Department of Mathematics and Philosophy

Undergraduate Research - Analysis (Real, Complex, and Nonstandard)


Ealy Clifton Ealy

Areas of Interest: Logic, Algebra, Group Theory, Nonstandard analysis

Description: I would invite students to take an undergraduate class they enjoyed and attempt to deepen their understanding of that subject by pursuing a project that picks up where the class leaves off. Such a project could explore connections of that subject to other subjects, or applications of that subject, or just explore the same subject from a different standpoint. For example, a student who had enjoyed Math 421 (Group Theory) could explore connections between group theory and graph theory. Or such a student's project might deal with the applications of group theory to cryptography or error correcting codes. A student who had enjoyed Math 435 (Real Analysis) might study how the subject could be developed using infinitesimals rather than epsilon-delta proofs.

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Lia Petracovici Lia Petracovici

Areas of Interest: Real Analysis, Complex Analysis, Dynamical Systems, and Differential Equations

Description: Some possible topics for undergraduate research would be chaotic dynamical systems (what are some different definitions of a chaotic dynamical system? how can we prove that these definitions are equivalent?), fractals (how do they arise? how can we produce fractals on the computer?), and visualizing conformal mappings of the complex plane. I would be happy to work with interested students to find other projects of interest to them.

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