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Undergraduate Mathematics Research

  • #1
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Main Question or Discussion Point

If you can bear with me reading this thread, I'm looking for comments and general direction on where to go next.

So in an ambitious attempt to hurl myself head-on into the world of mathematics, I managed to get involved in doing undergraduate research at my university. This is despite the fact that I haven't taken calculus yet.

I met with a professor who specializes in mathematical modeling, told him my background (which is mostly work experience in computer science, and one semester of calculus many years ago). I chose him as my first choice of mentors because the idea of mathematical modeling appeals to my interest in math, namely, "interdisciplinary mathematics" or what I think of as the "Mathematics of everything."

We went over my situation and background, which is that I have more work experience than education at the moment, especially in regards to my major (mathematics). The situation in puts me in is that we can use my life and work experience to generate problems and topics for research, though it's possible that not all the resulting problems (from a mathematical standpoint) will be things that I personally can solve.

This puts me on the other side of students that may have lots of math training, but no work experience, so they might not be able to generate the kinds of problems that someone with work experience could. (Though they have a better chance at solving them) Also, there may be problems that I would be able to directly solve using pre-calculus mathematics, so those are the ones I have to look for at the moment.

The plan of action is for me to establish a few general general directions that we could go in (perhaps related to computer science or other topics I am interested in or familiar with) and then find a few problems in each that could be addressed. This would probably have to start out in a non-mathematical language since I do not really have the vocabulary yet to put them in mathematical terms.

One of my main interests is of course physics, and if you're into physics, (or even if you're not) you are most likely into Astronomy and Cosmology. So, I met with my stellar astronomy and cosmology teacher. The class he teaches is for non-science majors and not math heavy. As far as research, he said, most of the current problems are of course going to require advanced mathematics. The question I asked him was "Well, is there just any raw data out there that can be looked at?"

Ah, we were getting somewhere. He recommended http://www.sdss.org/" [Broken]

As for what to *do* with the data, I am not sure yet. Keep in mind when I say that I am using pre-calculus mathematics, I 1) did have some calculus background and 2) am not opposed to learning new math by way of doing the research, which in a way is kind of the point. Does anybody have suggestions for a direction here?

Information technology:

I have worked in information technology for quite awhile. Though I wasn't involved deeply in computer science and didn't do much programming, I'm sure there are a lot of problems that can be somehow modeled mathematically. The general ideas floating around in my head are:

1) something having to do with networking, routing, load-balancing, data transfer

2) something dealing with data storage or increased computing power over time. Does "[URL [Broken] Law[/URL] still hold? Is there some kind of data that is tracking this or some other topic related to it?

Tangent to I.T.:

I spent a lot of time working in call centers. Call center managers are obsessed with particular numbers like "time to answer" and "resolution time" and "talk time." There are also routing tables that determine who gets what called, based on strengths of the various analysts answering the phones. i.e. someone who is more skilled in taking Excel calls gets a higher rating in the Excel queue and therefore will get more excel calls. Can I find something here to look at mathematically?

Musical Acoustics:

My last major was Music Technology and I've spent a lot of time playing and teaching music (classical guitar). Though I've always been aware of the relationship of mathematics to music (on various levels) I never have explored it very deeply. In our library I even stumbled across a book called "Computational mechanics of the classical guitar." Unfortunately I don't recognize any of the math in it with my background.

Yeah, I'm in slightly over my head, but can you learn anything otherwise?

Any guidance would be appreciated. Thanks,

-Dave KA
 
Last edited by a moderator:

Answers and Replies

  • #2
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776
That bad?
 
  • #3
AlephZero
Science Advisor
Homework Helper
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I would summarise your OP as:

I want to do undergrad level math research, but I don't know any undergrad level math, and I don't know what topic I want to research.

That bad?
Well, it's not "good", that's for sure.
 
  • #4
1,047
776
I would summarise your OP as:

I want to do undergrad level math research, but I don't know any undergrad level math, and I don't know what topic I want to research.



Well, it's not "good", that's for sure.
That is about the least helpful, least constructive response I could have imagined.

I presented a number of ideas and asked for feedback. If you have a constructive response or criticism to my ideas, for better or worse, then fine. They may be stupid ideas, but they are ideas.

-DaveKA
 
  • #5
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3,280
Well, I can see why AlephZero's comment can seem unhelpful, but I actually think he's right.

You seem to be very enthousiastic about research, and that's really a good thing. But it seems that you don't know much of mathematics yet. That way, you can't really research a problem, you will spend most of your time learning things you'll need. And that really isn't the point of undergraduate research.
You said you don't know any calculus, so any research in analysis, statistics, physics,... wouldn't work... Maybe there are other topics that you could be engaged in. But then we need to know: what courses have you already taken? What kind of mathematics do you like? Have you any experience with programming?

If you know some programming and abstract algebra, then maybe you can do some research in GAP (a programming language for algebra).
If you know some discrete mathematics, then maybe there are some accessible fields there...

All in all, things are not looking great. Maybe it's best if you learn some more mathematics, and try research next year...
 
