Math & Programming: Career Opportunities?

[nzashadow]

Hello everyone.

I am going to college and plan on majoring in mathematics because my enjoyment of it is very great.

Recently I have taken an interest in programming, and have been teaching myself python in my free time, and have been having fun with that lately.

My question is, how well do these subjects complement each other? Will I be able to find careers where these two expertises will coincide and make my life easier/more interesting? Or am I going to have two knowledge bases completely unrelated where I choose to make a career out of one, then the other becomes a hobby I do on my free time?

 

[micromass]

Hi nzashadow!

There is a lot of mathematical research that requires an ability to program. One obvious example is numerical methods where people research the most efficient/mistake-free way to program a certain algorithms.

In finite group theory and other kinds of abstract algebra, we often use languages such as GAP (=Groups Algorithms Programming) or Sage to solve computational problems such as "how many permutations can you perform on a Rubik's cube).

The four-colour theorem was recently also solved by programming and computers.

Differential equations also require a lot of programming as it's solutions can often only by approximated.

So a knowledge of programming can be very benificial in mathematics.

 

[nzashadow]

Thanks for the reply micromass :)

Teaching myself programming is proving difficult, with no programming experience already under my belt. Then again that's part of the fun.

It is good to know it won't be wasted if I continue, if I play my cards right lol

 

[chiro]

Hello everyone.

I am going to college and plan on majoring in mathematics because my enjoyment of it is very great.

Recently I have taken an interest in programming, and have been teaching myself python in my free time, and have been having fun with that lately.

My question is, how well do these subjects complement each other? Will I be able to find careers where these two expertises will coincide and make my life easier/more interesting? Or am I going to have two knowledge bases completely unrelated where I choose to make a career out of one, then the other becomes a hobby I do on my free time?

Hello nzashadow and welcome to the forums.

Programming and math have more in common than you think.

If you are thinking of areas where math is applied in programming, one obvious area that stands out is scientific computing. Any kind of simulation framework whether it is scientific (ie engineering platforms that do physical, biological, chemical simulations), or entertainment (video games, animation for games and movies) or something along those lines.

Also you need to understand that things like computation theory, information theory. algorithm theory and so on are all mathematical: they all use mathematical language (like set theory, logic and so on) to describe the current thinking of these fields.

I'm actually reading information theory stuff myself and I recently read a book called Algorithmic Information Theory by Gregory Chaitan and its a great book for exploring the link between computation, information theory and mathematics, and based on what you've said in your post I would recommend it if you want to see how computation and mathematics are related at a deep level.

If you look, you'll find a lot of material out there that talks about deep connections between standard math and computation.

One other thing that comes to mind is signal processing and artificial intelligence. Both of those are very math heavy and should keep you busy for a while (maybe even a lifetime!)

 

[Pyrrhus]

Optimization theory or Operations Research requires a lot of programming as well for algorithms to find the optimal solutions.

 

[nzashadow]

Thanks guys, this gives me confidence to continue doing hobbies that I enjoy, lol

I'm also just realized that programming has the potential to do the tedious computations for you, making life easier and letting me focus on more important things dealing with the problem.

For example, my girlfriend and a friend of mine complained to me about how they hate doing the quadratic equation, calling it tedious, which I can agree to. So then with a little thought, I whipped up a program to do the calculations necessary, thereby relieving the duty of doing it by hand, and doing all the work for you in less than a second.

Through that, however, I can see how it requires understanding of the material, and things I've never thought about before, I just may have to so I can write the program effectively. Also, the alternative is true, where attempting to write the code for the math, I improve my understanding of programming itself.

Even without the career opportunities, the two skillsets seem to complement each other perfectly as study tools going both ways, which is plenty motivation to continue going down both paths simultaneously.

It is a good plus to know this also gives me plenty of career options :D

Though this raises another question. Will teaching myself programming, with the assumption that I am an excellent self teacher, be acceptable? I mean to say, when I am applying for a job that requires both skillsets, will my employer need proof of my skill in programming via certification or college degree? ...or can I just show them my proficiency by including code I've written on my own in my resume?

 

[chiro]

I'm also just realized that programming has the potential to do the tedious computations for you, making life easier and letting me focus on more important things dealing with the problem.

