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Undergraduate Research-Math 444

WelchName: Larry Welch

Areas of Interest: Logic, Set Theory, Real Analysis, Complex Analysis, Topology

Description: There are many advanced functions, like the Jacobi elliptic functions or the sine integral, whose basic properties are within the abilities of an advanced undergraduate student to investigate. I would help a student to grasp the properties of one or two such functions, to understand their uses, and to develop some skill in applying them to mathematical and scientific problems. I would also encourage him or her to investigate similar functions that may arise in some problems but that may not be analyzed in the literature, with an eye to seeing if they are derivable from those under study. In the case of a really ambitious student I might suggest that one of these other functions become the main topic of research.

This research would lead to the production of a paper detailing what the student has learned. Besides the necessary rigorous mathematical analysis, it would entail the use of a computer algebra system to investigate the graphical properties of the functions, find particular values of them, and so on.