Final Project

Goals and Objectives: You will research a topic related to the course that you are interested in and will communicate your expertise in a Maple document and poster presentation. This is to be an individual project (unless you make a good case to Dr. Sarah which explains why it should be a group project) and the topic must be pre-approved by Dr. Sarah. 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).

Your final project will be turned in as a Maple document, which will be put on the web, and a poster presentation. Your Maple document should follow the guidelines listed on You should create a poster that complements your Maple document.

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). Your poster should summarize the important points of your Maple document. Some laptops will be available to showcase Maple files. You are encouraged to bring in your own laptop and have that set up next to your poster. The purpose of the poster is to allow people to easily read aspects of your project without having to go to a computer. The Maple files will remain up on the web page for people to look at later. During the other session, you should briefly look over everyone's project, and choose three or four people (who are standing by their poster) to evaluate using the peer review form that will be given to you. A portion of your final project grade will be determined by the depth, quality and clarity of your peer reviews, which will be read by Dr. Sarah, but not by the project presenter. Each peer review must demonstrate that you read the project carefully.

The project will be graded based on the depth of the mathematics, the clarity of the explanations and poster presentation, and your peer review.

Sample Project Ideas (come see me in office hours for topic approval, references, or additional suggestions)

  • 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
  • Gershgorin Circle Theorem and Applications to Flutter of an Aircraft
  • Harvesting a Grizzly Bear Population
  • History of Linear Algebra
  • 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
  • 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