What is LEMMA?

The Lab of Experimental Mathematics and Math Applications (LEMMA) is a semester long course mentored by a graduate student in the Department of Mathematics focused around a hands-on engaging project. Projects slated for the the Spring will be proposed at the end of the prior Fall semester, and Fall projects will be proposed at the end of Spring and once again in late Summer. Students can apply to a project by emailing the director at lemma@iu.edu, noting their project interests and any other information asked for in the project proposal. If accepted to LEMMA, Student have the opportunity to enroll in 2 credit hours of MATH-S 499, which counts as an honors research math course.

Who is LEMMA for, and why?

LEMMA is meant for any undergraduate student who is interested in the proposed projects! The goal each semester is to have projects which span a wide varieties of topics, with at least one project that does not require prerequisites. So, for any given semester, there should be a project for you! Given the hands on nature of LEMMA, students should have some self-motivation to solve problems and learn. Depending on the project, you might be able to get some simulation work done, add to your programming or art portfolio, write an undergraduate research paper, and more. What you get out of LEMMA is contingent of how much you put into the project.

LEMMA Obligations

Meetings and Coursework

During the first week of the semester, the mentor should reach out to schedule a time to meet with their student(s). Regular meetings should begin starting week 2 and should be around two hours per week. At the discretion of the mentor, students may be assigned up to an average of two hours of work to do outside of the meeting time per week. This work should not exceed 4 hours during any given week. How meeting time is used is up to the mentor. The following are examples of how instructors of the past have structured class:

• Students are assigned readings, then students present to and discuss with peers while the mentor guides the conversation and clarifies any confusion
• Meetings are structured like a standard lecture course
• Students are posed questions to work through with guidance. This could be work towards understanding a new topic or time spent on completing a project

Hands-on Projects

The main thing that distinguished LEMMA from other programs is the projects. The course should be split between learning the necessary background information needed to do a project, and the project itself. Projects can take many forms and the final format is ultimately at the discretion of the mentor. Some examples of projects types (with examples of past projects) include:

• Create illustrations of a mathematical concept (e.g., using 3D modeling and sculpting construct a model of a 4-dimensional sphere)
• Model or simulate (e.g., train AI models on PDEs to predict the rate of melting icecaps)
• Work on cases (e.g., solve cases to get data to find patterns in active research problems)
• Create manipulables (e.g., create modules to help compute grid homology of a knot)
• Expository Write-up (e.g., write up an expository account of graduate level topic or write up a proof for an undergraduate audience where a good exposition does not already exist)

Gatherings and Presentations

We have two required gatherings per semester where everyone taking LEMMA meet:

• Mid-semester Gathering: The goal in this gathering is for everyone to introduce themselves and the work they have done so far in the semester. Each LEMMA group gets a maximum of 3 minutes per person to let others know what math they are working on, what they have learned, and what they are planning to learn and do for the rest of the semester.
• End-of-semester Gathering: The goal is for everyone to summarize the work they have done and to let people know about their project. Each LEMMA group gets 5-8 minutes per person to present their work and the background material for that work. Note: The audience is the other LEMMA participants, so presentations should focus on the big picture and the intuition of the work rather than the details.

For More Information

Contact the graduate student director of LEMMA at lemma@iu.edu