Columbia University

What you'll study

The Master’s in Applied Mathematics combines core mathematical theory with computational practice to address real-world problems. Typical course topics include partial and ordinary differential equations, numerical analysis and scientific computing, real and complex analysis, linear and nonlinear dynamical systems, optimisation, probability and stochastic processes, mathematical modelling, and computational methods for high-dimensional data. Electives often let students specialise in areas such as computational fluid dynamics, inverse problems, numerical linear algebra, machine learning and statistics, or mathematical biology.

The programme usually offers flexible pathways: a coursework track focused on advanced classes and electives, and a research/project track that culminates in a substantial capstone project or master's thesis under faculty supervision. Courses emphasise both rigorous theoretical understanding and practical implementation: students commonly complete programming-based assignments, develop simulation codes, and use contemporary software and high-performance computing resources.

Entry requirements

Applicants are expected to hold a bachelor’s degree in mathematics, applied mathematics, engineering, physics, computer science or a closely related quantitative discipline. A strong foundation in calculus, linear algebra, differential equations and basic real analysis is required; coursework or experience in probability, numerical methods and programming is strongly recommended.

Typical application materials include academic transcripts, a statement of purpose outlining mathematical and research interests, two or three letters of recommendation from academic or professional referees, and a current CV. International applicants must demonstrate English language proficiency through an accepted test unless exempt. Admissions committees evaluate preparation and fit rather than specific numeric cut-offs; some applicants may present prior research experience, publications or relevant industry work.

Career prospects

Graduates of the programme move into a broad range of careers that demand strong quantitative and computational skills. Common destinations include quantitative analysis and algorithm development in finance, data science and machine learning roles in technology companies, modelling and simulation positions in engineering and energy sectors, and research or technical roles in biotech and pharmaceutical firms. The programme also prepares students for doctoral study in applied mathematics, computational science or related interdisciplinary fields. Employers value the programme’s combination of theoretical depth and practical programming experience.

Why study at Columbia University

Columbia offers access to leading researchers across mathematics, engineering, computer science and the physical sciences, encouraging interdisciplinary collaborations that are central to applied mathematics. Located in New York City, students benefit from proximity to a dense network of industry partners in finance, tech and biotech for internships and projects. The university provides modern computational facilities, regular seminar series and opportunities to engage with faculty research groups.

Columbia’s career services and alumni network further support transition to employment or doctoral study, while the department’s emphasis on both rigorous analysis and practical computation equips graduates to tackle challenging quantitative problems in research and industry.