infinite series, etc., and those things then appear all over the place, unlike most things listed it's something that you can expect to encounter almost regardless of what domain you are interested in.
I mean, the guy asks what should replace Calculus and then the first answer includes "Asymptotics", "basic limits, sequences and series", so actually calculus. In general I cringe a little every time I hear Computer Science people should focus on "discrete math", because without tools from analysis you can only solve the most trivial discrete problems. And yes, calculus by itself is hardly ever applicable in CS, yet you still have to learn it, tough luck. In general what is not stressed enough I think is that applying math is hard and you need to learn a lot of it before you have enough tools to tackle problems anywhere close to real-world complexity.
The top answer also lists random concepts. I am learning probability currently, for applications in machine learning. "Discrete spaces, Bayes theorem and expected values" you can learn in a day, "Markovs, Chebyshev and Chernoff inequalities" are mostly only useful for further theoretical work, so is "the law of large numbers". What will really be useful will depend a lot on the applications, if you are a theoretical computer scientist, mastery of generating functions and transforms will be useful, and it's one of those instances where discrete problems are solved via tools from calculus/analysis. For machine learning you need to know everything about the normal distribution by heart, and this means you have to know everything about the exponential function by heart, so again back to calculus. Notions from information theory are useful, but of course none of the ones he listed. The comment "This is a must for modern programmers." sounds just comic.
Re: Math topics useful for computer science/programming
#4This does not seem very informed, starting from the false premise in the question up to the random concepts listed in the answers. Calculus is actually important for Computer Science, it's actually important for everything, it's where you learn how to handle the exponential function and the natural logarithm, how to do approximations and bounds, how to handle infinite series, etc., and those things then appear all ov…
> Calculus is actually important for Computer Science, it's actually important for everything, it's where you learn how to handle the exponential function and the natural logarithm, how to do approximations and bounds, how to handle infinite series, etc., and those things then appear all over the place,
It's still interesting to think about which branches of math are actually applicable to programming itself.
People tend to talk about programming and math as very strongly related, and of course there is the obvious relationship that "some computer programs do particular kinds of math" like you're talking about here.
But there is no (intuitive) overlap between writing, say, a web application and doing algebraic or calculus computation on paper. However, there are things like:
- Set theory underpinning relational databases
- Typed lambda calculus underpinning functional programming
I'd be interested in other examples like this.
Re: Math topics useful for computer science/programming
#5"Many students struggle with the idea of recursion..."
I still remember one of the worst bugs I'd ever introduced (in terms of pain to me). I was maybe 2-3 years out of my bachelors, and I thought recursion was so nifty that I'd use it where ever I could. I was coding C++, at the time. And, I got the dreaded 2am call after all of the production servers went down hard. Like terminate and corrupt data hard.
Lesson learned: it's good to know recursion, but it's also good to know maximum stack sizes.
Re: Math topics useful for computer science/programming
#6This does not seem very informed, starting from the false premise in the question up to the random concepts listed in the answers. Calculus is actually important for Computer Science, it's actually important for everything, it's where you learn how to handle the exponential function and the natural logarithm, how to do approximations and bounds, how to handle infinite series, etc., and those things then appear all ov…
>Calculus is actually important for Computer Science, it's actually important for everything
This.
If you take a look at the MIT course "Mathematics for Computer Science"[1] you'll see that the only prerequisite for learning the math for cs is ... calculus!
[1]http://ocw.mit.edu/courses/electrical-engineering-and-comput...
Re: Math topics useful for computer science/programming
#7This does not seem very informed, starting from the false premise in the question up to the random concepts listed in the answers. Calculus is actually important for Computer Science, it's actually important for everything, it's where you learn how to handle the exponential function and the natural logarithm, how to do approximations and bounds, how to handle infinite series, etc., and those things then appear all ov…
Also I'm not sure how you can mention information theory in the context of programming and not mention PCM or the Shannon-Nyquist sampling theorem...
Re: Math topics useful for computer science/programming
#8This does not seem very informed, starting from the false premise in the question up to the random concepts listed in the answers. Calculus is actually important for Computer Science, it's actually important for everything, it's where you learn how to handle the exponential function and the natural logarithm, how to do approximations and bounds, how to handle infinite series, etc., and those things then appear all ov…
>Calculus is actually important for Computer Science, it's actually important for everything This. If you take a look at the MIT course "Mathematics for Computer Science"[1] you'll see that the only prerequisite for learning the math for cs is ... calculus! [1] http://ocw.mit.edu/courses/electrical-engineering-and-comput...
I was a TA for that course last semester. I think the actual reason calculus is a prerequisite is just so that students will have some mathematical maturity beforehand. We didn't really teach any concepts that actually used calculus (that I remember).
That said, I totally agree that calculus is good to know for a CS student.
Re: Math topics useful for computer science/programming
#9In my experience, I've seen a lot of students entering CS not comfortable with even basic arithmetic and algebra, despite it not being mentioned in any of the linked responses.
As for calculus, I think its importance is overrated - unless you are specifically doing some numerical computation that requires it.
Re: Math topics useful for computer science/programming
#10Earlier quoted context omitted.
>Calculus is actually important for Computer Science, it's actually important for everything This. If you take a look at the MIT course "Mathematics for Computer Science"[1] you'll see that the only prerequisite for learning the math for cs is ... calculus! [1] http://ocw.mit.edu/courses/electrical-engineering-and-comput...
I was a TA for that course last semester. I think the actual reason calculus is a prerequisite is just so that students will have some mathematical maturity beforehand. We didn't really teach any concepts that actually used calculus (that I remember). That said, I totally agree that calculus is good to know for a CS student.
Oh, you do use calculus, at least in the notes, actually touching on the topics I mentioned, so it's a good illustration. For example in the chapters about generating functions and on sums and asymptotics:
http://ocw.mit.edu/courses/electrical-engineering-and-comput...
http://ocw.mit.edu/courses/electrical-engineering-and-comput...