Math 5230 (Fall 2022) Final Project Information

Final Projects:
Final Project & Presentation Guidelines and Suggested Topics:

Instead of a Final Exam, we will have a final "project" of sorts. I would like everyone to select a topic somehow related to this class (I have suggestions listed below). This needs to be something that we didn't cover or at least didn't cover in detail.
  • Pick and topic and clear it with me (in person or via email).
  • Study your topic.
  • Create a handout. This should be at least one page front and back.
    • Your classmates are your audience. Build off of background from class.
    • Let us know where to go for further reading somewhere in your handout.
      [Cite any valuable resources - like websites and textbooks - that you found.]
    • You might want to give a brief historical blurb.
    • Do worked out examples help us understand your topic? If so, include a few.
    • Is your topic about a "big theorem"? Include its proof or a sketch of its proof.
  • During the final exam period, everyone will give a brief presentation of their topic. 8 people x 15 minutes = about 2 hrs. So 10-15 minutes a piece should be good. A little longer or shorter should be ok too.
  • The presentation could use slides (like tex or powerpoint) or just use the whiteboard and handout.
  • Several people can work on related topics. If so, you'll need to coordinate presentations and handouts. However, everyone should be creating their own unique handout (that work should be individual not group work).
If you want to use LaTeX slides, my Fall 2020 MAT 2110 page has some samples. Or Slides (.pdf) [Source: (.zip)] from a recent talk I gave.

Handout? Why not model after one of my monstrosities.
For example: Differential Algebra and Liouville's Theorem (.pdf) [Source: (.tex)] or Some differential Galois Theory (.pdf) [Source: (.tex)]

Topics taken so far:
  • Sam - Boundary Value Problems
  • Margaret - Singular Values and Singular Value Decomposition
  • Maddie - Markov Chains
  • Elizabeth - Probability / Markov Chains [somewhat accidental sort of duplicate]
  • Brian - Modular Arithmetic / Hill Cypher
  • Nic - Fourier Stuff
  • Wolfgang - Multivariable 2nd Derivative Test
  • David - Conditioning Numbers / Numerical Issues
Other suggested topics/ideas:
  • Tensor products of vector spaces and/or multilinear algebra
  • Hurwitz's Theorem, Quaternions, Octonions, or other weird algebras
  • Infinite dimensional duals - proving the dual space is bigger.
  • Quadratic and bilinear forms
  • Sylvester's law of inertia
  • More on functions of matrices
  • Systems of DEs or PDE stuff
  • Wronskians
  • Fourier stuff
  • Transforms like Laplace, Fouier, or other Integral Transforms
  • Various special orthogonal polynomials
  • What is a Jordan algebra? A Lie algebra?
  • Group representation theory/character theory
  • Ring module theory (What if our scalars aren't drawn from a field?)