# University of Utah Math Modeling Workshop

Can roads be designed to reduce road rage? Where are the optimal locations for ambulance dispatches so that the most number of people are served in the least amount of time? How do infectious diseases spread and what are the most effective containment mechanisms?

In this workshop, students will be introduced to the fundamental ideas of mathematical modeling that can be used to tackle the three questions just posed (and more!). Particular topics include the mathematical modeling process, basic statistical ideas, as well as programming and doing data analysis in Python (no prior experience necessary!).

During this workshop students will have the opportunity to work in small groups to practice developing models to real world problems, as well as gain valuable experience presenting their models by writing up and presenting their work to their peers.

Students that take part in this workshop will be well prepared for two national math modeling competitions: (1) the High school Mathematical Competition in Modeling (HiMCM), a two-week long competition in November 2021, and (2) the Mathworks Math Modeling (M3) Challenge, a day-long competition that takes place in February 2022; students are welcome to attend without the intent of competing.

More about the HiMCM can be found on the COMAP website: https://www.comap.com/highschool/contests/himcm/index.html

More about the M3 Challenge can be found on the SIAM website: https://m3challenge.siam.org

There is no cost to take part in this workshop.

An information session was held on Wednesday, September 1st at 6pm, giving an overview of this workshop. The slides used can be found here: https://docs.google.com/presentation/d/1l2GSbQ9MRfp-cFO7yJcAKVlWS_y0X5qSJ8J0yI_Lfrs/edit?usp=sharing

After registering, you will receive a confirmation email containing information about joining the meeting.

# Math Modeling Workshop

**Intended audience**: high school students, and motivated middle school students. The M3 Challenge is open to juniors and seniors, HiMCM is open to any high school students, and the HiMCM and MiMCM (middle school version) are open to middle school students.- Please complete the Liability Waiver Form and email the pdf file to hsmathmodeling@math.utah.edu.
**To register**: please fill out this form to register for this workshop.

The workshop will meet once a week for two hours (except during university holidays). Generally the workshop will be split into two approximately hour long parts, with a short break in the middle:

- Active lecture on an aspect of math modeling, programming/data analysis, statistics, etc. Designed to introduce students to core topics in math modeling.
- Group work, in which students break into teams and practice developing models/brainstorming approaches, or analyze winning solutions to previous competitions.
- Since 1 hour is not much time to dive in deep with a problem, early problem solving sessions will focus on brainstorming approaches and developing a plan for if they had more time to work on the same problem. Later problem solving sessions (maybe after Fall break) may focus on the same problem across multiple weeks, to help prepare students for the HiMCM.
- Only one or two solution analysis sessions are necessary, to help point students towards what is important to look for, how to effectively skim a solution, etc. After later sessions, solutions will be given to students to read on their own time if they wish.

- Students will be able to apply general modeling principles to real world problems:
- Defining the mathematical problem statement, making assumptions, and defining variables,
- Building the model,
- Analyzing and assessing the model.
- Students will use Excel spreadsheets and the Python programming language to analyze data and run simulations to develop and support their mathematical models.
- Students will be able to apply basic statistical tools and tests to support their models.
- Students will be able to read, analyze, and identify strong aspects of model reports. As a case study, students will analyze winning solutions to previous HiMCM and M3 competitions and compare and contrast the models different teams implemented.
- Students will utilize good writing and presentation practices to report their models to peers.

Week 1 (Sep. 6 - Sep. 10): An overview of **the math modeling process**, along with a guided problem solving session to help students get comfortable with
the math modeling process.

Week 2 (Sep. 13 - Sep. 17): An introduction to **basic programming and Python** principles, with code, using google Colab.

Week 3 (Sep. 20 - Sep. 24): An **introduction to data analysis**, data types, and effectively using Excel and Python to analyze data.

Week 4 (Sep. 27 - Oct. 1): An introduction to the **SIR disease spread model**, **difference equations**, and **differential equations**. No calculus background will be required.

Week 5 (Oct. 4 - Oct. 8): A discussion of **ways to measure error**, and measure “**stability**” of models.

Week 6 (Oct. 11 - Oct. 15): FALL BREAK

Week 7 (Oct. 18 - Oct. 22): An introduction to **linear regression, correlation, and some other fundamental statistical ideas** that are important in model assessment.

Week 8 (Oct. 25 - Oct. 29): An overview of typesetting softwares, as well as **good writing****practices **(organization, grammar, etc.).

Week 9 (Nov. 1 - Nov. 5): contest starts!

- SIAM has free workbooks on Mathematical Modeling available on their website.
- Resources from a previous iteration of this workshop can be found here.
- An entirely online introduction to Python can be found at W3 schools (via the “Try it yourself” sections).
- An introduction to Google Colab notebooks and their Python environment can be found here.

For more information about the program, please contact: hsmathmodeling@math.utah.edu