Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Math topics useful for computer science/programming

matheducators.stackexchange.com

Post reply on HN
Print view View original

31–40 of 69 posts

Re: Math topics useful for computer science/programming

#31

Post by j2kun »

Betelgeuse90 wrote: post #19
j2kun wrote: post #2

I 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 rec…

I largely agree with your sentiments. However, you should keep in mind that these lists are intended as an answer to "What Math should we teach freshmen undergrads?", not an answer to "What Math do all the CS-people need to know?". The latter is naturally a very small subset of Math, the 'logicish' type. I do STRONGLY agree with you that we should help students figure out the areas that they find interesting, and let…

But the question is one and the same in this instance: they're asking what should be taught in "the" math class for a CS degree. If that doesn't contain the math that all CS-people need to know, then what should it contain?

The OP describes universal algebra and term rewriting, which is what I claim is the logicish type that is not as crucial as, say, linear algebra if you want to find widely applicable mathematics for CS/programming.

Re: Math topics useful for computer science/programming

#32

Post by j2kun »

nmrm wrote: post #30
ThrustVectoring wrote: post #16

Earlier quoted context omitted.

I have a couple simple ones off the top of my head: - You write a recursive program the same way you write an inductive proof - Abstract algebra and category theory are likely relevant, especially for metaprogramming. My math education hasn't included this, so I can't say much more. - Linear algebra is just ridiculously important - Statistics for machine learning. Also for figuring out how to combine data in a meanin…

> Abstract algebra and category theory are likely relevant, especially for metaprogramming. In general, the whole "oh yeah CS people should know some category theory and abstract algebra" is pretty hilarious. First, it's a bit like saying "oh yeah CS people need to know the undegraduate basics and also the generalization that most mathematicians don't encounter until a couple years into grad school." Second, most peo…

More simply (but hard to appreciate without going through semesters of work): know that structure-preserving mappings are the important parts.

Re: Math topics useful for computer science/programming

#33

Post by nraynaud »

j2kun wrote: post #2

I 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 rec…

I agree, I have had to learn Newton's methode for differential equations (for simulation), I've had to use logic and an automatic prover (for system validation), I've had to do some complexity analysis (for everything), I've had to play with linear applications, matrices and all the stuff around 3D, I've had to dig into geographical projection equations for another job (in GIS). I'm currently toying with computational geometry. I think what is important is some kind of math to understand how those people write (which far from obvious), and then random stuff to learn to switch.

Re: Math topics useful for computer science/programming

#35

Post by j2kun »

alok-g wrote: post #34

What would be a good writeup for understanding term-rewriting? (My current background level: I understand most of what OP has listed in "actually useful" and "can run into", and "automata theory" from the third list.)

I wouldn't recommend it as being as important as the OP claims, but if you must: http://www21.in.tum.de/~nipkow/TRaAT/

Re: Math topics useful for computer science/programming

#36

Post by Bahamut »

userbinator wrote: post #9

In 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.

Calculus gives you some of the intuition for figuring out a good big O bound for the computing time of an algorithm.

Re: Math topics useful for computer science/programming

#37

Post by RogerL »

I went to an engineering University. Besides having a wide variety of math required (3 semesters of Calc, 1 semester of either stats or probability, 1 semester of either linear algebra or matrices), we also had to take 3 semesters of physics, and 2 of chemistry. Most of us (those not just looking for a piece of paper) went considerable deeper in at least one area.

No, you don't need to understand organic chemistry to write a CRUD app. But, you don't need university to write a CRUD app.

I think I received an excellent education that prepared me for about any job out there. And, I've done it. I've done cancer statistics for the NIH. I've worked in avionics and simulation. Well, blah blah, no one cares about my resume, I'll just say I couldn't have done any of it without the education I received. I haven't done financial quant stuff, as an example, but how could I without the math background? Or how could I program a controller in a factory without understanding PID (done that)? How can I get a piece of that neat drone project (done that)? Hey, that computer vision stuff looks interesting, all I need to know is ...derivatives, statistics (done that too).

For most of us, university is the last and/or best chance to really understand how the world works. For that you need quite a bit of math and science. Another example. We have a voluntary Arduino robotics workshop going on at work, coupled with 3D printing. Naturally, people are excited, and have all kinds of ideas. But, how do you execute on that if you don't understand how to design an op amp circuit, or filter data with something more sophisticated than a moving average? Robotics spans a number of fields, and to actually produce something more than a gimmick requires a lot of knowledge. Knowledge that you can pretty easily pick up in University, but knowledge you mostly just long for as you have to rush home at 5:30 to pick up the kids and make dinner.

I guess this is a cranky rant from an old guy. But I hear about University programs that are nothing more than Java voc ed systems and I despair. $100K in debt to learn something most anyone on here could just pick up on their own. You don't need university for that stuff.

Re: Math topics useful for computer science/programming

#38

Post by shoki »

nmrm wrote: post #30
ThrustVectoring wrote: post #16

Earlier quoted context omitted.

I have a couple simple ones off the top of my head: - You write a recursive program the same way you write an inductive proof - Abstract algebra and category theory are likely relevant, especially for metaprogramming. My math education hasn't included this, so I can't say much more. - Linear algebra is just ridiculously important - Statistics for machine learning. Also for figuring out how to combine data in a meanin…

> Abstract algebra and category theory are likely relevant, especially for metaprogramming. In general, the whole "oh yeah CS people should know some category theory and abstract algebra" is pretty hilarious. First, it's a bit like saying "oh yeah CS people need to know the undegraduate basics and also the generalization that most mathematicians don't encounter until a couple years into grad school." Second, most peo…

Well, frankly you can get along not knowing the "Gang of Four" design patterns and write Java. By the same token, you don't need to know about iterables and comprehensions to write Python, smart pointers to write C++, Graph theory to use a Graph database, macros to write LISP, etc.

By analogy, you don't need to know abstract algebra and category theory to write Haskell. But as in the other cases, knowing helps.

Re: Math topics useful for computer science/programming

#40

Post by nmrm »

shoki wrote: post #38
nmrm wrote: post #30

Earlier quoted context omitted.

> Abstract algebra and category theory are likely relevant, especially for metaprogramming. In general, the whole "oh yeah CS people should know some category theory and abstract algebra" is pretty hilarious. First, it's a bit like saying "oh yeah CS people need to know the undegraduate basics and also the generalization that most mathematicians don't encounter until a couple years into grad school." Second, most peo…

Well, frankly you can get along not knowing the "Gang of Four" design patterns and write Java. By the same token, you don't need to know about iterables and comprehensions to write Python, smart pointers to write C++, Graph theory to use a Graph database, macros to write LISP, etc. By analogy, you don't need to know abstract algebra and category theory to write Haskell. But as in the other cases, knowing helps .

I think you misunderstood my criticism.

"Different sorts of mappings" is NOT synonymous with "category theory". Not even close. Heck, Euclid knew about "different sorts of mappings".

Most everything in Gamma et al is arguably useful for everyday programming in Java. Maybe 5-10 pages of MacLane is useful for everyday programming in functional languages.

Unless by "Category Theory" you mean "5-10 pages of MacLane", Category Theory -- on the whole -- is a horrendously inefficient way of teaching about "different sorts of mappings useful in functional programming."

Unless you want to use functional programming as an environment for doing pure mathematics, there's no reason to actually study actual Category Theory.

Post reply on HN