Friday, June 7, 2019

A Final Reflection

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.

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! 

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.

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 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  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!

Tuesday, June 4, 2019

Day 21: Math and the Mouse by the Numbers

As we reflect on our time here, we (the professors) thought we'd pass along some data on the types of experiences we've had during Math and the Mouse.  We'll have one more blog post later this week to report on our last day in the parks and final group projects, but for now we'll give you a look at our May Experience by the numbers.
  • 12 Furman students
  • 2 Furman professors  
  • 2 vans (including "Hot Dan the Math Van")
  • 11 math courses' content represented
  • 13 majors/programs/minors represented (Applied Math, Math, Math-Econ, Physics, Economics, Computer Science, Chemistry, Health Sciences, Business Administration, Musics, Politics and International Affairs, Studio Art, Latin American Studies)
  • 8 guest speakers (including two Math and the Mouse Furman alumni)
  • 56 hours spent on a backstage tour
  • 5 unique group projects
  • 6 engaged learning activities
  • 8 Lightboard videos viewed by students
  • 13 learning modules led by faculty
  • 65 dice used in Liar's Dice competition
  • 95 workers needed to staff Yak and Yeti in the Workforce Scheduling project
  • 3 mobile Mickey Bar Stands modeled
  • 4,250 utility points for winning knapsack team
  • 6 permutations of the big three Epcot rides
  • 13,293,600 points scored on Toy Story Midway Mania during final project data collection
  • 672 FastPasses used
  • 3 rides on a maintenance service elevator (maximum per person in our group)
  • 26 trips to the Twilight Zone
  • 203 train rides to see Disco Yeti
  • 46 trips where the ostrich eggs didn't hatch
  • 1,837 total miles walked 
  • 13,390 average steps taken daily by each person
  • 49 different attractions visited
  • 13 hours without water at the hotel
  • 324,900 high score on Toy Story Midway Mania
  • 265,200 high score on Toy Story Midway Mania using non-dominant hand to shoot
  • 64.9 miles per hour on Test Track
  • 1 iguanadon inexplicably, but helpfully, holding up a log
  • 3 animals whispered to by Hannah 
  • 15.189 gallons of gas pumped by students who had never pumped gas before
  • 1 "Ma'am" at Yak & Yeti
  • 2 accidental lunches at Tiffins
  • 1 trip to the Minute Clinic
  • 80 bajillion coughs
  • 20 percent of her coughs that Madison suppressed
  • 10 glasses of POG enjoyed
  • 65 stickers picked up off the ground (but 6 honorary custodian stickers earned)
  • 0 chicken dances at Biergarten
  • 2 birthday celebrations
  • 5 floor naps
  • 5 broken screens
  • 12 project presentations
  • 200 hypothetical dollars to spend on preferences ($100 at a time)
  • 93 data points gathered to compare posted versus actual wait times
  • 1 podium impact
  • 12 student maximum capacity of oversized Twistee Treat chair
  • 49 Twistee Treats
  • 9 hot breakfasts
  • 1 failed pancake lunch
  • 86 food stops while eating around the world
  • 28 Dole Whips consumed
  • 44 Starbucks drinks
  • 10 Mickey Bars enjoyed
  • 3 crunchy, not gooey, num num cookies
  • 33 bottles of ketchup brought to our table at Whispering Canyon 
  • 14 Boma comas
  • 16 days of 90 degree high temperatures or above
  • 2 hours of rain
  • 1 Memorial Day bus ride 
  • 10 rope drops
  • 9 park closings
  • 2 teams who won the Traveling Tourist Problem
  • 390 minutes for the winning groups to complete the Traveling Tourist Problem
  • 177 total attractions visited during the Traveling Tourist Problem
  • 2 Indiana Jones Stunt Show extras 
  • 5 aux "accidents"
  • 714 FastPasses
  • 4 days seeing fireworks while riding the wildest ride in the wilderness
  • 5 visits to the Copa Cabana
  • 28 buffets
  • 2 private Pirates lunches
  • 5 sledding trips with Elsa
  • 15 "We're Celebrating" buttons worn (and possibly lost or smudged)
  • 21 consecutive days in Disney Theme Parks 
  • 16 pairs of mouse ears
  • 79 forehead selfies
  • 29 golden FastPasses
  • 85 breakfast bags
  • Infinite memories made

