Linear Algebra Project - Exploring Applications of Linear Algebra
The goal of this project is to explore applications of linear algebra to advanced topics in mathematics or the sciences, and to practice communicating mathematics.

Topic
What are your interests for future studies? Choose an area of math or science that you find interesting. Your goal is to see where and how linear algebra plays a role in your topic.

Work
There are several sections and chapters in our book that we have not covered, that include applications of linear algebra. You should choose a section to read carefully and teach the an example to the rest of the class.

Possible topics include:
• 1.6 - Applications of Linear Systems (Chemical Equations and Network Flows)
• 1.10 - Linear Models in Business, Science, and Engineering (Diet, Electrical Networks and Difference Equations)
• 4.6 - Applications to Difference Equations
• 4.9 - Applications to Markov Chains
• Chapter 10 - More Markov Chains (Google Page Rank, Baseball Statistics, etc.)
Note: We already covered sections 2.6 and 2.7 that cover other applications. There are several other sections throughout the book that provide other applications. Any of those are fair game, although they may require background we have not yet covered in this class.

Your textbook is a useful reference, but is not your only reference. Your chapter will be the focus of your work, but I encourage you to look at other sources, such as books or research papers. The arxiv is a great source for browsing math research papers.

Write-up
When you have found an interesting application, you should prepare a short presentation (around 10 minutes). Your discussion should include the following:
• Discuss any necessary background from your topic
• Where do matrices play a role in the topic?
• How are matrix invariants useful in interpreting the topic?
• Give a sample calculation and interpret its significance
You should make sure every member of your group has a chance to speak. Slides are encouraged but not required. You will want to include mathematical content, but you should also prioritize clarity of presentation.

Logistics
Your project is due Friday, May 4. You should work in a small group (~3 students per group). Your grade will be determined based on quality of mathematics (10 points), and quality of presentation (5 points). You will also receive a peer grade (5 points).