Given that we do not know exactly where animals will go, how do we set up a network of sensors to track them?
I managed a group of four undergraduates through a semester-long research project concerning the placement of sensors in an environment where the travel patterns of animals is unknown. My responsibilities included:
- defining the scope of research and breaking goals down into explicit deliverables,
- overseeing timeline of research progress, keeping students on deadline,
- developing outlines of software and clearly defined what their contributions would be.
We chose to define a problem that everyone had some shared interest in and that would be relevant to Distance Geometry (the topic of the Math Clinic that semester). I limited the problem to a two-dimensional environment with no obstructions so that the computational complexity would be manageable. If enough ground-work was laid in this stage, additions to the problem complexity would accelerate.
Owing to the limited background of the students, our approach mostly focused on how to turn the problem constraints into a properly-posed optimization problem, and then learn how to use numerical solvers to arrive at feasible solution sets. I ensured they were given reading to help guide their studies and implementation, but did very little hands-on mathematical work, focusing instead on management and editing final submissions.
At the end of the semester, we presented results to the class, demonstrating some basic approaches rooted in optimization and discussed how extensions could be made in the context of inverse problems.