Final Project: Linear Algebra Connections

You may work alone or with one other person. Topics are first-come-first served with a maximum of 2 people per topic and they are approved as a Message to me on ASULearn.

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. Your project must exhibit effort that is appropriate for your background and major. Your project will be graded based on the linear algebra connections, the clarity and creativity.

    A presentation and a visual with the following components (the visual can be a combination of printed pages taped to the wall, your laptop, physical models, etc):
  1. Review and Summary of the Relationship of Linear Algebra to Your Topic (equivalent of at most 3-pages)
    Include relevant definitions, theorems, and examples in order to review the major concepts from class and homework that relate to your topic as you explain the connections. We will divide up the class into two research sessions. During your session, you must stand by your visuals to present your work and answer questions. During the other session, you will talk to others about their projects and fill out peer review sheets. If you work with another person, they will be in the other session so you should be prepared to present the entire project.
  2. Printed Annotated Bibliography
    Most projects should use different types of sources, including scholarly references and library sources. Submit a separate annotated bibliography of all of the sources you used in your project, with annotations explaining what content in the reference relates to your topic, how you used each reference, where any pictures or code came from, etc. Use as many pages as you need for the bibliography and annotations.
  3. Peer review and self-evaluation that you will fill out that day - you'll need to bring paper with you to do so.
All components must be products that you create yourself in your own words, and that look professional and flow well.

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).

Sample Project Ideas

  • Applications of higher dimensional vector spaces to computer learning in order to diagnose heart disease, breast cancer, and the use or 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
  • Conway's Game of Life
  • Cramer's Rule
  • Computer Programming with One Aspect of Linear Algebra
  • Diagonalization of inertial tensors to find the principle axes
  • Eigenfaces and Facial Recognition
  • The Eight Queens Problem
  • Financial banking and eigenvectors
  • Gershgorin Circle Theorem and Applications to Flutter of an Aircraft
  • Golden Mean and Matrices
  • Google's PageRank Algorithm
  • Harvesting a Grizzly Bear Population
  • Hammer Juggling, Rotational Instability, and Eigenvalues
  • History of a Topic in Linear Algebra
  • How Does the NFL Rate the Passing Ability of Quarterbacks?
  • Image Edge Detection and Linear Algebra
  • Least Squares Solutions and Matrices
  • Loops and Spanning Trees and Matrices
  • Lights Out Game and Linear Algebra
  • Linear Algebra and Archaeology
  • Linear Algebra and Graphic Design
  • Linear Programming
  • Mixing Calculus and Linear Algebra: Is There a Good Reason for This?
  • Linear Algebra involved in Nash Equilibriums
  • 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
  • Shear Matrix Applications
  • Singular Value Decomposition in Image Compression
  • Special Unitary Groups
  • Strassen Algorithm
  • Support Vector Classifier or Machine (SVM)