Monday, June 3, 2019

Day 20: Venture to the Void

Outside of the Void
"Alright, now just remember- bunny gets the pancake, kitty gets the milkshake. Got it?" These were the words spoken to us at the start of our day before we entered a Wreck It Ralph Virtual Reality simulation game at Void in Disney Springs. While one group earned points shooting desserts at cute animals, the others did a different simulation where they entered a Galaxy Far Far Away as rebels pretending to be storm troopers so they could take over the Empire. Both the Wreck it Ralph group and the Star Wars group had a lot of fun experiencing Virtual Reality gaming.

Toy Story Mania project group
When playtime in the Void was all finished, we headed over to our favorite plaza for lunch. Many students had Panera while others had Chipotle. Then it was time to get to work on our projects. We headed back to the hotel and split into our groups to finalize our research findings and prepare for our presentations. The Toy Story Group that Sam is in finished up some hypothesis testing and messed around in Tableau to create visuals to represent our data. The FastPass group that Rosie is in worked on the visualization of data as well to complete the two different parts of the project. We are very excited to share what we learned tomorrow.

In the evening, we visited Hollywood Studios. We had three FastPasses for Toy Story Mania, Star Tours, and Rock 'n' Roller Coaster. Since the majority of data collection was in Hollywood Studios, a lot of us took group pictures to use for our final presentations tomorrow. After the group split up, Sam and Macie got to ride one of Disney's newest rides - Slinky Dog Dash. Even though there were several groups split off to do different things, all 12 of us happened to gather together to ride Rock 'n' Roller Coaster, the last ride of the day! Some of us loved the ride so much we decided to ride it twice in a row. 

Ride Efficiency project group
FastPass project group ourside Alien Swirling Saucers
We had another exciting adventure to end the night on the way back to the hotel. Two of our students, Rosie and Bailey, had never pumped gas before so the professors decided to make one more learning experience out of this trip! (I mean, if this is not the real Furman Advantage, then I don't know what is!) The two girls successfully accomplished the task and earned Slurpees for the whole class. Now that the students had their sugar fix, it was time to end the day. 

First time gas pumpers
We can't believe tomorrow will be our last day together in Disney. Tomorrow the students pass off the baton to the professors to write the blog. We all have greatly enjoyed writing the blog posts every night and would like to thank the professors for all they have taught us. We are so grateful for this learning experience and all the unforgettable memories that came with it. We are looking forward to cherishing our last moments together at the park tomorrow!


Sunday, June 2, 2019

Ducking into Day 19

Good evening everybody! It is hard to believe that the 2019 Math and the Mouse group has just left Epcot for the last time. William and Kelly are here with full bellies from eating around the world to tell you about our antepenultimate day at Disney. 

A morning spent in Hollywood Studios is a great way to start the day!
Dr. Hutson, William, and Bailey work on the simulation website while in line
As we have mentioned in previous blog posts, three groups of students are working on independent projects of our choosing. This morning, a few of us went into Hollywood Studios to collect data for the Toy Story Mania group. They are looking at how a player's usage of a non-dominant or dominant hand to play the game would affect their score and accuracy. After some successful data collection, we returned to the hotel to individually work on our projects with the professors. 

Throughout the day, students used a website to simulate loading passengers onto rides to create sample models for a group of students doing a project on the efficiency of rides. 

Instead of having peanut butter sandwiches, soup, pizza rolls, or other sub-par microwavable foods, we had a pancake lunch. After a victorious battle with the hotel room appliances, we nonetheless enjoyed our pancakes with a variety of toppings.

After group meetings with the professors to discuss our projects, the class headed into the parks. The groups of students who are doing their project with FastPass usage journeyed over to Hollywood Studios from Epcot to gather more data. Their project requires a variety of wait times and FastPass usage for numerous rides throughout the day. The rest of us remained in Epcot and embarked on one final trip around the world. 

The class with Mickey at Epcot!

After meals in France, England, Germany, and Italy, we met Donald (or as Dr. Hutson calls him "Donaldo") Duck in Mexico for a few photos and dessert. We also attended a few attractions like Spaceship Earth and looked for hidden Mickeys in Soarin'. 

