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Mathematics Thesis Project

by kensavell
Tags: mathematics, project, thesis
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kensavell
#1
Mar26-05, 12:05 PM
P: 3
Fall Semester is my Thesis class - and I still have no idea what to do.

Course description is :

This is a capstone course which includes a major research paper and presentation as well as additional experiences designed to aid students in making the transition from college to graduate school or industry




So, I need a topic for my research paper, and I'm really coming up empty.

I like number theory & set theory, don't like statistics all that much. Not terribly interested in cryptology.


So I'm looking for ideas - Any and all are welcomed.. Just throw them out there.
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mathwonk
#2
Mar26-05, 04:19 PM
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coming up with the project topic is as important an exercise as carrying it out, so you should give it a good shot. since you like number theory, as yourself why? what theorems or topics in number have caught your attention?

are there theorems in number theory that you have wondered how to prove, that you might like to learn the proof of?

or are there theorems you know the proof of that you think you might be able to generalize?

i.e. are there statements that you find interesting that admit of variations?

leasrning the proof of a big theorem would ential learning some new and useful techniques, while generalizing the statement of a theorem would teach "problem finding", which some people consider a much more important and rare skill than "problem solving".

you might start by reviewing the main results and topics from number theory that you have studied.

the advantage to generating your own problwm, is not only the valus you obtain from the exercise, but also it will be more fun to work on it.


good luck
kensavell
#3
Mar26-05, 07:09 PM
P: 3
I like math, just ended up majoring in it by accident.

I have been dreading this thesis based class for nearly 3 years, and now that I'm on the proverbial doorstep, I need ideas.

If you could study anything, what would it be?

gnome
#4
Mar27-05, 04:21 PM
P: 1,046
Mathematics Thesis Project

Here's a thought. Try looking at math professors' websites. Many will have links to some of their publications, in which you may find some topics that you would like to explore.
mathwonk
#5
Mar27-05, 09:12 PM
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kensavell, i tried suggesting how to come up with some ideas. are you willing to try any of the suggestions? you need to have some faith in your own ideas. your ideas are as good as anyone else's.

for instance: an interval has 2 endpoints, a square has 4 sides, a cube has 6 faces. how many faces do you think a 4 dimensiopnal cube has? an n dimensional cube?

new discoveries are usually found by just following a pattern. but first you have to analyze the data you already have in a systematic way.

if you refuse to think about this challenge you are missing the opportunity to find your own vision.
Eratosthenes
#6
Mar29-05, 08:51 AM
P: 74
This gives ideas http://www.math.sunysb.edu/~tony/und_res_projects.html
kensavell
#7
Mar30-05, 05:08 AM
P: 3
Quote Quote by mathwonk
kensavell, i tried suggesting how to come up with some ideas. are you willing to try any of the suggestions? you need to have some faith in your own ideas. your ideas are as good as anyone else's.

for instance: an interval has 2 endpoints, a square has 4 sides, a cube has 6 faces. how many faces do you think a 4 dimensiopnal cube has? an n dimensional cube?

new discoveries are usually found by just following a pattern. but first you have to analyze the data you already have in a systematic way.

if you refuse to think about this challenge you are missing the opportunity to find your own vision.

I didn't mean to be disrespectful to your logical and appropriate recommendations, nor did I intend to suggest I ignored them. The school I attend part time (evening - non traditional student for the past 13 semesters) is very light when it comes to the math and sciences. The previous Thesis presentation I attended (There has only been one the past five years) was incredibly weak, having to do with hyberbolic geometry as it relates to MC Escher's work. It was not quite what I expected, and the professors websites are uninformitive. I've spoken with many of the professors on several occasions for guidence on narrowing down or selecting a topic, with little results. I am usually offered the statement "what are you interested in", or "That's not my area".

My intent was to get suggestions which may lead me to identify an area, topic which I may have missed or overlooked. Something akin to a brainstorming session which hopefully will plant the seeds of a project.


Your example given in the above post is an excellent idea, pretty much the concept I am looking for - ideas.

I do thank you and everyone else who regularly posts here for your generous time to help, I have lurked this forum in the past for help with projects, problems, exercises.
gnome
#8
Mar30-05, 10:47 AM
P: 1,046
Quote Quote by kensavell
... the professors websites are uninformitive ...
Broaden your horizons. You can go to the website of practically any university, find a link to the webpage of the math department, and from there link to the webpages of the faculty.

mathwonk is absolutely right -- you should choose a topic that interests you, but if nothing comes to mind I don't see anything wrong with looking at other people's publications for ideas. Presumably that's one of the reasons papers are published. Not that you should necessarily follow in someone else's footsteps, but you may be reminded of something that interested you in the past, or you may come across an idea that you want to take in a completely different direction, or you may find a topic that's completely new and exciting to you.


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