Final Project

Objective

The goal of this project is to give you chance to explore a topic of your interest that has some connection to linear algebra, and to share what you learn with your peers. It can be something purely mathematical, or it can involve an application of linear algebra to an area of your choice.

Description

You’ll form groups of 2-4 and collectively choose a topic you want to work on. Your group and topic will need to be approved by me: one person in each proposed group should send me an email letting me know who you’ll be working with and what you’ll be working on, by 11:59pm on the third Tuesday.

For the last day of class, you’ll prepare a handout and a digital presentation about your topic.

• The handout should be one typewritten page (front and back). It should give an introduction to the topic, and incorporate a detailed and substantial proof and/or example. It need not be entirely original (ie, you don’t need to prove a brand new theorem about linear algebra), but it should be fully explained in your own words. If you can incorporate the results of some computer calculations, that would be awesome! The handout should also include a list of works that you referenced, so that someone who wants to learn more about your topic knows where to start.

  Bring some copies of your handout to the presentation (at least one for me, and then a few more in case any of your peers would like to take one).

• The presentation should convey the main ideas of your topic and some insightful examples. It should take about 10 minutes. We’ll use the big data visualization wall in the library, and you can format the presentation however you like (slides, a giant digital poster, …). Pictures and videos are always nice, if at all possible, but remember that, if you don’t make it yourself, you have to attribute it to whoever did. All of the nitty gritty mathematical details do not need to appear during the presentation (that’s what the handout is for), but make sure you do incorporate some mathematical content at least at a high level. You should be prepared to answer any questions me or your peers might have, after your presentation is over.

Keep in mind that the intended audience is one of your classmates: someone who knows something about the topics in linear algebra that we’ve discussed in our class, but may not know anything specific about your topic.

I encourage you to use TeX to typeset mathematics. It’s not too hard to get used to, and will probably be useful for you in the long run.

Grading

Your project score will be based on the following criteria.

• Content (out of 4 points). There should be correct and substantial mathematical content involved (during the presentation, or on the handout).
• Clarity (out of 3 points). The topic should be clearly explained and logically organized, in a way that is appropriate for the intended audience.
• Participation (out of 3 points). You’ll get full credit on participation if it is clear that everyone in the group understands the topic at the same level (in particular, everyone should have a substantial role in the presentation).

Possible Topics

There are so many possibilities! I encourage you to be creative. I only ask that it not be something that we’ve spent time discussing as a class. If you’re not majoring in math, I’m almost certain you’ll be able to find an application of linear algbera to whatever field you are majoring in. If you do plan on majoring in math, there is plenty of linear algebra to explore beyond what we’ve discussed in this class.

If you’re struggling to find things, you probably haven’t looked :P Here’s a short list of things to get you going. I’ll keep adding to this list as I think of more.

• Perspective and projective geometry.
• Computer graphics.
• Electrical networks.
• Coupled oscillators.
• Stress tensors.
• Algorithms for computations in linear algebra (for calculating determinants, or for matrix multiplication, or…).
• Page ranking.
• Linear support vector machines.
• Leontief input-output model.
• Lines of best fit.
• Markov chains.
• Singular value decomposition.
• Jordan form.