Math Project Ideas for Summer Scholarship | Field Theory Topic Search

[gazzo]

Hi,

I'm thinking of applying for a summer scholarship (in dec) from our maths department where we undergo study for 8 weeks with a project in maths. We have to have our proposed topics in by 7/Sept but I'm really stuck for ideas.

I'm a freshman at my university, and have taken/taking:
the usual calculus (not to Vector calculus though, that's next year),
a course on proof theory (principles of math),
discrete math (set theory/logic/simple combinatorics)
into. to applied and computational math (matlab/ODEs/various numerical methods).

I'm also auditing a senior course on Algebra (groups/rings/fields/extensions/all the juice bits),
and after the mid-semester break i'll be auditing a sophomore logic course and studying things like formal logic systems/decidability/completeness. One of my friends is a senior logic student and is an excellent mentor.

I want to do a small project involving field theory, but can't think of any topic that I could do. I think they expect it to be original, and my inability to choose a topic probably means that I don't know enough to be doing it in the first place. But I really want to get stuck in, and have been studying the topics involved.

A couple of people in my calculus class are doing it too, although I'm not sure what in (something with physics). I'm going to approach my Algebra lecturer but his next available office hours are really close to the deadline.

I think being tossed into the deep end, will at least, let me into the maths department and meet people who I wish to spend a lot more time with in the future years. But also, if I do badly it might stop me from being able to do it next summer, when I will be more mature mathematically.

 

[Eratosthenes]

Since nobody has replied here are a few unsolved problems. Now the chance of solving one is really slim I imagine but it might give you ideas. Mathworld has lots of other different things also.
http://mathworld.wolfram.com/topics/UnsolvedProblems.html

Here is one that I thought was interesting.
http://mathworld.wolfram.com/Union-ClosedSetsConjecture.html
You should be able to at least understand that problem. Although you might not know what this: http://mathworld.wolfram.com/Union-ClosedSet.html is, but now you know if you clicked that:) a lot of the unsolved problems are complicated, and require more math unfortunately. I think maybe if you present something in a new way that would work. Maybe provide a new proof to something that's always been proven the same way or something. Not really sure, just trying to give ideas.

I've never done any kind of research so maybe someone who has can comment and help you. Anyways take my advice with a grain of salt:) Goodluck.

 

[scholar]

I've already applied for the same scholarship. :D

Which papers are you taking this semester? Just wondering if you are in any of my classes. ;o

 

[neurocomp2003]

mmm you good at programming in c/C++ if so build a math engine...thats a preset to numerical engine.
Integer,Rational,Complex,Polynomial
Point,Vector,Matrix,Quaternion,Frustum,Camera, Coordinate System
Geometry: Lines, Circles, Planes, Polyhedrons, Meshes etc(torus)
Numerical: Linears systems, Eigensystems, FFTs

IF not...
[1]mmm something to do with math biology might be fun...predator prey dynamics using senior level dynamical systems...Viral Modelling...plant modelling
[2]FIeld theory applied to Quantum.
[3]Learning Cryptography(or i think field theory is also applied to number theory...number sieve something something)
[4]Classical Mechanics and large particle systems.