PhD/EngScD Applied Mathematics at Columbia University

Programme overview

The PhD/EngScD in Applied Mathematics covers applied and computational mathematics methods with applications in physics, engineering, bioengineering, biophysics and the social sciences. Research areas include deterministic and stochastic PDE analysis, numerical analysis, large-scale scientific computation, fluid dynamics, dynamical systems, inverse problems and algorithms for data and machine learning. It prepares students to work as researchers, independently or collaboratively, with emphasis on mathematical modeling, analysis and computation.

Faculty: Columbia Engineering | Department: Applied Physics and Applied Mathematics | Study mode: full-time | Location: New York, NY, United States

What you will study

Core courses include Applied Linear Algebra, Applied Analysis, Dynamical Systems, Applied Functional Analysis, Partial Differential Equations, Applied Stochastic Analysis, Analytic Methods for PDEs and Numerical Analysis of PDEs, with numerical methods courses and specialisation courses in physics, computer science, earth sciences and mathematics.

Official programme page

Application information

Entry requirements

Columbia Engineering graduate admissions (faculty level): bachelor's degree from an institution of acceptable standing; application with transcripts, three letters of recommendation, personal statement and resume/CV; GRE not required for the 2026 admission cycle and scores not penalised when omitted (Physics GRE is required for the Applied Physics doctoral track; not required for Medical Physics); applicants whose bachelor's degree is from a country other than Australia, Canada, Ghana, Ireland, Kenya, New Zealand, Nigeria, Singapore, the UK or the US submit one English test (TOEFL iBT, IELTS Academic, PTE Academic or Duolingo), with no minimum score set; application fee $85. Note: MS is the usual route to the PhD/EngScD in Columbia Engineering.

Requirements published at faculty level.

Tuition is charged per credit, so the total depends on the modules you register for each year. Current fees are listed in the official fee schedule.

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