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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,