Our group recollected and left for the hotel to work on our projects and rest. Tomorrow we look forward to doing a virtual reality experience at Disney Springs as well as preparing our final projects to present!

Saturday, June 1, 2019

Day 18: "Look at all this good math!"

Hallie and William collecting data!
Hey guys! It's Hannah and Kelly and we're super excited to tell you all about our last Saturday in Disney! We started off the morning by heading over to Magic Kingdom to gather some data for the FastPass group's project. We split up into groups of two or three and positioned ourselves outside of the entrances and exits of five rides with FastPass lines: Splash Mountain, Big Thunder Mountain Railroad, Haunted Mansion, Aladdin's Magic Carpet, and Peter Pan's Flight. We took notice of people entering the standby and FastPass lines at the same time, and then recorded when they exited the lines to show how effective the FastPass was.

Dr. Bouzarth teaching us about Physics!
After gathering data in the Magic Kingdom, we headed back to the hotel for lunch and class time. Class was especially interesting. We learned the physics and calculus behind rollercoasters. We reviewed Newton's Laws of Motion and the basic definitions of force, acceleration, and inertia. We discussed how energy is the ability to do work and work is the transfer of energy. We learned that mechanical energy is the type of energy you encounter on a rollercoaster. This energy will dissipate as time passes on the ride because of the opposing forces of drag, fiction, and heat. We discussed how magnetism is also often used in amusement parks. For example, Rock n' Rollercoaster uses electromagnets to create a repealing force to push the coaster from 0 to 60 miles/hr in 2.5 seconds.

Hallie and Hannah stuck on Kali River Rapids!
Lastly, we reviewed some basic concepts of calculus and discussed how these applied to Walt Disney World and rollercoasters in general. Understanding the position, velocity, and acceleration of an object is important in the realm of physics. Velocity of an object can be found by taking the derivative of the position function. Furthermore, acceleration can be found by taking the derivative of the velocity function or the second derivative of the position function. However, in the real world with discrete data which is not continuous, this is not always possible. Today, we learned sometimes you have to use the slope of the secant line to estimate the slope of the tangent line (the derivative). The closer the points you use for approximation of the secant line the more accurate your estimation of the tangent will be. We finished class by specifying that the Euler's Method can be used to calculate the error you make in this approximation of the tangent line.

After class, we headed into Animal Kingdom so our efficiency group could gather data at Kali River Rapids for our project. Even though we were set back a few hours by the ride breaking down (and Hannah and Hallie getting stuck at the top of a hill) we were able to collect valuable data for our project. We counted how many empty seats there were in the boats and also the party size of each group getting onto the ride. We will use that data later to calculate how efficiently the ride is being loaded and compare the results to Tower of Terror. With one final ride on Expedition Everest (which brings the group total up to 19), we headed back to the hotel to prepare for another day of collecting data!

Friday, May 31, 2019

Day 17: "I Speak Fluent FastPass"

Hi everyone, it's Bailey and Kat to tell you about our fabulous day at Hollywood Studios! This was definitely our longest day with a total of 14 hours in the park. We left the hotel at 8:00 this morning to rope drop at Hollywood Studios to collect data for the Toy Story Mania group. Every pair of students was tasked with playing with their dominant and non-dominant hands to analyze the difference in score and accuracy.

Kat and Rosie's dominant hand scores 
Kat and Rosie's non-dominant hand scores
After everyone collected data for this project, people split up to work on the other two projects.  The group doing the project that focuses on FastPass usage went to Rock n Rollercoaster and Star Tours to time people when they entered and exited the ride.

Star Wars Launch Bay
We would write down when people entered the FastPass and stand-by lines as well as the time and current posted wait.  Then, we would go to the exit of the ride and note when they got off, so that we could analyze the usefulness of a FastPass.
The other group is studying the efficiency of ride seating. They sat by the exit of Tower of Terror near the PhotoPass monitors to count the empty seats in every elevator to see if the cast members were optimizing the ride capacity. In addition, Dr. Bouzarth's father developed an app for us to help the ride capacity group with their data. It shows a Tower of Terror or Kali River Rapids ride vehicle and gives a number of guests for us to seat in under a minute.

