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.
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):
All components must be
products that you create yourself in your own words, and that look
professional and flow well.
- 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.
- 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
- Peer review and
self-evaluation that you will fill out that day - you'll need to bring
paper with you to do so.
- For every person in the other poster session:
1) Name of the person you are reviewing
2) Their topic
3) List a couple of positive aspects of the project.
4) List a few things that you wished had been done with the project.
5) Invent a significant question about the project.
6) Ask your question and write down the person's answer.
- Self Evaluation:
1) Your name
2) For your own project, list the aspects that went well.
3) What could have been improved?
4) List some things that you wished you had done with your project.
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...
Cubic Spline Interpolation,
Equilibrium Temperature Distributions,
Genetics, or something else
Conway's Game of Life
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
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
Support Vector Classifier or Machine (SVM)