Final Project Suggestions

Here are some suggestions for the final project and some references to get your started (I have additional paper references for you too.) You may also find other topics to work on, but then you must find your own references.

Topics Where Dr. Sarah Gives You References

  • Wavelets and Linear Algebra (one of the leading image compression methods)
    http://www.wired.com/wired/archive/3.05/geek.html Wavelet Image Compression
    An introduction to wavelets through linear algebra by Michael W. Frazier in the library
  • Matrices and Game Theory
    http://mathforum.org/library/drmath/view/52174.html "Yahtzee Probabilities and a State Matrix - what are the odds of rolling 5 of a kind within three rolls of the dice?
    http://www.miskatonic.org/ pd.html The prisoner's dilema
  • Rotation matrices, Gimbal lock, and the Space Shuttle
    http://mathforum.org/library/drmath/view/52904.html
  • Coding Theory and Matrices
  • Applications of vectors to graphic design problems.
  • Applications of higher dimensional vector spaces to computer learning in order to diagnose heart disease, breast cancer, and/or use sonar signals to distinguish rocks from mines.
  • Orthogonal Matrices, Gram Shmidt and applications to computer science
    Section 5.3 in book
  • Special Unitary Groups and their application to physics
  • Principal Axis Theorem in linear algebra and its applications
    http://mathforum.org/library/drmath/view/51974.html
  • Population dynamics and the Leslie matrix
    http://mathforum.org/library/drmath/view/52002.html and LAMP Module 6.3 Problem 5
  • Stationary vectors and applications
    http://mathforum.org/library/drmath/view/52003.html
  • Matrices, color specification and image coding.
  • Gershgorin Circle Theorem and applications to flutter of an aircraft. Olga Taussky-Todd's work
  • Applications of matrices to transformations of computer graphics
  • Applications of matrices to geometry
  • Applications of matrices to biology
  • Applications of matrices to graph theory
  • Applications of matrices to Economic Models
  • Applications of matrices to Forest Management
  • Applications of matrices to Equilibrium Temperature Distributions
  • Applications of matrices to Genetics
  • Applications of matrices to Cubic Spline Interpolation
  • Applications of matrices to Computed Tomography
  • Applications of matrices to Fractals
  • Least Squares Solutions and matrices LAMP Chapter 7 Module 3 and Section 5.4 and 5.5 in book
  • Loops and Spanning Trees and matrices LAMP Chapter 5 Module 4

    • Topics Where You Find Your Own References

  • What do paint companies use as a mixing set for paint mixing? Is this set linearly independent - are there two different ways of making the same color?
  • Additional applications of eigenvalues and eigenvectors to real life.
  • Additional exploration of some other application of matrices that we have discussed in class.
  • Computer programs for various matrix operations, Cramer's rule, or something else.
  • Other topics - I encourage you to be creative and find a topic that relates to linear algebra that you are interested in. Some examples: Matrices and Neural Networks, Rubik's Cubes, Contra Dancing, Missle Guidance System...