Round 1 Results
Round 2 Results
After a long morning of data collecting, the professors treated us to lunch at the ABC Commissary and we found a "quiet" place to have class in the Star Wars Launch Bay. The Imperial March was epic background music for Dr. Bouzarth's lecture about agent-based modeling. We discussed the ideas of carrying capacity and modeling populations; then we compared it to Agent-based Modeling, which is a more individualistic model with rules and goals. After a group of Storm Troopers walked past our class, we decided to take it outside in front of the Chinese Theatre to play a fun game that demonstrated agent-based modeling. For the first round, we were each given two specific people to watch out for. We needed to keep person #1 in between ourselves and person #2. This resulted in a huge circle of mass chaos when we were following each other around. The next challenge was to put ourselves in between our assigned people and we clumped together. The goal of this activity was to demonstrate how individuals in a group move when given rules designed by agent-based modeling.

After class, we had a FastPass for the Frozen Sing-along Celebration, which Dr. Hutson thoroughly enjoyed! We are surprised Kelly, Rosie and Macie did not lose their voices singing along with Elsa, Anna and Olaf!

Then, we had dinner at Mama Melrose including dessert! Then, we were off to Fantasmic (Bailey's favorite)! We enjoyed the show full of fireworks, music and fun characters after a long work day in the park. Tomorrow, we can look forward to rope dropping Magic Kingdom to collect FastPass and ride capacity efficiency data. Thanks for reading!!


Day 16: For the Blog

Group picture during our tour (including our
tour guide!)
Hello, everyone! Hallie and Duncan here to tell you all about our sixteenth day in Disney World! We left the hotel bright and early, at 7 am, for our Keys to the Kingdom Tour in the Magic Kingdom. Our tour guide, Natalie, led us through this behind-the-scenes experience where we got to explore the utilidor system, the "tunnels" that the cast members walk through under the Magic Kingdom; rode Haunted Mansion and Pirates of the Caribbean; and learned lots about Disney history and special effects! One fun fact that many of us didn't know before the tour was that the Pirates of the Caribbean series actually came out after the ride, and then they added Jack Sparrow animatronics to the ride after the movie. This goes to show that sometimes the rides inspire the movies, instead of being the other way around. In fact, right now, Disney is making a movie based on the ride Jungle Cruise.

Pirates of the Caribbean during the tour
After the tour, we grabbed lunch in the park at Columbia Harbour House and made a quick Publix run. Back at the hotel, we met with the professors to brainstorm for our final projects, solidifying our ideas and figuring out what data we need to collect. Yesterday, we were broken into three groups, so we will be collecting and analyzing data for three different projects. One project will look at scores and shooting accuracy in Toy Story Mania, comparing performance between dominant and non-dominant hands. Another will analyze the FastPass system, hoping to see at what point in the day a FastPass becomes most valuable and what percentage of the posted wait time the FastPass line has to wait. Lastly, the project that Hallie and Duncan are working on will study the efficiency of Tower of Terror in Hollywood Studios and Kali River Rapids in Animal Kingdom.

The professors riding Toy Story Mania to collect data!
This evening, we started collecting data for the FastPass project in Epcot by using FastPasses for Soarin'! We took note of the posted wait time, the time we entered the line, and the time we got on the ride. We were going to do the same thing with Spaceship Earth, but, unfortunately, that ride went down. Then, we finished the night in Hollywood Studios, where we were able to collecting data for all three projects! Many students rode Toy Story Mania twice -collecting good data. The FastPass group observed the FastPass and Standby lines of Alien Swirling Saucers to collect wait time data, and the ride efficiency group was able to examine the efficiency of Tower of Terror. Some groups felt like the Disney employees were getting suspicious of us mathematicians, hanging out, watching people, and making notes, but it's okay; that's what the professors' business cards and our Disney contact are for!

Tomorrow, we are looking forward to rope dropping Toy Story Mania in order to get more data for that project, as well as collecting more data on the other projects; having class; and experiencing a dinner and show in Hollywood Studios, featuring Mama Melrose as the dinner spot and then Fantasmic, the Hollywood Studios nighttime show.