Math-Heavy Computer Science

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Hello PF, I'm a high school student in a math and science program. I'm currently planning on doing a double major in math and computer science, and I have a couple questions. Firstly, are there areas of computer science that heavily use math and require originality? I understand that most likely I will end up in a computer science job, but I would like to work in an area that heavily draws on mathematics in its problem solving. I'm aware of theoretical computer science, which would seem to be great for me, but are there significant job opportunities in industry for it?

And also, I'm beginning to be concerned that I may not be as good at math as I thought I was. I'm getting to the "wall" I've heard about where I'm starting to have to study to get A's in math (currently in accelerated trig), and the fact that I seemed to hit this wall so early makes me worry that eventually my intellect just won't be good enough to succeed in higher mathematics. As I am only a high school student, I'm unsure if this is the case. I've read a lot about various areas of math, but I don't know enough to make sense of most of it. I am having a good time reading through Pinter's A Book of Abstract Algebra though.

Thanks, and any advice is appreciated.
 

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  • #2
FactChecker
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You might want to look into Operations Research. It combines a lot of math and computer science for solving optimization problems. The techniques include computer simulation, statistics, linear and nonlinear programming (optimization of linear and nonlinear problems).

Another area that might interest you is control laws. It is often in the aerospace engineering department, which would require a lot of other aero subjects. Control law design includes very interesting mathematics.
 
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QuantumQuest
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And also, I'm beginning to be concerned that I may not be as good at math as I thought I was.
As a piece of advice, don't hasten to conclude if you're good or not at math. It's quite a bit early. University math is a whole different world from high school math. You definitely build a strong base studying hard at high school, but critical thinking is what is needed for university. I highly recommend taking a look at Keith Devlin's course "Introduction to Mathematical Thinking".

Firstly, are there areas of computer science that heavily use math and require originality?
Computer Science is all about algorithms, so you see the profound relation to math from the outset. Now, if you mean dealing heavily with math all the time, Theoretical CS is your thing. About job opportunities, it depends on what is the market in your country or where you intend to work and how good can you get. The second is obviously even more important, so you have to roll up your sleeves and work for it.
 
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As a piece of advice, don't hasten to conclude if you're good or not at math. It's quite a bit early. University math is a whole different world from high school math. You definitely build a strong base studying hard at high school, but critical thinking is what is needed for university. I highly recommend taking a look at Keith Devlin's course "Introduction to Mathematical Thinking".



Computer Science is all about algorithms, so you see the profound relation to math from the outset. Now, if you mean dealing heavily with math all the time, Theoretical CS is your thing. About job opportunities, it depends on what is the market in your country or where you intend to work and how good can you get. The second is obviously even more important, so you have to roll up your sleeves and work for it.
You might want to look into Operations Research. It combines a lot of math and computer science for solving optimization problems. The techniques include computer simulation, statistics, linear and nonlinear programming (optimization of linear and nonlinear problems).

Another area that might interest you is control laws. It is often in the aerospace engineering department, which would require a lot of other aero subjects. Control law design includes very interesting mathematics.
Thank both of you very much! I'll definitely look into those subjects and that course. For theoretical computer science, I guess what I'd like to know is if companies like Google or Amazon would have any interest in theoretical computer science. Is there any market for it in the United States?
 
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Theoretical computer scientists are employed in nearly every industry. If you want an example of unexpected job opportunities, I know one who got a "temporary" job at a library just out of college, and got taken on permanently and promoted due to how useful his problem solving skills were.
 
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Theoretical computer scientists are employed in nearly every industry. If you want an example of unexpected job opportunities, I know one who got a "temporary" job at a library just out of college, and got taken on permanently and promoted due to how useful his problem solving skills were.
Wow, I definitely wasn't expecting that! Thanks very much, now I'm really excited about this!
 
  • #7
You might want to look into Operations Research. It combines a lot of math and computer science for solving optimization problems. The techniques include computer simulation, statistics, linear and nonlinear programming (optimization of linear and nonlinear problems).

Another area that might interest you is control laws. It is often in the aerospace engineering department, which would require a lot of other aero subjects. Control law design includes very interesting mathematics.
Is control law design part of Industrial engineering, I kind of would like to work in air port.
 
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Another possibility is scientific computing or numerical analysis but I am not sure what requirement would be for that. I know numerical analysis uses algorithm like euler algorithm and coding to solve problem in differential equations and linear algebra but most of these jobs seems to be for the government.
 
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Thank both of you very much! I'll definitely look into those subjects and that course. For theoretical computer science, I guess what I'd like to know is if companies like Google or Amazon would have any interest in theoretical computer science. Is there any market for it in the United States?
I suggest you have a look at The Art of Computer Programming by Donald Knuth -- https://www-cs-faculty.stanford.edu/~knuth/taocp.html

Bill Gates has said that if you can get through that, he has a job for you.

I second the suggestion of @FactChecker regarding Operations Research, beginning with basic SIMPLEX pivoting on a single tableau, progressing through sensitivity analysis, etc., and continuing with branching out into decision support , multivariant linear and non-linear regression analysis, in support of logistics, actuarial work, materials science, etc..

Whichever area you settle into, please be aware that you'll likely have to endure some tedium and drudgery before, during, and even after, getting into the swing of things.

Even so, much of the time, solving problems is very satisfying.
 
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Is control law design part of Industrial engineering, I kind of would like to work in air port.
Control law design is not a normal part of IE. It is usually in aero engineering or electrical engineering. It will be a huge growth area as robots and drones become more popular. It is always nice to be in a subject area that has a lot of jobs.
 
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  • #11
StatGuy2000
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To the OP:

I second @FactChecker's suggestion on Operations Research, as an ideal combination of math and computer science to solve many optimization problems.

I also agree with @QuantumQuest in that the essence of computer science is about algorithms, which in essence involves mathematical reasoning, so a combined background in math and computer science will strengthen the level of reasoning necessary to be a good programmer in a variety of industries.

I would only add that there are opportunities in areas like cryptography (the study of creating secure codes) which combines strong background in math with computer science, as well as "data science", which combines computer science and statistics.
 
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StatGuy2000
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Another possibility is scientific computing or numerical analysis but I am not sure what requirement would be for that. I know numerical analysis uses algorithm like euler algorithm and coding to solve problem in differential equations and linear algebra but most of these jobs seems to be for the government.
Scientific computing or numerical analysis is an area open to those with a combined background in both math and computer science (or in physics and computer science).

As far as jobs are concerned, numerical analysis methods like solving differential equations are widely used in finance, engineering design, and data science, among many other areas.
 
  • #13
DrClaude
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The OP hasn't been here in 3 years.

@homeylova223, if you have questions, start you own thread instead of reviving an old one.

Thread closed.
 

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