Practicality of Abstract Algebra

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  • #1
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well the title itself seems to be a paradox, but,
What are some applications of abstract algebra (like groups, fields, and rings)? Apparently this determines the symmetry of particles in physics but what are some real-life, money-making application of group theory? (Yes, I money is one of my biggest concerns so I am also considering mathematical finance or acturial science. If I were to pursue pure math, number theory, analysis are still applicable to industry. But how about abstract algebra?
 

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  • #2
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Well, first of all, abstract algebra is applicable to number theory and analysis, so, by transitivity...
An obvious application would be modern cryptography, which is largely the domain of algebraic number theory.
 
  • #3
mathwonk
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Even so simple a concept as vector addition has application to reading i believe they are called cardiograms, in medicine. One of my physician friends showed me this and because I knew vector addition i was immediately able to read the otherwise confusing looking picture of a heart beating that he showed me. It has been over 40 years so i may recall the context poorly, but it was quite striking.
 
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I am glad to hear that, but seems like all math-related jobs (quantitative analyst, computer science engineer) have to sit in front of a monitor for 12+ hours a day. But I have a medical condition. I cannot sit on a chair more than two hours. Or I feel really dizzy when I get up and sometimes I almost passed out.

Is there any math-related job that does not involve much programming work?
 
  • #5
chiro
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I am glad to hear that, but seems like all math-related jobs (quantitative analyst, computer science engineer) have to sit in front of a monitor for 12+ hours a day. But I have a medical condition. I cannot sit on a chair more than two hours. Or I feel really dizzy when I get up and sometimes I almost passed out.

Is there any math-related job that does not involve much programming work?
A lot of these kind of jobs require computer work and not just programmers.

Maybe you could think about teaching.

Also if you could put with technical work for a short period of time (say 5+ years) then you could move to a more managerial or business role.

Given your condition, I don't know who would employ you in a technical capacity with your condition unfortunately :(
 
  • #6
phyzguy
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well the title itself seems to be a paradox, but,
What are some applications of abstract algebra (like groups, fields, and rings)? Apparently this determines the symmetry of particles in physics but what are some real-life, money-making application of group theory? (Yes, I money is one of my biggest concerns so I am also considering mathematical finance or acturial science. If I were to pursue pure math, number theory, analysis are still applicable to industry. But how about abstract algebra?
There's a reason why they call it abstract......
 
  • #7
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one day I was making LaTeX document for three hours. When I got up, everything went blurry and I had to go to bed right away.

anyhow so my career options are
-actuary : hope this does not involve many programming hours
-engineering : mostly field work I hope
are there any other options that involve less programming hours?
 
  • #8
Vanadium 50
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Parallel parking. It only works because translations and rotations do not commute.
 
  • #9
AlephZero
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Parallel parking. It only works because translations and rotations do not commute.
Great answer. Whether you think abstract algebra is "practical" or not is a function of YOU, not a function of the algebra.

If you can use it to get insights into something that nobody has thought of before, nobody's going to stop you.
 
  • #10
phyzguy
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one day I was making LaTeX document for three hours. When I got up, everything went blurry and I had to go to bed right away.
Have you tried getting up and walking around for a few minutes every 15-30 minutes? The work doesn't have to be non-stop for hours. It's also possible to work standing up if this helps. I'm afraid that it is hard to escape using a computer these days.
 
  • #11
HallsofIvy
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I once read a math article on applying tensor analysis to parallel parking. It showed that if you can make arbitrarily small angles with your steering tires and arbitrarily small "back and forth" movements, you can park in a space an arbitrarily small amount longer than your vehicle!
 
  • #12
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(Yes, I money is one of my biggest concerns so I am also considering mathematical finance or acturial science. If I were to pursue pure math, number theory, analysis are still applicable to industry. But how about abstract algebra?
If you're interested in the class then take it. If your only reason for taking that class is to have practicality then I wouldn't take it. I took an entire year sequence (3 quarters) of Abstract Algebra. The class itself was incredible but it was a lot of work so be ready.
 
  • #13
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-actuary : hope this does not involve many programming hours
Actuaries work at computers all day. The exceptions are those actuaries who are important enough to be in meetings all day. You won't start out being one of those.
 
  • #14
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I once read a math article on applying tensor analysis to parallel parking. It showed that if you can make arbitrarily small angles with your steering tires and arbitrarily small "back and forth" movements, you can park in a space an arbitrarily small amount longer than your vehicle!
frickin' awesome :)
 
  • #15
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How proficient should I be if I apply for a quant or mathematical finance-related jobs? C++ keeps appearing on job posts. So like, are quants as proficient as computer science majors in C++?

Also, are all mathematical fiance jobs expected to sit in front of a compuer for 12+hours?
 
Last edited:
  • #16
chiro
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How proficient should I be if I apply for a quant or mathematical finance-related jobs? C++ keeps appearing on job posts. So like, are quants as proficient as computer science majors in C++?

Also, are all mathematical fiance jobs expected to sit in front of a compuer for 12+hours?
I don't know about the math side, but on the programming side, you need to have some real experience with complex projects that include production code.

A degree is not enough preparation unless you have actually worked in the environment described above in conjunction with whatever over training you had had.

If you haven't done this, I don't think you will stand a chance come technical interview time.
 
  • #17
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Apparently this determines the symmetry of particles in physics but what are some real-life, money-making application of group theory?
1) sigma algebras used a lot in mathematical finance

2) Also a lot of this stuff is just good for you. There aren't that many direct practical applications to lifting weights or doing push-ups, but it will help you when you have to split logs or move sofas.
 
  • #18
atyy
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1) sigma algebras used a lot in mathematical finance

2) Also a lot of this stuff is just good for you. There aren't that many direct practical applications to lifting weights or doing push-ups, but it will help you when you have to split logs or move sofas.
But a sigma-algebra isn't an "abstract algebra" algebra, is it? Isn't it just a formality to say, well, we shan't assign a probability to getting the Cantor set as an experimental outcome?
 
  • #19
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How proficient should I be if I apply for a quant or mathematical finance-related jobs? C++ keeps appearing on job posts. So like, are quants as proficient as computer science majors in C++?
Depends on the job, but it can range from basic literacy in C++ to people that can write compilers in their sleep. If you aren't a C++ expert, you'll need to find something else that you are an expert on.

Also, are all mathematical fiance jobs expected to sit in front of a compuer for 12+hours?
Same as the answer for actuaries.
 

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