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October 12th, 2018, 07:37 AM   #1
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Any ideas for career paths?

Hello all,

I'm in my third year of a masters degree in mathematics. My plan A is to try to get onto a PhD in something pure and go from there into academia. As such, I am only taking pure modules in my third and fourth years (With a couple of exceptions of applied modules). However , I've struggled to identify a plan B that I can get behind. I've tried searching career prospects on google and looked around , but it seems like the suggestions are tailored to those with finance and economics flavored mathematics degrees ...

I guess the only use for pure guys that I'm aware of is in education and research (high school up to university level etc). My question is , what other areas of work would I be employable for as a holder of a (mostly) pure degree? It seems as though all the options are unrealistic unless I take a second degree (not happening).

In case you are wondering , here is a break down of what will probably be my final degree:
Statistics: an introductory module in the first year , nothing more.
Discrete: Some very basic game theory , a second year module in algorithms , some graph theory this year.
Applied: A classical mechanics and applied vector calculus module , both in year two. A pretty detailed course on PDE's this year.
Pure: The standard stuff in years one and two. This year , Galois theory , hilbert spaces , algebraic topology , complex analysis and (probably) group theory dissertation. Year four will be some basic hyperbolic geometry , geometric group theory and semi group theory , differential geometry and a dissertation on who knows what.

As you can see , lots of pure but not a great idea of what to do with it besides academia. All advice appreciated.

My regards,

Magnitude.
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October 12th, 2018, 08:44 AM   #2
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The single best advice I can give you is to learn some programming skills. Even if (I'd actually say ESPECIALLY if) you are going into pure math. If you are unable to do some sort of coding, it has a significant negative impact on your ability to find modern jobs.
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October 12th, 2018, 09:32 AM   #3
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It's harder to think of a career you wouldn't be able to go into for having specialized in pure rather than applied or stats. For most jobs, the importance of a degree isn't the specific knowledge you've gained, but more the general skills you've developed.

Regarding the PhD application, I've very recently gone through the same process you're about to - I'm also from the UK, finished a masters in pure this year, and have just started a PhD in pure. So if you have any questions, I'd be more than happy to help.
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October 12th, 2018, 02:27 PM   #4
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The single best advice I can give you is to learn some programming skills. Even if (I'd actually say ESPECIALLY if) you are going into pure math. If you are unable to do some sort of coding, it has a significant negative impact on your ability to find modern jobs.
I would go further than this. I would suggest you become a truly excellent coder. I worked with a fair number of pure math guys and the two that were truly useful were the ones that take a problem, reduce it to first principles, and code up software that solved it from that and derivations thereon.

Both of their coding was a bit remedial by today's standards, FORTRANish, but they could get the job done.
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October 14th, 2018, 04:39 AM   #5
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thanks for the replies. You've convinced me that coding is a skill I'll need (right now , the best I have is a distant acquaintance with python alone). Romsek , could you elaborate ? i.e what coding languages would be useful , or any advice on how to go about doing this?
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October 14th, 2018, 05:17 AM   #6
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thanks for the replies. You've convinced me that coding is a skill I'll need (right now , the best I have is a distant acquaintance with python alone). Romsek , could you elaborate ? i.e what coding languages would be useful , or any advice on how to go about doing this?
C++ is a good start for an all-round sort of introduction to programming. You can begin with basic procedural programs and then try something object orientated. Then try work with something higher level like R.

To actually 'start', I strongly recommend you come up with a project of your own and then try to implement it. Use c++ to collect/generate data for some phenomena maybe, then do use the data and do some analysis in R. The possibilities here are endless, but the point is to expose yourself to different languages, compilers, programming styles etc.
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October 14th, 2018, 05:59 AM   #7
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I might suggest that you also consider learning assembler language - specifically IBM mainframe assembler.

a) There are still jobs available in that field and (I suspect) relatively few people pursuing programming in that specific field.

b) Assembler language has a direct one to one correspondence to machine language; other languages are derivatives and are generally somewhat removed from machine language. Even if you don't end up pursuing a career as an assembler programmer, you will have a much better understanding of what is actually going on at the lowest level.

I spent almost 30 years as a developer of mainframe systems software, all written in assembler language. There are still large corporations, banks and government agencies all over the world running software that I coded (and sometimes designed). It is not high on the radar any more, but organizations with a need for high security and reliability will continue to rely on mainframes for the foreseeable future.
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October 14th, 2018, 06:54 AM   #8
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. . . and (I suspect) relatively few people pursuing programming in that specific field.
Then who would maintain software written in assembler?
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October 14th, 2018, 08:36 AM   #9
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Then who would maintain software written in assembler?
I didn't say 'none,' I said relatively few. But...

A few years ago, after the company I had worked for for many years was bought out and the new ownership was not to my liking, we parted ways by mutual agreement. I then briefly worked for another leading mainframe software company in New Jersey; they offered me a permanent job, but at that point I couldn't absolutely guarantee I would move up there so the offer was withdrawn.

Anyway, when I first interviewed with them I mentioned that I was 64 years old. The response was: "Oh, you'll be one of the youngest programmers on our staff." There are a lot of old people in that particular industry.

The industry must go on; the programmers will die off or retire. That's why I suggested that it's a good opportunity for a talented young programmer. There will be jobs.
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October 14th, 2018, 07:39 PM   #10
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Originally Posted by RichardJ View Post
I might suggest that you also consider learning assembler language - specifically IBM mainframe assembler.

a) There are still jobs available in that field and (I suspect) relatively few people pursuing programming in that specific field.

b) Assembler language has a direct one to one correspondence to machine language; other languages are derivatives and are generally somewhat removed from machine language. Even if you don't end up pursuing a career as an assembler programmer, you will have a much better understanding of what is actually going on at the lowest level.

I spent almost 30 years as a developer of mainframe systems software, all written in assembler language. There are still large corporations, banks and government agencies all over the world running software that I coded (and sometimes designed). It is not high on the radar any more, but organizations with a need for high security and reliability will continue to rely on mainframes for the foreseeable future.
I've always been curious about this. I think most engineering undergraduates these days don't have any direct exposure to assembler language, maybe just a mention. In fact when I learned about it my prof. said it would be the last time he'll be including it in his course (not too long ago).

While I see your point, I don't think the suggestion is suitable given the OP's current situation.
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