Physical Sciences and Mathematics Commons^™

Elegance Or Alchemy? An International Cross-Case Analysis Of Faculty And Graduate Student Perceptions Of Mathematical Proofs, Brooke Nicole Denney

Masters Theses

Artist Marcel Duchamp once said, ``The painter is a medium who doesn’t realize what he is doing. No translation can express the mystery of sensibility, a word, still unreliable, which is nonetheless the basis of painting or poetry, like a kind of alchemy" (Moffitt, 2012). Just as there is a puzzling aspect of creating art or writing poetry, the aesthetic quality of mathematical proofs is a mysterious and ill-defined concept. Like many other subjective terms, it can be difficult to reach a consensus on what elegance means in a mathematical context. In this thesis, I try to better understand faculty …

Numerical Methods For Stochastic Stokes And Navier-Stokes Equations, Liet Vo

Doctoral Dissertations

This dissertation consists of three main parts with each part focusing on numerical approximations of the stochastic Stokes and Navier-Stokes equations.

Part One concerns the mixed finite element methods and Chorin projection methods for solving the stochastic Stokes equations with general multiplicative noise. We propose a modified mixed finite element method for solving the Stokes equations and show that the numerical solutions converge optimally to the PDE solutions. The convergence is under energy norms (strong convergence) for the velocity and in a time-averaged norm (weak convergence) for the pressure. In addition, after establishing the error estimates in second moment, high …

Mathematical Modeling Suggests Cooperation Of Plant-Infecting Viruses, Joshua Miller, Vitaly V. Ganusov, Tessa Burch-Smith

Chancellor’s Honors Program Projects

No abstract provided.