Princeton’s Ph.D. in Applied and Computational Mathematics is at the forefront of theoretical modeling and numerical computing. The following dissertation ideas enable deep exploration of partial differential equations, high-performance computing, and modern mathematical modeling frameworks.
Numerical Methods for Solving High-Dimensional PDEs in Finance
Mathematical Modeling of Infectious Disease Spread in Urban Networks
Error Estimation in Finite Element Simulations for Multiphysics Problems
Topology Optimization in Mechanical Structures Using Level Set Methods
Inverse Problems in Medical Imaging with Bayesian Inference
Sparse Matrix Techniques in Large-Scale Linear Algebra Systems
Stochastic Differential Equations in Quantitative Biology
High-Order Schemes for Turbulent Flow Simulations in Aerodynamics
Mathematical Theory of Deep Neural Networks Generalization
Spectral Methods for Climate Modeling and Prediction
Reduced Order Modeling for Parametrized PDEs in Real-Time Systems
Multigrid Methods for Solving Elliptic PDEs in Engineering Domains
Nonlinear Optimization Algorithms for Computational Neuroscience
Graph-Theoretic Approaches in Computational Social Sciences
Data-Driven Discovery of Governing Equations Using Sparse Regression
Numerical Stability of Discontinuous Galerkin Methods in Electromagnetics
Quantifying Uncertainty in Machine Learning Models with PAC Bounds
Computational Fluid-Structure Interaction in Biomechanics
Multiscale Modeling in Materials Science and Nanotechnology
Fast Solvers for Fractional Laplacian Operators in Image Processing
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