In what areas of programming is mathematics actively used?

Question

Programming

Quite a lot of questions were asked on the toaster, is it possible to become a good programmer without knowing mathematics? The answer is obvious: it all depends on the field of activity. Actually, my question is: in what areas of programming is a serious mathematical apparatus used (except for games)?
The fact is that I'm trying to find myself in programming, so to speak, my field. I know for sure that mobile applications and the web, as well as games, are not of interest at all. But I would like the tasks to be closely related to mathematics. I did not have any achievements in mathematics at school (I studied at 4-5), and also now, at the university, but there is a desire to learn. For some reason, matan is especially attractive, although it is clear that it is rarely used in programming.

Answer 1

Offhand:
1) image processing, computer graphics and vision - geometry and algebra
2) search - graph theory
3) artificial intelligence - mathematical statistics, terver, game theory
4) modeling, robotics - this is where matan, numerical methods, control theory
AND in vain you are so about matan, just have not yet reached the logical application of this subject. The crown of its use is the control theory, which in turn is applicable to the programming of complex mechanical controllers (turbines of nuclear power plants, generators of thermal power plants)

Answer 2

Who said that matan is rarely used in programming? If you move a little further than business card sites, then it will be hard without a matan.
Any digital signal processing is full of hellish obscenity. There is a lot of mathematics and economics in the development of high-frequency trading systems and financial analysis systems. Glonass / GPS monitoring systems for the development of additional features also require non-acidic knowledge of mathematics and geometry.
In general, it is easier to choose an area of ​​interest and look for a use in it.

Answer 3

In general, you have everything painted here. However, I will add a little with my humble opinion:
The basics of arithmetic and Boolean logic are needed everywhere. What are the basics - the deeper the better.
Now matan. @newross is right - in cybernetics, the one that deals with signal processing is full of swearing. Of course, it is not hellish, but it will take a lot to differentiate, integrate and decompose in the Fourier, as well as build correlations and autocorrelations. Moreover, the signals are everywhere, around - the bluetooth radio signal, GSM, FM, sound, video codecs, images - all these are also signals. discrete or continuous. And of course, applied science - wherever matan and automation of calculations are required - there is a lot of work for a programmer-mathematician.
Fuan here is used much less frequently. In general, it is rarely used anywhere, usually it is some kind of exotic, where serious physical models are required - any aviation, space, hydro-simulation. In general, mostly applied programming, that is, you will have to not only program, but understand the mat. parts.
One more thing about analyzes - due to the finiteness of computer resources, there are constant transitions from smooth and infinite to discrete and finite through banal restrictions, limits, integrations and splits. So without discrete mathematics, there is nothing to do at all in science-intensive areas. A discreet, in fact, is programming. Some of its parts have crept into all areas - from media to data transmission channels and their protection. Although it is relatively simple, there are huge gaps in it. And of course, it rarely comes to homomorphisms, but all sorts of laws of large numbers are used to the fullest. Well, here you have graph theory, and number theory, and combinatorics, and logic. Why, algebra, with its 2 + 2, is discrete mathematics. In general, as he said - in fact, computer science is an application to the discrete.
Everything else is used exactly when it comes down to it, except for the very basics of structures and spaces. Well, from transformations, arithmetic and analysis. Everything else is the most common application. Here mathematicians need to calculate something quickly, then applied programmers appear.

Answer 4

in the brain

Answer 5

in the processing of exchange data, a matan is very necessary, and, as everyone here has already said, in the development of AI, too, a matan, well, and so in the economy (all sorts of banking systems). the first thing that came to mind.