Columbia University

What you'll study

This interdisciplinary undergraduate programme brings together core mathematics and computer science. Students typically take foundational coursework in calculus, linear algebra, discrete mathematics and probability alongside computer science fundamentals such as programming, data structures, algorithms and computer architecture. As you advance, modules commonly include real analysis, abstract algebra or advanced linear algebra on the mathematics side, and courses in algorithms and complexity, operating systems, compilers, databases, machine learning and systems or networking on the computer science side.

The curriculum emphasises both theory and practice: problem sets and proofs develop mathematical maturity, while programming assignments, labs and projects develop implementation skills. Many students undertake a senior project or honours thesis, participate in research with faculty in areas such as theoretical computer science, cryptography, machine learning, numerical analysis or scientific computing, or take project-based electives that culminate in capstone work.

• Core mathematics: calculus sequence, linear algebra, discrete mathematics, probability and statistics, real analysis or advanced proof-based courses
• Core computer science: intro programming, data structures, algorithms, systems courses (operating systems, architecture), theory of computation
• Advanced electives: machine learning, databases, computer graphics, cryptography, numerical methods, optimization
• Research, independent study or senior thesis/capstone project
• Opportunities for cross-disciplinary study with fields such as statistics, economics, engineering and the natural sciences

Entry requirements

Admission to Columbia is competitive and looks for strong academic preparation across the curriculum. Successful applicants typically present excellent grades in mathematics and quantitative subjects, coursework beyond the minimum where available (for example, advanced mathematics, computer science, or IB/A-levels), and evidence of analytical and problem-solving ability. Prior programming experience is helpful but not always required; applicants often demonstrate this through coursework, personal projects, programming competitions or online portfolios.

Typical application elements include secondary-school transcripts, teacher recommendations (preferably including a mathematics or science teacher), a personal statement or essays, and any standardised tests if submitted according to the university's testing policy. For transfer applicants or those coming from other tertiary institutions, a record of strong college-level mathematics and computing coursework is expected.

Career prospects

Graduates with a combined mathematics and computer science degree are in demand across a wide range of sectors. Common career paths include software engineering, data science and analytics, machine learning engineering, quantitative analysis in finance, systems engineering, cybersecurity, and roles in consulting or product management. The programme also provides a solid foundation for graduate study in computer science, mathematics, statistics or related engineering disciplines.

Columbia students frequently take internships and full-time positions with technology companies, financial firms, startups and research institutions. The mathematical training also opens opportunities in research labs, government and industry roles that require strong modelling, optimisation and theoretical reasoning skills.

Why study at Columbia University

Columbia offers this programme in the context of a major research university with a distinctive undergraduate Core Curriculum that broadens intellectual perspective while allowing deep technical study. Located in New York City, the university provides access to a vibrant technology and finance ecosystem, plentiful internship opportunities and collaborations with industry partners. Students benefit from faculty who are active researchers across theoretical and applied areas, as well as research centres and institutes that support interdisciplinary work.

The university’s resources include computing facilities, project labs and numerous student organisations and hackathons that foster practical experience and community. Small seminars, opportunities for undergraduate research, and formal advising help students tailor their course of study toward academic, industry or entrepreneurial goals.