What Are Good Self-Directed Research Topics for a Math Master's Graduate?

[cjohnson7198]

I have a master's degree in math, and unable to work on my PhD at this time, I am continuing my studies on my own. I am looking for a project/question that I could work on at a masters level that might lead to original work. I would greatly appreciate any suggestions or direction.

 

[chiro]

I have a master's degree in math, and unable to work on my PhD at this time, I am continuing my studies on my own. I am looking for a project/question that I could work on at a masters level that might lead to original work. I would greatly appreciate any suggestions or direction.

Hey cjohnson7198 and welcome to the forums.

I think your question is a little vague for the reason that you haven't said what your masters is in, what your background is, what your interests/focii for the project is amongst other things.

It would help us if you gave us this information so that more specific suggestions can be made.

 

[micromass]

This is really not something you should discuss with strangers on the internet. You should contact some professors in whatever field interests you and see what they have to say.

 

[Stephen Tashi]

cjohnsion7198,

It isn't clear whether one of your objectives is to do research that would be eventually useful for Phd. work. If that is a goal then you need to investigate what topics are favored by specific professors at whatever universities you aspire to attend. You can be interested in a legitimate and important mathematical question and if you can't find a professor who is also interested and willing to direct your research, you won't get anywhere in a graduate program.

If you just want to do research for your own satisfaction, you should explain your interests.

If your main goal is to impress the mathematical community by original research, then I'm sure you can get hundreds of suggestions, each one reflecting the particular interests of the person who suggests it.

 

[cjohnson7198]

Sorry for the vague post. My masters emphasized algebraic topology. Since graduating, I have been studying continuum theory, dynamics, and algebra on my own. I have 6 hours in modern algebra and I am currently working through Hungerford Algebra.

I published my first paper studying symbolic dynamics on one dimensional dynamical systems. Basically, this is what I would like to do again. I am looking for interesting questions to pursue for my own pleasure that may lead to new results. In Algebra, I am interested in SO(n), symmetries of 3d bodies, dyhedral groups, etc. In continuum theory, I am interested in PseudoArc, PseudoCircle, etc. In dynamics, I am interested in symbolic dynamics, discrete systems, etc.

Basically, working on my own without a course or advisor, my biggest challenge has been direction. I would appreciate any suggestions.

 

[cjohnson7198]

Any suggestions?

 

[chiro]

Any suggestions?

What about looking at abstract symmetries on dynamical systems?

You mentioned SO(n) and dynamical systems, so I'm wondering if you could pursue some kind of path to look at more abstract symmetries of large classes of dynamical systems.

One approach might be to investigate connections with certain kinds of groups with toy classes of dynamical systems and then slowly include more classes to ascertain new group structures that describe those systems.

If you have very abstract group relationships for describing dynamical systems, then you can investigate dynamic systems from this perspective which will give you another tool to analyze through, and there are lots of published works on groups.

Anything that is interdisciplinary is a good suggestion IMO, because doing this will broaden your perspective and provide you with a lot more original ideas since a lot of people that become experts tend to sometimes have a very narrow focus which means that the interdisciplinary thing has a lot of potential for new original ideas.

Also interdisciplinary approaches are actually only a new recent thing in terms of things like setting up courses in universities, PhD programs and so on. It is starting to be encouraged for people to do interdisciplinary things like say mixing chemistry with math or statistics with biology and so on, and because this is a recent thing, it means plenty of opportunities for new researchers to find undiscovered ground.

 

[cjohnson7198]

Thanks very much! This is an excellent idea. I will start playing with this and see where it goes.