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.
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