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 Mathematics has a dual nature: it is a gathering of beautiful ideas as well as
an array of tools for practical problems. It can be appreciated aesthetically for
its own sake and also applied towards understanding how the world works. I
seek to engage students in discussing and contemplating both aspects of math-
ematics so that they can appreciate the art and apply the analysis inherent in
mathematical thought.
My philosophy is that teaching should involve both lecture and guided discov-
ery.I generally begin a class by reminding the students of something they have
seen in the past, and then develop the new topic based on their previous knowl-
edge. Because it is essential that the students grapple with each concept on their
own, I almost always have a period during class for discussion or practice. I try
to close each class period by indicating how the material will progress. During
the past 7 years I have instructed a variety of mathematics and statistics classes
as a teaching assistant, as an Instructor and as a mentor.
I have observed that as mathematics surrounds us in our daily lives, and a
well-trained student can nd pleasure in picking out these occurrences. Thus I
choose illustrations and exercises that are related to other elds or to natural
and cultural objects. In an ordinary calculus class, when hyperbolic functions
are introduced, we compute the length along the side of the St. Louis Gateway
Arch”, which has the shape of a catenary hyperbolic cosine. At Texas A&M uni-
versity, in my business calculus classes, I have designed an optimization project
where groups of students work together to maximize the volume of a box they
make from a piece of foam and the winner group gets to present their solution
to class for extra credit. Based on the idea of my research, in dierential equa-
tions class, I involved my students in inspecting a simple physical model of rigid
body motion and its integrability and in linear algebra class we talked about
nding its critical points of rank 1. When teaching college algebra in Collin
college, since more than 50% of classes are dual credit high school students,
I use videos and games to keep students engaged. On the other hand, in my
lecture when discussing slope, I dene derivatives and their applications brie
and ask students to solve an approachable problem related to it. The same goes
with the concept of limits when teaching graphing functions with asymptotes.
My purpose is twofold: to prepare those students who wish to take calculus and
to provide a basis for informed scientic discussion among those who do not.
Students’ feedback during the course has indicated that they found the material
both challenging and benecial. Several of them did continue to take Calculus
or minor in mathematics or physics, even though the students in this particular
class would not normally be expected to do so.
In University of Wisconsin-Eau Claire, I have had the pleasure of teaching more
advanced math classes such as Complex Analysis. I looked into my own past
and I realized, math majors get excited about the history behind a theorem
so, I prove any theorem with a short biography of the mathematician involved
in proving it. Also, by introducing students to several MATLAB commands,

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