What are the Real-World Applications of Different Fields in Mathematics?

[SrVishi]

Hello, I am currently an undergrad mathematics major who is still unsure in exactly what field of mathematics to study post grad (if I get such an opportunity). All the subjects I have taken so far seem equally interesting, and I could see myself engaging in post grad study in each of the areas, but that is sadly not likely to happen. Despite me desiring to be a pure mathematician, as a way of narrowing things down I have decided to go into an area that would have the most applications and such (just to make my potential field seem a little more fulfilling). I thus ask if you all may answer these three questions if possible.
1) what are the major real-world applications of each of the najor math subjects?
2)While you can say that one subject has applications in one area, but how important are they really? I feel like they can sometimes be over exaggerated.
3)One thing that really interests me is artificial intelligence/consciousness and computer science in general. What math subjects would have the most important contributions to these areas?

I realize that a lot of mathematicians do it just for the math itself, but having the answers to these questions, would put the icing on the cake that I could choose to eat (lame analogy). Thanks in advance for Any response!

 

[axmls]

From what I understand, applied areas involving PDEs can be very useful. Many industries typically don't require their workers to prove many theorems in real analysis, but the problem solving abilities one learns in math (combined with a skill like programming) are useful in pretty much any industry you can think of. Especially in artificial intelligence.

Unfortunately I'm unable to provide concrete examples for say, what a graduate-level understanding of abstract algebra might contribute to industries.

I do know that the NSA (if you're into that sort of stuff) is the largest employer (besides universities) of mathematicians in the US. In particular, they like pure mathematicians. You know, cryptography and all that. I'm sure that involves a fair amount of number theory and algebra.

 

[mathman]

I doubt if you need to decide now. The typical program for a first year graduate student will consist of several (usually 4) courses each serving as an introduction to a particular branch of mathematics. While taking them you will get a better feel for what you want to go into.