### 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:
- an abstract presented orally in 1-3 minutes
on our last day of class
- 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.
- peer review and
self-evaluation that you will fill out that day - you'll need to bring
paper with you to do so.
- 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)