PhD in Applied Mathematics - Applied Analysis and Partial Differential Equations in Ithaca United States | Cornell University

Graduate study options cover all specialization areas represented by over one hundred faculty members across multiple disciplines. These professors come from fourteen departments spanning the College of Engineering, College of Arts and Sciences, College of Agriculture and Life Sciences, and the Samuel Curtis Johnson Graduate School of Management. Students can further broaden their studies through minor subject selections. The Applied Mathematics program admits graduate students with diverse educational backgrounds that include substantial mathematical training, typically accepting only PhD candidates. The program currently has approximately forty students and generally takes four to five years to finish.

Natural phenomena frequently manifest through nonlinear partial differential equations (PDEs) or optimization problems, forming the foundation of mathematical analysis. Applied analysis uniquely balances theoretical development with practical problem-solving, creating a mutually beneficial relationship between mathematical modeling and analytical techniques. For instance, precise existence theorems can validate or challenge a model's predictive accuracy, while understanding solution discontinuities in differential equations enables the creation of hybrid analytical-numerical approximations that outperform conventional discretization methods.