1. Mathematical Modeling: Examples and Opportunities
Holly Zullo and Allison Carson
Westminster College

2. Overview MCM Alli share MCM work Contests for high school students
Preparation
Benefits
Resources

3. Mathematical Contest in Modeling (MCM)
96-hour competition in January
Team of 3 students
Designed for undergraduates, but high school students can participate
Students pick one of 6 open-ended applied problems
Cost: $100 per team

4. MCM Problems A: continuous B: discrete C: data insights
Hot bath
B: discrete
Space junk
C: data insights
The Goodgrant challenge
D: operations research/network science
Measuring the evolution and influence in a society’s information
E: environmental science
Are we heading towards a thirsty planet
F: policy
Modeling refugee immigration policies

5. Bathtub Problem
After you sit in a bath for a while, the temperature cools. If you turn on the faucet again, what is the best method to keep the bath water at constant temperature and as close to the original temperature as possible?

6. Assumptions The bathtub is of a rectangular shape.
The room temperature is constant and there is no outside airflow.
The faucet delivers immediate hot water to the bath.
Evaporation is constant over time.
Mixing the water will assure a perfect mix throughout the tub.
Heat moves through a liquid similar to how it moves through a solid

7. Model Theory Discretize the heat equation: Newton’s Law of Cooling
𝑇 𝑖+1,𝑗 = 𝑇 𝑖,𝑗 + 𝜅Δ𝐴 2 𝑇 𝑖,𝑗 − 𝑇 𝑖,𝑗−1 − 𝑇 𝑖,𝑗+1 Δ 𝑥 2
Newton’s Law of Cooling

8. Model Theory
Differential Equations for perfect mixing
*assumptions!

9. Experiment!

10. Simulations

11. Simulations

12. Results

13. HiMCM High school version of MCM 36-hour contest
Time window in November (this year is Nov 4 – 17)
Teams of 4 high school students
Students pick one of two problems
Cost: $75 per team

14. Problem: City Crime and Safety
What can we make of the massive amount of crime statistics collected in major cities?
Beyond just reporting numbers, how can we use these data to determine the safeness
of a city?
Assume that you and your modeling team live in My City, a large international hub of
commerce, technology, finance and travel, with a current population of 2.8 million
people impacted by a metropolitan area of an additional approximately 6 million people.
The data set provided (My_City_Crime_Data.xlsx) shows two weeks from police
reports in My City and includes crimes listed by case number, date of occurrence,
primary and secondary crime descriptions, crime location, whether an arrest was made,
whether or not this was domestic crime, and the beat number of the police route.
Part I: Using mathematical modeling, analyze the data. Create a safety rating for
My City. Use your safety rating to specify a measure of how safe My City is.
Part II: In addition to the HiMCM contest format, prepare a 1-2 page non-technical
report for the Mayor of My City to describe your findings.

15. International Mathematical Modeling Challenge
Up to two teams per country can compete
All Finalist, National Finalist, and Outstanding teams from HiMCM invited (about top 10%)
5-day contest in April
Top two papers forwarded for international judging
Teams and advisors ranked Outstanding invited to awards ceremony
Hope to grow to same prestige as International Mathematics Olympiad
In 2nd year, had 40 teams from 23 countries
Problem: insurance for athletic world-records

16. Moody’s Mega Math Challenge
14-hour contest
Registration open in November; contest February 24-27, 2017
3 to 5 students per team; juniors and seniors only
Limit of two teams per high school
One problem
2016: Share and (car) share alike
Cost: free!
Scholarship prizes total $150,000

17. Preparing Students Brainstorm on old problems Simplifying the problem
Writing the paper
Equation editor
Winning papers freely available from IMMC and Moody’s
Study for common sections
Writing the summary
Group work
Respect
Keeping everyone busy
Time management

18. Benefits Sense of accomplishment Increased confidence
Solved big problem
Immersion
Learned new math & better understand old concepts
Worked without assistance from teacher
Increased confidence
Worked with applied math instead of just algebra and computations
Better idea of how math might be used in careers
Something to discuss on college/scholarship applications

19. Resources
GAIMME (free download):
Modeling Handbook (free download):
Math Models (membership $29/year):
Has solutions to MCM, HiMCM, and IMMC contests
Holly Zullo
Alli Carson