![]() Taking advantage of my software development background, I have collected problems with a familiar quality around which I could build a compelling mathematical narrative. Summer 2015 - Math 6B Vector Calculus and Intro to PDEs (37 students, survey)Īs detailed by the survey results, 69-87% of students in each course responded with the top rating when asked to ``rate the overall quality of the instructor's teaching." This compares with the department average over time of 42% for graduate student instructors.Summer 2014 - Math 6A Vector Calculus (74 students, survey).Spring 2013 - Math 6A Vector Calculus (129 students, survey).These goals are shaped by having instructed three classes at UCSB: Finally, I strive to build accessible interdisciplinary mentoring networks, in particular through my position in the UCSB Student Chapter of the SIAM. Second, I structure my courses to encourage students with a diverse array of learning styles to spend the time necessary to master computational aspects of the material, to absorb the ``how". First, I share problems-both mathematical and applied-which build intuition and inspire students to integrate the course material into the broader context of their education, to convey the ``why". In my teaching and service I aim for three goals, each of which addresses an aspect of this definition. My teaching philosophy is encapsulated by the following definition: Learning is the iterative process of asking and answering questions. ![]() I will speak about the quasilinear results during the upcoming Joint Mathematics Meetings in Seattle. I have also identified potential research projects related to my dissertation work which are suitable for undergraduates. More generally, smoothing effects play a crucial role in the well-posedness and control theory of nonlinear dispersive equations, topics which I intend to pursue in future research. Ponce, we demonstrated the result for a family of quasilinear KdV-type equations. However, propagation of regularity does not depend on the equation being completely integrable or even having constant coefficients. Segata, we extended this propagation of regularity phenomenon to equations in the KdV hierarchy. For the Korteweg-de Vries (KdV) equation, it was recently shown that appropriate regularity present in the initial data on the positive, or right, half-line travels to the left with infinite speed. My dissertation research focuses on smoothing properties of solutions to dispersive nonlinear partial differential equations. Journal of Dynamics and Differential Equations, arXiv:1502.01796 Smith, Propagation of regularity and persistence of decay for fifth order dispersive models. Smith, On the regularity of solutions to a class of nonlinear dispersive equations, submitted for publication October 2015.
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