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Better question: what areas aren't?

chubot 10y ago
Good question... Calculus? Of course it has a long history with computing, but I would say that probably less than 10% of programmers outside scientific fields use any calculus. There is calculus in machine learning but I think that counts as less than 10% of programmers, and it will probably become its own specialty separate from programming in the coming decades (to some extent it is already) From what I know of topology, you use logic and algebra as tools to learn about it, just as you use logic and algebra in computing. But you probably wouldn't use topology to say anything about computing. Number theory is relevant to crypto, but I would be hard pressed to say it is practical for programmers in general. You could probably have a pretty long and successful career in programming without knowing basic things like what a prime factorization is.
- santaclaus 10y ago
  > Good question... Calculus? Of course it has a long history with computing, but I would say that probably less than 10% of programmers outside scientific fields use any calculus. Calculus is pretty useful in computer graphics and vision, if you want to understand what is going on there are integrals left and right. Audio processing and finance too.
- blt 10y ago
  Topology is useful in robotics and control to define the set of achievable states in a system and their connectivity.
  - chubot 10y ago
    On further reflection, it does seem pretty hard to find a subfield of math which isn't relevant to SOME subfield of computing. I was going to say non-Euclidean geometry, but that's very relevant if you're doing mapping software. But that's a different thing than saying that a particular subfield of math is "practical to programmers". I would say that programmers need the foundations of logic, algebra, and probability, and a bit of calculus (less than I was taught). And THEN they can learn topology, number theory, non-Euclidean geometry or advanced calculus if they need to, for their specific domain. You never know what you're going to end up doing 10 years down the road. And of course that seems to be what happens in a good undergrad CS education, so apparently people better than us have thought about it :) Indeed college is supposed to give you the ability to learn how to learn, when new things come up, as they always do in programming. Quantum computing is basically a ton of linear algebra as far as I can tell.
- brlewis 10y ago
  Most programmers can forget the specifics of calculus, but the conceptual ideas of integration and differentiation are important. Many problems are better solved when you transform a series of changes into a whole (integration) and/or vice versa (differentiation).
- Grue3 10y ago
  Calculus (yes, continuous calculus) is pretty much the most important area of math you need to know to program well. In my books, if one can't integrate/differentiate a formula, they shouldn't be allowed to program a computer. Because that's how you end up with algorithms that take way too long to finish because the author couldn't bother to estimate how much computation the algorithm needs to perform at large inputs.

Good question... Calculus? Of course it has a long history with computing, but I would say that probably less than 10% of programmers outside scientific fields use any calculus. There is calculus in machine learning but I think that counts as less than 10% of programmers, and it will probably become its own specialty separate from programming in the coming decades (to some extent it is already) From what I know of topology, you use logic and algebra as tools to learn about it, just as you use logic and algebra in computing. But you probably wouldn't use topology to say anything about computing. Number theory is relevant to crypto, but I would be hard pressed to say it is practical for programmers in general. You could probably have a pretty long and successful career in programming without knowing basic things like what a prime factorization is.

santaclaus 10y ago
> Good question... Calculus? Of course it has a long history with computing, but I would say that probably less than 10% of programmers outside scientific fields use any calculus. Calculus is pretty useful in computer graphics and vision, if you want to understand what is going on there are integrals left and right. Audio processing and finance too.
blt 10y ago
Topology is useful in robotics and control to define the set of achievable states in a system and their connectivity.
- chubot 10y ago
  On further reflection, it does seem pretty hard to find a subfield of math which isn't relevant to SOME subfield of computing. I was going to say non-Euclidean geometry, but that's very relevant if you're doing mapping software. But that's a different thing than saying that a particular subfield of math is "practical to programmers". I would say that programmers need the foundations of logic, algebra, and probability, and a bit of calculus (less than I was taught). And THEN they can learn topology, number theory, non-Euclidean geometry or advanced calculus if they need to, for their specific domain. You never know what you're going to end up doing 10 years down the road. And of course that seems to be what happens in a good undergrad CS education, so apparently people better than us have thought about it :) Indeed college is supposed to give you the ability to learn how to learn, when new things come up, as they always do in programming. Quantum computing is basically a ton of linear algebra as far as I can tell.
brlewis 10y ago
Most programmers can forget the specifics of calculus, but the conceptual ideas of integration and differentiation are important. Many problems are better solved when you transform a series of changes into a whole (integration) and/or vice versa (differentiation).
Grue3 10y ago
Calculus (yes, continuous calculus) is pretty much the most important area of math you need to know to program well. In my books, if one can't integrate/differentiate a formula, they shouldn't be allowed to program a computer. Because that's how you end up with algorithms that take way too long to finish because the author couldn't bother to estimate how much computation the algorithm needs to perform at large inputs.