As Math and the Mouse 2019 comes to an end, we, the professors, want to emphasize the academic experiences these students have had. We design the course so the students are introduced to applications of mathematics in the real-world in three parts: mathematical modeling and algorithm design, data analytics, and dealing with uncertainty. In the three-week course, the students have learned (and sometimes re-learned) material that appears in eleven different mathematics courses at Furman (MTH 150—Calculus I; MTH 151—Calculus II; MTH 160—Vectors and Matrices; MTH 250—Vector Calculus; MTH 255—Differential Equations; MTH 330—Combinatorics and Graph Theory; MTH 335—Mathematical Modeling; MTH 337—Operations Research; MTH 340—Probability; MTH 341—Mathematical Statistics; and MTH 435—Scientific Computation)! We believe that by exposing students to this material in the context of the operations at Disney that they will have a better understanding of how the skills that they are learning can be used in the real world.
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Kyle, Kelly, Hallie, and William present the Mickey Bar
project during their meeting with Disney professionals. |
We started the course by introducing the students to some foundational topics in data analytics. Two problems we worked on heavily were the classification problem and the prediction problem. Given a data set, the classification problem asks one to partition or cluster the data into different segments. For example, given characteristics of individual families, Disney might want to know which characteristics define a family who will stay at a Disney resort versus one who would not. One of the methods that we talked about to accomplish this was k-means clustering. The prediction problem seeks, using past data, to forecast a future result. Here, Disney might try to predict how much a family with certain characteristics will spend in the parks each day. Our students’ first project involved using k-means clustering to pinpoint where to put a mobile Mickey Bar stand throughout the day to interact with the highest traffic areas of the park. We, the professors, would classify the project as a huge success. The students worked very hard, and their presentation to Disney professionals on this project was fantastic!
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Rosie, Samantha, Macie, and Madison present the Yak & Yeti
workforce scheduling project to the Disney professionals. |
The second main topic in the course was modeling and algorithm design. 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 sophisticated and difficult modeling project involving assigning workers to shifts at the Yak & 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. Several students commented to us that completing this project was extremely challenging, but it paid off when hearing a Disney professional in the Industrial Engineering Department give a presentation on modeling at Disney and many of the same types of things they were learning showed up in her presentation. The same Disney professional was impressed with our project and presentation on this project as well.
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Hannah, Duncan, Katherine, and Bailey present the Traveling Tourist
Problem activity to the Disney professionals. |
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, the students’ ability to design algorithms was put to the test in two competitions during the course. The first activity was the Traveling Tourist activity where the students tried to solve an instance of the Time-Dependent Traveling Salesman Problem by finding a tour of 18 different Magic Kingdom attractions that minimized the time it takes to complete. This is the same problem that companies like UPS, FedEx, and TouringPlans.com solve on a daily basis. It was a grueling competition, but the students were able to discover for themselves heuristic algorithms to solve this problem that are similar to those actually used in practice. They were also able to interact with Len Testa, the President of TouringPlans.com. As a result, they have a fuller understanding of how Testa’s company designs algorithms to solve the Disney touring problem for its customers. The second problem where the students designed an algorithm was to solve the Knapsack Problem. Think of this as the packing problem. A student, packing for a trip, has many things to bring, all of which has a different utility to the student, but must fit in one suitcase. The question is “what should the student pack in order to maximize utility/usefulness/value?” We played the game in Animal Kingdom by giving each ride a utility and asking who could maximize utility consumption within a four-hour time frame (time being the suitcase here). The students quickly discovered the most widely-used heuristic to come up with solutions to this problem which is called “Bang for the Buck.” Here, you judge each ride by the utility per time it takes to consume the ride, and greedily try to consume as much of it as time will allow. Both of these activities were enjoyable (in retrospect), but they have the payoff of showing the student that they are problem solvers and can design algorithms.
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. Further, we discuss how Disney and other companies use simulation to test different possible cases that could arise from models as the likelihood of the inputs of the model change. Most of the students’ final projects incorporate some sort of probabilistic or statistical analysis such as hypothesis testing to determine whether FastPasses become more valuable at different times of the day, to determine whether one scores higher on Toy Story Midway Mania with his or her dominant or non-dominant hand, or to determine whether our simulated loading procedure for Tower of Terror and Kali River Rapids was the same as Disney’s loading procedure. We are very proud of each group’s effort on these projects and how they bonded and worked as a team.
Outside of these larger themes that get woven into course projects, we also spent time discussing other aspects of quantitative and scientific importance in Walt Disney World. After spending lots of time exploring theme parks, either in structured or unstructured ways, the students had a lot of curiosity about a variety of things. To address some of this curiosity, we talk about some of the physics of attractions and elements of “the show” that Disney presents to its guests. We talked about the physics of rollercoasters, simulator rides, fireworks, crowds, and arcade games. We discussed the technology behind MagicBands, projection shows, 3D experiences, and interactive animated attractions. We explored the rich history of Walt Disney’s ideas for audio-animatronics both in class and during our backstage tour experience.
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. We also hope that by exposing them to professionals working at Disney and companies tangential to Disney that they will appreciate how the concepts they are learning are used in industry. By meeting with Math and the Mouse alumni that are now working for Disney, we hope they see opportunities for growth in their pathway through Furman and beyond. Hopefully, as a result of the course, the students will discover that at Furman they are building the tools in they need to succeed in industry. The students are discovering how to learn new things quickly in a way that they can communicate technical information in an effective way to their teammates, to the general public (via this blog), or to a more technical audience. They learn the importance of working together and communicating effectively with visual presentations, writing, and speaking. 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.
We feel very lucky to have shared this experience with these students! Not only did they rise to the academic challenges that we gave them, but they also brought joy and laughter to the process. There was a lot of sweat, and maybe even some tears, but people came together to accomplish a task many times. We all learned about each other in a way that enhances the time we spend learning together. We are very fortunate to have the opportunity to get to help these students learn and to also get to know them as people. Thanks for all the memories!
