Day 20: Rewinding the Course

As Math and the Mouse 2024 winds down, we give the students a break from the blog and give you a professor’s perspective on the course. Over the next few days, we will blog on “Math and the Mouse by the Numbers” and a final reflection. Today, we thought we would give a brief update on the day, but then reflect, from an academic perspective, what exactly the students have accomplished in the course.

The day began with a morning class where Dr. Bouzarth talked about the history of animatronic advancement in the parks. Starting from a base of the Abraham Lincoln animatronic from the 1964 World's Fair, she mapped how these attractions advanced from the simple pneumatic devices of the Enchanted Tiki Room to the complex Audio-Animatronic featured in the Navi River Journey ride in Animal Kingdom. She threw in a discussion of the mathematics of projection mapping images onto Cinderella’s Castle and Tower of Terror and ended with some cheap 3D tricks (a Muppet Vision reference from our discussion on how a three-dimensional image can appear from a two-dimensional movie screen). Students also worked on their final projects to conclude the morning.

In the afternoon, we headed to Epcot to get lunch and say goodbye to that park for this trip. Epcot is home to the Guardians of the Galaxy: Cosmic Rewind ride, a fan favorite of both the students and the professors. The ride is known for playing different 80’s songs as you ride. The group’s favorite was “Conga” by the Miami Sound Machine. Although, Dr. Hutson just learned that “Everybody Wants to Rule the World” by Tears for Fears is one of the six songs in rotation, and now wants to go back to sample more rides tomorrow to hear this. We enjoyed saving the world a couple of more times with the help of the Guardians as well as Soarin’ Around the World, testing cars for performance and power at Test Track, and traveling to Mars in Mission: Space. Afterwards, we returned back to the hotel for the students to finish up their final project work and make their presentations. We look forward to these tomorrow and will update you on those presentations in the upcoming days. 

As we look back through the course, we want to emphasize the academic experiences these students have had. We designed the course so the students are introduced to applications of mathematics in the real-world in three parts: data analytics, mathematical modeling and algorithm design, and dealing with uncertainty. In three weeks, the students have learned (and sometimes re-learned) material that appears in eleven different mathematics courses at Furman (MTH 120—Intro to Statistics, MTH 150—Calculus I, MTH 151—Calculus II, MTH 160—Vectors and Matrices, MTH 245—Statistical Methods in R, MTH 250—Multivariable Calculus, MTH 335—Mathematical Modeling, MTH 337—Operations Research, MTH 340—Probability, MTH 341—Mathematical Statistics, and MTH 435—Scientific Computation)! The course is quick, exhausting, and intense, and our students have responded to the challenges. Let’s rewind the course from an academic perspective.

The first project, the Mickey Bar Project, asked the students to study how the crowd density changes throughout the day to move a mobile concession stand to where the people are at different times a day. The solution method involves using a data analytics tool called k-means clustering to locate a central point within a park-wide distribution of crowds. Think of this as putting tug-of-war participants of varying strengths on each ride, and they are each pulling a rope tied to the concession cart. Stronger participants (more dense crowds) pull the cart more than weaker participants, but as the crowd moves and wait times fluctuate throughout the day, the tug-of-war landscape changes, some become weaker and some stronger, and the cart moves. Facility location problems like this have a great history in mathematical fields as logistics companies compare alternatives to place warehouses and governments have to decide where to place fire stations to better serve their communities. One of the group’s final projects is using another data analytics technique, regression analysis, to determine what factors best predict a person’s score on Toy Story Mania, a video-game-like ride in Hollywood Studios.

In the second week of the course, the students learned to model real-world optimization problems such as those involving logistics, scheduling, and resource allocation. These types of problems are not only applicable to Disney’s operations but serve as foundational material for professionals working in the areas of industrial and systems engineering and operations management. The students completed a fairly sophisticated modeling project involving assigning workers to jobs in Yak and Yeti restaurant to cover the demand throughout the day. Although their problem was a factor of 100 smaller than the ones solved by Disney, the concepts learned by students through the project were the essential concepts Disney (or your local McDonald’s) uses to schedule workers.   Further, one of the student group’s final projects involves designing and comparing different algorithms for filling seats on Tower of Terror, a resource allocation problem where information is not known with certainty.

Once the students learned how to form a mathematical model, we showed them how to exploit the mathematical structure present in their created models to design algorithms to produce an optimal (or near optimal) solution. Their investigation of algorithms consisted of those normally used to solve the types of optimization problems we discuss in the class. However, one of the hallmark activities of the course, the Traveling Tourist Problem, involves the students trying to solve an instance of the Time-Dependent Traveling Salesman Problem. This is the same problem that companies like UPS, FedEx, and Amazon solve on a daily basis to route pickups and deliveries in an efficient fashion within a complex transportation network. In fact, the students employed many approaches used by these types of companies to produce quick solutions to a very hard problem.  Afterwards, we helped the students understand the types of algorithms that Touring Plans uses in producing tours of Disney attractions for their customers so that when the students met with Len Testa, the President of Touring Plans, they are able to have a fuller understanding of that industry.  

In the final stage of the course, we introduce students to some basic concepts in probability and statistics so that they might understand that all models are wrong because the inputs to those models are not always known with certainty and thus experience high variability. Most of the students’ final projects incorporate some sort of probabilistic or statistical analysis ranging from a chi-squared test to see if different rides have different party size distributions and a hypothesis test of whether omnimover rides, those with a continuous loading system like Peter Pan’s Flight and Spaceship Earth, have a more accurate posted wait time than other rides.  

We would like to emphasize that we throw a lot at these students during the three weeks. We don’t expect all of it will stick, but we hope that what they hear will pique their interests and inspire them to learn more by taking more classes in the mathematics curriculum. However, we are always impressed at how much they actually do absorb from the course. To those parents out there, we are really proud of this group, and we hope by emphasizing the academic content in the course that you will be impressed by them as well.

Some additional photos from today:

Furman FAN Club