Final Project

Goals and Objectives: You will research a topic related to the course that you are interested in and will communicate your expertise. The presentations are modeled after what happens at research conferences, Appalachian's student research day, and science fairs. You project will be graded based on the depth of your linear algebra connections, and the clarity and creativity of:
  1. an abstract presented orally in 1-3 minutes on our last day of class
  2. a presentation and a visual (the visual can be printed paper taped to the wall, a laptop, posterboard, etc). We will divide up the class into two presentation sessions. During your presentation session, you must stand by your visual to answer questions (and your answers must demonstrate expertise of your topic). During the other session, you will talk to others about their projects and fill out peer review sheets. If you work on your project with someone else, you will each be in different presentation sessions.
  3. peer review and self-evaluation that you will fill out that day - you'll need to bring paper with you to do so.
  4. an annotated reference list (to turn in). The annotations are brief comments about how you used each reference in your project. Most topics should utilize journal articles or books from the library or Dr. Sarah's office.

You may work with one other person and the topic must be pre-approved by Dr. Sarah as an ASULearn message. Your project must exhibit effort that is appropriate for your background and major.

Your research may take the form of topics in the book that we did not cover, further examination of something we did, or something else related to linear algebra. I encourage you to be creative and find a topic that relates to linear algebra that you are interested in. I am happy to give you some suggestions of topics and/or references (see below for some sample ideas).

Poster Sessions We will divide up the class into two poster sessions. During your poster session, you must stand by your poster to answer questions (and your answers must demonstrate expertise of your topic). During the other session, you will talk to others about their projects and fill out peer review sheets. If you work on your project with someone else, you will each be in different poster sessions.

Sample Project Ideas From Previous Semesters

  • Applications of higher dimensional vector spaces to computer learning in order to diagnose heart disease, breast cancer, and use sonar signals to distinguish rocks from mines.
  • Applications of Matrices to...
          Geometry,       Biology,       Contra Dancing,       Computed Tomography,       Cubic Spline Interpolation,
          Economic Models,       Equilibrium Temperature Distributions,       Forest Management,       Fractals,
          Game Theory,       Genetics,       or something else
  • Cramer's Rule
  • Determinants and the Eight Queens Problem
  • Financial banking and eigenvectors
  • Gershgorin Circle Theorem and Applications to Flutter of an Aircraft
  • Golden Mean and Matrices
  • Harvesting a Grizzly Bear Population
  • History of a Topic in Linear Algebra (must be a different topic than the extra credit topic, if you completed that project)
  • How Does the NFL Rate the Passing Ability of Quarterbacks?
  • Least Squares Solutions and Matrices
  • Loops and Spanning Trees and Matrices
  • Linear Algebra and Archaeology
  • Linear Algebra and Graphic Design
  • Linear Programming
  • Mixing Calculus and Linear Algebra: Is There a Good Reason for This?
  • Neural Networks and Linear Algebra
  • NP-Complete Solutions in Linear Algebra using 3-SAT
  • Orthogonal Matrices and Gram Shmidt
  • Principal Axis Theorem
  • Rotation matrices, Gimbal lock, and the Space Shuttle
  • Singular Value Decomposition in Image Compression
  • Special Unitary Groups
  • Support Vector Classifier or Machine (SVM)