Linear Thinking from Sports to Pixar

Guest Post: Tim Chartier, Davidson College | 02.17.2015

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Learning new ideas can be exciting, enlightening, and even life-changing. The "ah-ha" moments might connect to comments like "I've never thought of that," or "I've never known how to do that." Ideally, the effects of such insight extend beyond a course. Learning to analyze writing can help a math major communicate discoveries on theoretical structures. Tackling problems through computing hones various problem-solving techniques that can help with a social science study. The balance between the exciting and seemingly irrelevant is an important one.

In some class that you've taken there probably came "the thought." Yes, the thought that in math makes pencils heavier, word problems harder, and students wish they were somewhere, anywhere but where they are. There are many ways this thought turns into a question. A common one is "Why am I learning this?" Such pondering can lead to a teachable moment. Yet, in a setting like edX, such a question can result in a student pausing an online video, possibly with no return.

In my DavidsonX MOOC on Applications of Linear Algebra, I hope to engage the question: "Why?" In a sense, it is a main focus of the course. Participants will use linear processes to create images. For example, the image below is constructed entirely with numbers, emphasizing how matrices encode information -- in this case visual information.

Matrix operations are frequently used in computer graphics and data mining. The image below and on the left uses an equation to blend images of an adult lion and a cub; look carefully and you'll see both in the image. Then the image below on the right combines hundreds of handwritten digits to aid a computer in reading handwriting. Participants will learn these ideas, but more importantly, they get to creatively explore them. For example, what images would you blend?

In the MOOC, we'll explore the "why" of learning such ideas beyond the DavidsonX classroom. We'll consider questions like "Why do computer scientists at Pixar learn these ideas?" or "Why would someone running a super-computer use linear algebra?" or "How can you do sports analytics with these methods?" These questions motivate the topic of linear algebra and math at-large. Interested in the answers? Many students are and dive into the content and its application to discover the answers.

From Buzz Lightyear to the characters in Monsters University, characters in Pixar films are created with linear processes. First, wireframes of the characters are themselves created with linear processes. In fact, a process called subdivision creates the smooth seamless characters we associate with modern animation. In the MOOC, Tony DeRose, a Senior Scientist and the lead of the Research Group at Pixar Animation Studios, will discuss how linear algebra is used in the movies. Linear algebra plays a role in every frame in a Pixar movie. In the progression below, the image on the left show the process known as Modeling in the computer by technical directors. Once the storyline for a sequence is completed, the scene is created in the computer. The frame in the middle shows the beginning phase known as Layout, in which a virtual camera is placed into a shot. After animation, simulation and lighting are added, the final frame is created.

Supercomputers solve some of the largest and most complex linear algebra problems. In the MOOC, we'll hear Van Henson, a computational mathematician in the Center for Applied Scientific Computing at Lawrence Livermore National Laboratory (LLNL), discuss how computing has become a central part of modern science. Henson specializes in devising highly accurate fast linear methods for problems in cybersecurity and in data mining for intelligence applications. LLNL houses several of the fastest supercomputers in the world, such as the Sequoia supercomputer.

Finally, we'll discuss methods that can be adapted to analytics and specifically sports analytics. Why learn linear algebra? One reason will be to answer a sports analytics problem posed by John Brenkus, host and creator of ESPN's Sport Science.

Delving broadly into the "why?" of math and linear algebra will probably ignite the question "what else can I do with these ideas?" The creative exercises of this MOOCare designed to help participants look within themselves for answers to such questions. How else can such methods be used? What comes to your mind? Your answer may be the next, new and exciting application.

DavidsonX Applications of Linear Algebra Part 1 starts on February 23. Sign up today , join a global learning community and be ready to investigate your own ideas.