As an educator I get to work with hard-working students who are creative and willing to tackle ill-posed problems with messy data sets and complex dynamics. These students are a rare breed and it is a privilege spending eight weeks with them tackling a difficult problem. They need to learn a lot of mathematics that normally does not get covered until graduate school and they need to learn how to become a mathematical researcher in a very short timeframe. Furthermore, they need to take this newly attained skill set and assimilate it into their problem-solving abilities to address the REU problem they have selected. It is gratifying, as an educator, to work with students through this process and witness their development from inchoate to adept researcher in a compressed time interval. I am proud to be an instrumental part of their education.
As a researcher I am part of a larger team of collaborators from a variety of fields so I get several benefits from such an arrangement. Mathematicians, even those of us from the applied variety, do not often get to work with such an assortment. Typically we may work with a pair of collaborators such as a software developer and a scientific specialist. However, in the case of the LAKES REU, I am working with economists, anthropologists, sociologists, biologists, limnologists, and geographers. The benefits are manifold: (1) learning how each field solves problems offers me perspectives that push my problem-solving creativity (2) leveraging the expertise and abilities of these researches has enabled my team to advance our solution (3) helping these other teams has strengthened our problem-solving toolkit and (4) sharing results with these groups has led to questions that have sharpened our focus and made our applied mathematics more applicable. An added benefit has been that, as an intellectually curious person, I simply get to converse with people who have developed a tremendous expertise in their field and they share their knowledge and uncertainties with me.
As a citizen I am grateful that our community and nation are putting forth the resources to solve difficult problems and support budding researchers to attend graduate school and become the leaders and problem-solvers of our next generation. It is the current and previous generation’s responsibility to educate and inspire those that follow because our world is filled with problems that need solving. We need each other. Young researchers need our mentoring and we need them to carry on the work for ourselves and our children.
What do I learn from my students?
I have gained a lot of practical knowledge from them and I am grateful my students have been patient and hard-working through this process. These problems are complex and large in scope. It is very difficult, if not impossible, for me to attain perfect command of all the parameters and nuances of each process. Our problem, for example, requires us to model and understand a lake’s temperature dynamics, irradiance profile as a function of depth, turbulence, and morphology. Additionally, we need to model and understand the population dynamics of microcystis aeruginosa and their processes for producing chlorophyll. Then we need to model and understand how the dynamics of the chlorophyll concentration in the lake which brings us back to the lake’s physics mentioned earlier. We are modeling and simulating all of these processes for predictive and analytic purposes. I am an applied mathematician which means that I am not a limnologist, biologist, or water-quality specialist. But I know how to leverage the power of mathematics to create a functioning and applicable modeling and simulation toolkit for this problem. My students have taught me some of these processes and they have taught me the relevance or, in some cases, irrelevance of the model’s parameters. They have reminded me of values and have clarified dynamical processes.
Personally I learn how to be a better researcher from my students. They are bright and inquisitive so they ask tough questions which I struggle to answer. But working through these answers has crystallized my thoughts on the mathematics and the science of our problem. These questions also help me to sharpen my researching skills. It is through this dialectic process that I learn to distinguish between relevant and irrelevant processes and parameters. When a team is solving a problem they can easily get mired down in, at worst, canards or, at best, worthless details. But having my students present, to ask questions and to teach me some of the details they have learned, teaches me how to stay focused and how to discern the important from the extraneous. A sardonically enjoyable part of this relationship is that, as a mentor, I get to be the “backseat driver” and navigate our team through the problem. Daily I tell them to “turn here” or “you hit a dead end, put it in reverse” or “go forward, faster!” This relationship has resulted in much good-natured chiding, loads of sarcasm, and a heap of hilarity that I will miss when this experience is finished.