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Guest Post: Tim Chartier, Davidson College

On March 30th, DavidsonX Applications of Linear Algebra Part 1 ended. With Applications of Linear Algebra Part 2 starting this week, we wanted to highlight what students have learned so far and encourage learners to join us as we embark on Part 2.

We explored the use of linear algebra in computers graphics and data mining. We saw how to blend images, even in animations, like this one from one participant.

The vanishing head animation is constructed just using arithmetic. Below are other examples of other art work created by students in the course with matrix arithmetic.

There are various ways to create mathematical artwork with matrices. Rather than using multiplication or addition, you can also swaps submatrices. Can you see what images were combined to create this composite image? Hint: the piece is entitled “Mona Gogh”?

Composite image of Leonardo's Mona Lisa and Van Gogh's self portrait

The course concluded with sports ranking, which is an area of my research. Students learned to make brackets for March Madness, using math which allows students in countries not as tournament crazed to participate. Going into the Final Four, a bracket constructed by a member of the class is beating over 92% of the over 11 million brackets submitted on ESPN. In the very last section of the course, John Brenkus, host and creator of ESPN’s Sport Science show, posed a question. Here’s his question as posed to the class:

What’s the answer? It depends, in part, how you interpret the question, which we saw in our course with our analysis and discussion. We saw analysis for each answer and made comparisons to sports in other countries. The analysis came from baseball fans and participants new to the sport. We saw that math is indeed a tool allowing fans to mine through their own assumptions and for those new to a sport to have helpful insights through their mathematical knowledge.

With so much done in Part 1, what else can we do? There are many applications of linear algebra. On April 6, we launch into Part 2 of the course. Why have a second part? The first part was intended for a broad audience, which we saw. From high schoolers exploring applications alongside data scientists in various countries, we delved into applications together. Part of what made the course suitable for various audiences was the use of web applications developed by Davidson College students, an alum, and myself. Some students quickly found the code for the web applications and began tinkering with options beyond the scope of those offers on the Internet.

The activities in Part 2 will, like Part 1, still emphasize exploring ideas. Lectures are intended to launch discovery both individually and as a group. In the course, we’ll find which of the United States Presidents picture below I look most like, at least mathematically.

Photos of the last 12 U.S. Presidents.

We’ll learn how Pixar uses linear algebra to create the surfaces we see on the screen – from their characters to buildings. The algorithm was a significant advance in animation and played a role in developing the beloved characters we see below.

Image of Mike and Sully from Monsters, Inc.

©Disney-Pixar. All Rights Reserved. Used with permission.

So, why two parts to the DavidsonX course? Part 1 allowed a broad spectrum of people to learn applications of linear algebra. Part 2 may or may not be more restrictive. Time will tell. However, between the two, students worldwide with various interests can participate, explore, share, and learn together. Sign up today!

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