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. Fall projects will be proposed at the end of Spring and once again in late Summer. You can apply to a project by emailing the director at lemma@iu.edu, noting your project interests and any other information asked for in the project proposal. If accepted to LEMMA, you will have the opportunity to enroll in 2 credit hours of MATH-S 499, which counts as an honors research math course.

Who can take the LEMMA course? 

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, you 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 will reach out to schedule a time to meet. Regular meetings should begin starting week 2 and last approximately two hours per week. At the discretion of the mentor, you 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. The meeting structure is determined by the mentor. The following are examples of how instructors of the past have structured class:

• Students are assigned readings that they present and discuss with peers while the mentor guides the conversation.
• Meetings are structured like a standard lecture course.
• Students are provided questions to work through with guidance. This could be focus on understanding a new topic or or on completing a project.

Hands-on projects

The main thing that distinguishes LEMMA from other programs are hands-on projects. The course is 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 an expository account of graduate level topic or a proof for an undergraduate audience where a good exposition does not already exist)

Gatherings and presentations

We have two required gatherings per semester for LEMMA particpants:

• Mid-semester gathering: During this session, students and mentors introduce themselves and share their semester's work. Each LEMMA group has 3 minutes per person to explain the math topics they are working on, what they have learned, and what they plan to accomplish for the rest of the semester.
• End-of-semester gathering: At the end of the semester, participants summarize their work and explain their project to the other groups. Each LEMMA group gets 5-8 minutes per person to present their work and the background material for that work. Note: The audience is other LEMMA participants, so presentations should focus on the big picture and the intuition of the work rather than the details.

For more information

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