## Proposal for my senior paper in Applied Mathematics

**Numerical Solution of Parabolic Partial Differential Equations with Applications to Finance:**

The student will investigate the convergence, stability, and robustness of finite difference methods for linear parabolic partial differential equations in one, two, and three space dimensions. These numerical methods have important applications in the mathematical modeling of many financial instruments, including the Black-Scholes theory of options pricing. The scientific package MATLAB will be used for symbolic and numerical calculations, and for programming and visualization.