  • #6
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Well, I can see why AlephZero's comment can seem unhelpful, but I actually think he's right.
It's ok to be right, even frank. Snarky responses just to take a jab at someone is another story. That was really my issue with AlephZero. He seems like he has made great contributions here but that was not one of them.

You seem to be very enthousiastic about research, and that's really a good thing. But it seems that you don't know much of mathematics yet. That way, you can't really research a problem, you will spend most of your time learning things you'll need. And that really isn't the point of undergraduate research.
You said you don't know any calculus, so any research in analysis, statistics, physics,... wouldn't work... Maybe there are other topics that you could be engaged in. But then we need to know: what courses have you already taken? What kind of mathematics do you like? Have you any experience with programming?
I do have calculus, but it's a bit buried, and I can re-learn it as I go. I have programming experience in a few versions of C (also buried.) Basically I can pick up (and just as easily forget!) programming languages and environments without much trouble.

I do have two semesters of pre-calculus physics. Currently I'm enrolled in a Stellar Astronomy and Cosmology.

If you know some programming and abstract algebra, then maybe you can do some research in GAP (a programming language for algebra).
I'll look into that actually.

If you know some discrete mathematics, then maybe there are some accessible fields there...

All in all, things are not looking great. Maybe it's best if you learn some more mathematics, and try research next year...
Oh I know, it's just silly isn't it?

The reason I'm looking at mathematical modeling is that I am thinking that there must be some model somewhere that can be developed with little or no calculus (which I am relearning on my own to some degree.

Also, as I mentioned, one of my contributions this year might be simply to suggest topics, so while I might have to wait until next year to do any research myself, I'm wondering if any of the ideas I have are reasonable things to look into. It's just that I have been so estranged from academia I'm not sure how to even begin to present some of them.

I am also talking to my advisor about all of the above, as well as friends of mine in the various disciplines. But I thought PF would be a good network to tap. Anything even remotely helpful is..helpful. Thank you for your reply.

-Dave KA
 
  • #7
22,097
3,280
That's actually very good: try to research the topics now, see what courses you need and try the undergraduate research when you know all the stuff...

As for your suggestions, here's what I think of them:

nformation technology:

I have worked in information technology for quite awhile. Though I wasn't involved deeply in computer science and didn't do much programming, I'm sure there are a lot of problems that can be somehow modeled mathematically. The general ideas floating around in my head are:

1) something having to do with networking, routing, load-balancing, data transfer

2) something dealing with data storage or increased computing power over time. Does Moore's Law still hold? Is there some kind of data that is tracking this or some other topic related to it?
I guess that this isn't really mathematics. If you want to do this, then I think that you are better of with some computer science...

Tangent to I.T.:

I spent a lot of time working in call centers. Call center managers are obsessed with particular numbers like "time to answer" and "resolution time" and "talk time." There are also routing tables that determine who gets what called, based on strengths of the various analysts answering the phones. i.e. someone who is more skilled in taking Excel calls gets a higher rating in the Excel queue and therefore will get more excel calls. Can I find something here to look at mathematically?
This actually looks like a promessing subject. Of course, you'll probably need a lot of probability theory and statistics for this. And if you really want to do some concrete stuff, then you'll going to do some programming as well... But statistics will probably be a must...

Musical Acoustics:

My last major was Music Technology and I've spent a lot of time playing and teaching music (classical guitar). Though I've always been aware of the relationship of mathematics to music (on various levels) I never have explored it very deeply. In our library I even stumbled across a book called "Computational mechanics of the classical guitar." Unfortunately I don't recognize any of the math in it with my background.
Hmmm, this sounds like a really complicated subject. The book you mention is probably very advanced. There are other topics in music, but they probably require some knowledge in abstract algebra. Only take this topic if your really interested...
 
  • #8
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776
I guess that this isn't really mathematics. If you want to do this, then I think that you are better of with some computer science...
Well I guess my aim was to be interdisciplinary and develop or propose some sort of model. Since my post I've tuned this further and I'm wondering if I can look at Moore's law in light of organic components or quantum computing and see how that effects things. Heavy stuff I guess.

This actually looks like a promessing subject. Of course, you'll probably need a lot of probability theory and statistics for this. And if you really want to do some concrete stuff, then you'll going to do some programming as well... But statistics will probably be a must...
That is kind of what I figured.

Hmmm, this sounds like a really complicated subject. The book you mention is probably very advanced. There are other topics in music, but they probably require some knowledge in abstract algebra. Only take this topic if your really interested...
Thanks again for your feedback!

-DaveKA
 
  • #9
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776
Update if anyone cares.

The professor I've been meeting with hasn't given up on me yet, so it's not hopeless. :)

The strategy is to find topics first, then see what math I need. This is probably not a typical undergraduate approach to learning math, but my situation is not typical. In the meantime I can continue to suggest topics for others, while working towards my own. The call center problems look most helpful.

What I like is that I can independently (outside of classes, with a little guidance) learn the math I need, based on a practical need rather than just slogging through courses the normal way.
 

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