Indiana University

What you'll study

The programme emphasises numerical methods, scientific computing, and the mathematical foundations of computation applied to problems in science, engineering and data. Core topics typically include numerical linear algebra, numerical solutions of differential equations, approximation theory, and error analysis. Students also study algorithms for large-scale computation, optimisation, and computational statistics or data analysis, depending on elective choices.

Teaching is delivered through a mix of lectures, seminars and computer-based laboratories. Typical modules and subject areas you can expect are:

• Numerical Linear Algebra — iterative and direct methods, stability and conditioning, eigenvalue algorithms for large matrices.
• Numerical Solution of Differential Equations — finite-difference and finite-element methods, time-stepping schemes, stability and convergence.
• Scientific Computing — parallel computing, high-performance algorithms, implementation concerns and profiling.
• Approximation and Interpolation — polynomial and spline approximations, spectral methods.
• Optimisation and Inverse Problems — deterministic optimisation, regularisation techniques for ill-posed problems.
• Computational Probability and Statistics (elective) — Monte Carlo methods, stochastic simulation and uncertainty quantification.
• Project/Thesis — an applied research project or thesis that typically involves substantial computational work, often in collaboration with faculty across mathematics, computer science or domain sciences.

Students can usually tailor the programme by choosing electives from computational science, applied mathematics, computer science and statistics. The department supports access to campus research computing resources for experiments at scale.

Structure

The programme is typically completed through a combination of coursework and a research component. Options generally include a thesis route for students intending to pursue doctoral study and a non-thesis route that emphasises coursework and a capstone project. Full-time completion normally spans multiple semesters, while part-time study is often accommodated.

Entry requirements

Applicants are expected to hold a recognised undergraduate degree in mathematics, applied mathematics, or a closely related discipline such as physics, engineering or computer science with substantial mathematics content. Typical preparation includes courses in calculus, linear algebra, differential equations and an introductory course in numerical analysis or scientific computing.

Admissions commonly consider a strong academic record, letters of recommendation, a personal statement describing research and computational experience, and prior programming experience (for example in C/C++, Python, MATLAB, or similar). Where relevant, applicants may be asked to demonstrate quantitative readiness through transcripts or by submitting sample work. International applicants must meet English language requirements as set by the university.

Career prospects

Graduates with a master’s in computational mathematics are well placed for roles that require mathematical modelling, algorithm development and computational implementation. Typical career paths include:

• Quantitative analyst or model developer in finance and risk management.
• Data scientist or machine learning engineer in technology and industry.
• Scientific programmer and computational researcher in engineering, climate science, bioinformatics or physics.
• Software developer focused on numerical libraries, simulation tools or high-performance computing.
• Continuation to PhD study in applied mathematics, computational science or related disciplines, leading to academic or advanced research careers.

Employers value the programme’s emphasis on rigorous analysis combined with practical computational skills; many graduates find roles in industry, government labs and research institutes, or continue into doctoral programmes.

Why study at Indiana University

Indiana University’s Department of Mathematics offers a strong community in applied and computational mathematics with faculty working on numerical analysis, scientific computing and interdisciplinary applications. The university provides access to substantial research computing infrastructure and collaborative centres that support computational research across disciplines.

Students benefit from opportunities to work with faculty on interdisciplinary projects, links with computer science and engineering units, and access to seminars and workshops that connect academic research to industry challenges. The Bloomington campus environment and research facilities create a setting well suited to students who want a rigorous mathematical education with hands-on computational experience.