1. 1 Mike Sinclair Kalamazoo Area Mathematics & Science Center University of Notre Dame Random walks A tutorial for the tutorial!

2. 2 Random walks Welcome to the University of Notre Dame Center for Biocomplexity Random Walks tutorial. The primary audiences of these tutorials are high school students and undergraduates. However, teachers, researchers in related fields, and non- specialists are certainly invited to work through some of the tutorials as well; because you never know what you’re going to uncover that may be new and inspiring.

3. 3 Random walks This is the opening page for the Random Walks tutorial. Follow the links in the Venn diagram (at upper left of the screenshot) to work through the tutorial. Each step of the tutorial is designed for ease of operation. Feel free to explore without having to follow some specific order and please give each of the simulations (found in the Try it! section) several good runs.

4. 4 Random walks Under the How it works section, there are three activities for students to try. These are (1) a one-dimensional problem, (2) a two-dimensional problem, and (3) a simple computer simulation using NetLogo™. NetLogo is free and can be downloaded at ccl.northwestern.edu/netlogo. NetLogo also comes with a complete tutorial package as well.

5. 5 Random walks An example of a screenshot from the Running the model section shows what a simple two-dimensional random walk looks like. There are five models to test, each one increasingly complex. Finally, there is a Monte Carlo simulation that shows students how to calculate π using a series of random walks.

6. 6 Random walks One of the last steps in the tutorial is a link that allows students to either print out a copy of their work or email it to the instructor. The form is accessible as both a Word document or a PDF file.

7. 7 Random walks Good luck and enjoy the tutorial!