Columbia University

What you'll study

The Applied Mathematics programme emphasises both theoretical foundations and practical computation. Core coursework typically covers multivariable calculus, linear algebra, ordinary and partial differential equations, real analysis and probability. Students build computational fluency through numerical analysis, scientific computing, and courses using MATLAB, Python or C++ for simulation and data processing.

• Foundations: calculus sequence, linear algebra, proofs/analysis.
• Modelling and analysis: ordinary differential equations, partial differential equations, dynamical systems.
• Computational methods: numerical linear algebra, numerical solution of PDEs, scientific computing.
• Probability and statistics: probability theory, stochastic processes, statistical inference and applied statistics.
• Advanced electives: optimization, machine learning, computational biology, mathematical finance, fluid dynamics, and topics in applied analysis.
• Capstone / research: students often complete a senior thesis or independent research project supervised by faculty; many take part in summer research or departmental research groups.

Students may combine the major with electives from computer science, engineering, economics or the physical sciences to tailor the degree toward data science, quantitative finance, or engineering applications. Cross-registration and interdisciplinary opportunities allow practical experience with datasets, lab work and internships in New York City.

Entry requirements

Admission to Columbia is competitive. Successful applicants to the Applied Mathematics programme typically present a strong secondary-school record with substantial preparation in mathematics (including calculus and, where available, multivariable calculus or advanced problem-solving courses), and often one or more STEM subjects such as physics or computer science. Evidence of programming experience is an asset.

• Academic record: high achievement in mathematics and quantitative subjects.
• Preparation: courses in calculus and algebra; experience with proof-based mathematics is advantageous for advanced theory courses.
• Supplementary material: strong teacher recommendations (preferably from mathematics or science teachers), a personal statement describing quantitative interests and experience, and any relevant project or competition experience.
• Notes: Columbia considers the whole application; applicants from different secondary systems should consult the university for guidance on equivalencies and credit for advanced exams.

Career prospects

Graduates with an Applied Mathematics degree from Columbia enter a broad range of careers where quantitative modelling and computation are central. Typical destinations include:

• Data science and machine learning roles in technology firms, startups and research labs.
• Quantitative analyst or risk management positions in finance and insurance.
• Software engineering and algorithm development.
• Consulting that requires mathematical modelling and analytics.
• Research and development in biotechnology, engineering firms and government labs.
• Further study: many graduates pursue graduate programmes in applied mathematics, statistics, computer science, engineering or finance (Masters and PhD).

The programme’s emphasis on both theory and computation, combined with Columbia’s location, supports strong internship and recruiting opportunities across New York’s finance, tech and biotech sectors.

Why study at Columbia University

Columbia offers Applied Mathematics within a world-class research environment in New York City. Students benefit from access to faculty who work across pure and applied mathematics, data science, physics and engineering, and from interdisciplinary institutes such as the Data Science Institute. Columbia’s campus location provides ready access to internships, collaborators and employers in finance, technology and industry.

• Research and mentorship: opportunities for undergraduate research and faculty-supervised theses.
• Interdisciplinarity: ease of combining mathematics with computer science, engineering, economics or the life sciences.
• Professional networks: strong ties to industry partners and alumni in New York City for internships and graduate pathways.
• Resources: computing facilities, seminar series, and student organisations focused on applied and computational mathematics.

Overall, Columbia’s Applied Mathematics degree is suited to students who want a rigorous mathematical education with practical, computational and interdisciplinary options in one of the world’s major academic and professional centres.