Teaching

Why do math? How could I use math? I hope that my students, if nothing else, have answers to these questions years later when sitting at dinner tables with friends. My hope is that examples brought up in class can help them answer such questions and understand that math is powerful and influences our lives. Here are a few examples:


In Mathematical Modeling, we learn, among a variety of topics, how to create mathematically-generated brackets. They are produced via sports ranking algorithms. Students learn to create their own, personal ranking method which produces their own bracket for March Madness. In 2010, students had the option of submitting their bracket to the ESPN Tournament Challenge. Our brackets competed against each other as a class and against the near 5 million other brackets. In the end, a student won who also created a bracket (only one was allowed to be submitted in the class pool) which was in the top 99% of all brackets submitted! Can we create a bracket to score in the top percentile this year? Hard to say. It depends how well the underlying mathematical model matches this March’s tournament play.


Calculus is an important topic. In fact, some consider it one of the major discoveries of human thought. Think of it. A major achievement that was remarkable and controversial is now—an AP topic taught to teenagers around the country. Yet, I must admit I don’t marvel each time I drive my car, use my phone, or turn on a light. Calculus is full of application to our every day life. You can use vector Calculus to mathematically find a date after a group of people complete surveys. You can use Calculus 1 to determine estimate how far a Hollywood star is falling in a movie–although a better model uses differential equations. Finally, you can play with polar coordinates to warp a picture. To the left, you see a polar function applied to a picture of Marilyn Monroe, which is a great example on a Monday morning around the time of midterms!


My research area is linear algebra and numerical analysis. Here we see an example created by a student in a Computer Science seminar. We learned quick and easy color editing using linear transformations. Yes, someone figured out how to create a tie dye mandrill! We simply colored with matrix multiplication. This example started in a seminar and then progressed into numerical analysis and is an exercise now in my upcoming numerical analysis textbook coauthored with Anne Greenbaum.