This one fact alone has transformed many of the ways that math is taught. It takes the teaching in the direction of understanding concepts and more high level thinking than focusing on doing calculations and this is good for many reasons.

The consequence of this is that we can focus more on analyzing the interpretation of the results rather than devoting so much time to calculation, and its easy to see what benefits come about from this.

 

[nzashadow]

This one fact alone has transformed many of the ways that math is taught. It takes the teaching in the direction of understanding concepts and more high level thinking than focusing on doing calculations and this is good for many reasons.

The consequence of this is that we can focus more on analyzing the interpretation of the results rather than devoting so much time to calculation, and its easy to see what benefits come about from this.

So which is more important in the long run? Or should we be taught both approaches, or given the choice to choose which approach we will be taught...? This has been a subject I've been wondering about for a while... is it just up to personal preference of an individual... i.e. I hate doing calculations and number crunching by hand (especially repetitively, like homework). The appeal of math to me is all about understanding the concepts, and I take a lot of enjoyment out of doing proofs and working with generalizations, doing research maybe. However the other side of the coin may be just as important for different task, and may be more important in some cases, so people who enjoy doing that can work on those...

Also I want to reiterate this question: should I stick to teaching myself programming or will employers only consider me if I have my programming credentials on paper?

 

[jbunniii]

Though this raises another question. Will teaching myself programming, with the assumption that I am an excellent self teacher, be acceptable? I mean to say, when I am applying for a job that requires both skillsets, will my employer need proof of my skill in programming via certification or college degree? ...or can I just show them my proficiency by including code I've written on my own in my resume?

I can't speak for all employers, but I frequently interview people for software positions, and my advice would be that you should list a programming language on your resume if and only if you are comfortable answering questions about it and/or being asked to write some code in that language on a white board during the interview.

I have never asked an applicant where their knowledge of a language comes from; I don't care if it's self-taught or from a college course or what. I do ask them to write some simple routines for me, for example reversing a string or counting the number of "1" bits in the binary representation of an integer. These may sound brain-dead, but you would be surprised how many applicants can't do it.

I don't care about language-specific certifications; they're meaningless to me. We do require a bachelor's degree (master's preferred) in EE, CS, mathematics, or something closely related.

Don't put code on your resume; that's not what a resume is for. Don't submit code as part of your application unless you are asked to do so.

 

[chiro]

So which is more important in the long run? Or should we be taught both approaches, or given the choice to choose which approach we will be taught...?

The answer is that you need to be taught both. The difference though is that today we can focus more on the approach of interpretation and conceptual understanding of what a result really means, but you can't get away from doing mechanical exercises to compute things.

One reason is that the computation actually is one of the most important things to reinforce a conceptual understanding. Another reason is that you may get a situation where a standard formula doesn't work or can't be used, so you will have to start from first principles and generate some expression that you need. Another reason might be that your computer is down and you can't get immediate access to another computer or another computer with the right software on it. There are other reasons but these should get you thinking about them.

Every field does it. You do this in Accounting 101, just like you do it in Calculus 101 and the reasons are exactly the same for both subjects.

So I guess to answer your question, you need both approaches. If you didn't have the mechanical background you would be stuck in situations like I have said above and you didn't have the conceptual background, you would be fairly useless since you are just a monkey that pressed a button and had no idea what to make of that result.

 

[nzashadow]

Ah chiro, when you say it like that it seems like common sense, lol.

Thanks jbunniii. It's good to know there are some employers that don't care where the knowledge come from, I mean I'm sure you're not the only one who hires like that. Very enlightening.

 

[bcrowell]

You might enjoy majoring in computer science. A computer science degree is actually a math degree. Getting a computer science degree involves learning to program, but it's not mainly about learning to program, it's about the theory of computation.

 

[dimensionless]

The subject matters complement each other quite well. The combination is a good starting point for doing research. If you ever do research related to scientific computing, you will likely have access to new tools (nice computers) that researchers 10-15 years ago simply did not have. I don't, however, know the standard CS course curriculum so well.

Career wise, math is not so good. I would say the job market there, and also in scientific computing, is limited. Computer science, however, is among the least limited.