Math 5230 (Fall 2024) Final Project Information

Final Projects:
Final Project & Presentation Guidelines:

Instead of a Final Exam, we will have a final "project" of sorts. Everyone should select a topic somehow related to this class (suggestions below). This should be something that we didn't cover or at least something we didn't cover in detail. A good choice might be some application. Maybe a topic you would teach in an introductory linear algebra course.
  • 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.
    • This should be typed up nicely. While I prefer LaTeX, other word processing software (like Word) is ok too.
    • Your classmates are your audience. (Use class background.)
    • Let us know where to go for further reading.
      [Cite any valuable resources - like websites and textbooks.]
    • You might want to give a brief historical blurb.
    • Would 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.
  • Create a presentation of your topic.
    • Record a 5 to 10 minute video of your topic.
    • Your presentation could use slides (like tex or powerpoint)
      or you could record yourself writing on a whiteboard or tablet.
  • Email me your handout and video (or links to these things)
    by Monday, December 9th at 5pm.

Sample Slides:
• My Fall 2020 MAT 2110 page has some sample slides.
• Fuchs' Problem Slides [Source: (.tex)]
• Infinite Talk Slides [Source: (.zip)]

Example Handouts:
• Why not model after one of my monstrosities? [Posted below.]
• Examples where I cite some reasources:
   → Differential Algebra and Liouville's Theorem [Source: (.tex)]
   → Some differential Galois Theory [Source: (.tex)]

Random Topic Ideas:
  • Singular Values and Singular Value Decomposition
  • Conditioning Numbers / Numerical Issues
  • Numerically Solving Linear Systems - Ex: Conjugate Gradient Method
  • Markov Chains
  • The Google Matrix
  • Block Matrices
  • Gershgorin Circles / Approximating Eigenvalues
  • Polar Decomposition of a Matrix
  • Random Matrices
  • Positive Matrices
  • Parseval's Identity and Bessel's Inequality
  • Fourier Series
  • Transforms like Laplace, Fouier, or other Integral Transforms
  • Orthogonal Polynomials - Ex: Hermite, Chebyshev, Laguerre, etc.
  • Hessenberg Matrices
  • Quadratic and bilinear forms
  • Sylvester's law of inertia
  • Matrix Norms and Spectral Radius
  • Multivariable 2nd Derivative Test
  • 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.
  • More on functions of matrices
  • A Matrix is Similar to its Transpose
  • Systems of DEs or PDE stuff
  • Wronskians
  • 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?)