Math Awareness Month — Q&A with Dr. Tim Chartier

As part of our Math Awareness Month celebrations we asked Mathematics Professor, Dr. Tim Chartier, about how he incorporates his love for soccer and other sports with his passion for mathematics. Chartier is a professor at Davidson College where he specializes in numerical analysis and partial differential equations, and even taught a class on how to produce mathematical brackets for March Madness. He has been recognized by the Mathematical Association of America in 2007 when he received the Henry L. Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member.

PUP: What sports are you fond of?

Tim Chartier: In terms of sports that I am fond of analyzing mathematically, I enjoyed learning about the recent research into soccer. I learned about the research on soccer when I was investigating applications for a numerical analysis textbook I’m co-authoring. When I bumped into the work, I was captivated by the results and motivated to dig deeper and deeper into their work. In the end, I wrote a short expository article on the work which was prompted by an encounter with a student who responded quite enthusiastically when I talked about the work. I believed strongly that other students would respond similarly. I have found this to be an excellent example for Calculus, Differential Equations, Numerical Analysis or Modeling classes.

I have also conducted original research in sports ranking. We have applied our research to football, ice hockey and basketball. This academic year will be especially memorable as it was the first time I taught a class, “How to create mathematically-generated brackets of the NCAA Division I Men’s basketball tournament”. March was even more maddening as we watched our brackets compete in the class pool! In particular, our brackets were submitted to the ESPN Tournament Challenge in which close to 5 million brackets were submitted. One student produced a bracket (entirely generated from math) that scored in the top 99% of that competition!

As an individual, I do enjoy soccer, although these days my games are with my son who is in first grade and my daughter who is in pre-school. I also enjoy running and mountain biking. Growing up outside Philadelphia, I played considerable amounts of basketball although largely half court games or games of HORSE in which my arsenal of trick shots was handy.

PUP: Does your career in mathematics influence your appreciation for soccer and other sports?

Tim Chartier: The research in soccer underscored the influence of computational fluid dynamics in modern sports. If I am watching sports, be it an Olympic competition, a NASCAR race, or the Tour de France and an announcer mentions some innovative apparatus (suit, car design, or helmet) that increases an athlete’s speed, it is not uncommon for me to smile or even mention that mathematics made that possible! If I’m in the company of others, this can spark interesting conversations about applications of math and even capture the attention of a self-declared math-hater.

As another example, we can look to NASCAR. I live in Davidson, North Carolina. The town immediately north of Davidson houses many of the NASCAR garages. As such, a variety of my friends work in that industry. A few years ago, I learned that one friend who specializes in shocks uses the mathematical software Matlab in his job almost daily. I use Matlab in both my mathematical modeling and numerical analysis classes. Students generally have been very interested to learn that the software they use in class enhances a professional sport connected to our area. In fact, one student worked for a NASCAR team right after graduating from Davidson College and was hired, in part, for his skills in Matlab programming, which he used in his job.

PUP: Did you enjoy sports or mathematics first as a child?

Tim Chartier: This is difficult to answer. My mother notes that even as a young child, I liked games with numbers whereas my sister preferred games with words. I remember enjoying math in elementary school. However, I was also an avid fan of kickball! I grew up in a neighborhood where large numbers of children would gather daily to play conventional sports and games of our own invention.

PUP: How did you become interested in sports and/or mathematics?

Tim Chartier: My interest in soccer grew from the playground. Many of my friends played soccer, and I wanted to play with them at recess. In time, this grew to playing on school teams during my secondary education.

My interest in studying mathematics actually grew from my interest in the performing arts. Throughout high school, I performed throughout the Philadelphia area in puppetry and in college performed widely in puppetry and mime. During college, I studied math and computer science so I could find a job in those fields if the performing did not lead to full-time employment. The more I studied math, in particular, the more I wanted to learn. While I would eventually attain a doctorate in math, I continued to perform at national and international levels throughout my studies.

PUP: Do you find yourself using math while watching or playing sports? How?

Tim Chartier: Many people with whom I play sports comment that I use math to play. I often find angles that are apparently not as obvious to someone else. In basketball, I often would estimate the effect of a spin on ball’s bounce off the backboard. In soccer, I would often try to position myself as to reduce or eliminate the best angles of approach of my competitor. Frankly, many athletes probably do this. My friends often laughed as I would talk about it as angles and in mathematical ways. I do remember once in cross country trying to estimate how much longer my stride was to the lead runner directly in front of me. I tried to compute how long it would take to catch him if our rates stayed constant. I laughed later (having come in second and never catching that runner) that it didn’t work as it was cross country and the terrain didn’t allow for constant rates.

PUP: What can coaches or athletes gain by having an understanding of mathematics?

Tim Chartier: College football coaches already probably try to understand how to best optimize their chances for high ranking with the BCS ranking. Of the various ranking methods of the BCS, two are based in linear algebra. Clearly, winning all the time would be the best way to have a high ranking but that isn’t always possible. Further, players may need rest or even playing time to create a more robust line-up, an understanding of how these schemes work can help with coaching decisions.

The research on soccer demonstrated that the new stitching of soccer balls impacts how the ball flies through the air. I presume that athletes learn this effect through an understanding of the mathematics and physics involved or possibly intuition gained by trail and error. The insights of this work can play an important role for ball manufacturers as they may be able to design balls customized to differing levels of play.

I believe that athletes use mathematics all the time. Ice hockey would be difficult to play if one did not think about angles. Short track speed skating would be harder to win without thinking the effects of acceleration and velocity. Golfers must estimate the effect of wind resistance on a ball in order for some chip shots to land on the green. These examples are simply applications of Calculus. While one may not necessarily have deep understandings of mathematics for these applications, it also wouldn’t hurt. When it comes to those who design the modern equipment of sports – the aerodynamic cars of NASCAR, soccer balls for the World Cup, suits for Olympic swimmers, and the hulls for competitive sailboats, mathematics and computation play a vital role in success in the sport.