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 writing and 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
Once you have an area of focus, begin looking for examples of linear algebra at work. You might start with looking for basic examples of matrices and systems of equations, but you should be able to find examples with a little more meat. Try to find how the strength of the linear algebra tools we have learned in class provide useful information about the topic you are researching.

For instance, in the discussion of applications from knot theory we saw that the determinants of various matrices related to a knot could tell us how to distinguish one knot from another knot. In your topic, perhaps you have found an example of a matrix related to some other object. Does it mean something to multiply it by another such matrix? Does the determinant tell you something about the object? Perhaps the rank has significance, or the eigenspaces are meaningful. Your goal is to report how tools of linear algebra give an interpretation of calculations in your topic.

Your textbook is a useful reference, but should not be your only reference. You might look at some of the 'applications' sections in the text to find a topic. You should also read from 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 write up the details in a short paper. 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
Your paper should be 2-3 pages including an introduction and conclusion. You will want to include mathematical content, but you should also use correct grammar and punctuation, and write in coherent english.

LaTeX
When writing mathematics, we often need to use mathematical symbols in our exposition. For this reason, most mathematicians prefer to use LaTeX to write their math. For this project it is strongly recommended that you write your paper in LaTeX. If you have not used LaTeX before, a great resource for learning the basics is this wikibook. There are lots of other great resources available online (some listed below), so if you don't like this one, you can google and find a wide variety.

Logistics
Your project is due Friday, May 1, by 5 pm. You can work with a partner if you prefer. If you do, be sure to list both names on your paper. Your paper should be typed (preferably using LaTeX), and submitted by email. Your grade will be determined based on quality of mathematics (10 points), quality of exposition (5 points), and quality of presentation (5 points).

Other resources
Here are some other resources about working with LaTeX:
• Cloud-based LaTeX computing is available at www.writelatex.com and www.sharelatex.com.
• DeTeXify can help you find a symbol you need to use.
• TeX Stack Exchange is a Q&A site with descriptions of some of the more complicated TeXing techniques.
• The Comprehensive LaTeX symbols list.
• Symbol Search
• A general introduction
• Another brief introduction