Cost & earnings at Indiana University Bloomington What students borrow here, and what they go on to earn
The PhD in Mathematics with a focus on Computational Mathematics at Indiana University Bloomington is a research-led doctoral programme for students who want to develop advanced numerical and algorithmic tools for modelling, simulation and data-driven science. It suits students with a strong background in pure and applied mathematics who seek careers in academic research, high-performance computing, or industry roles that require deep expertise in numerical analysis and scientific computing.
The PhD in Mathematics (Computational Mathematics) combines rigorous coursework in analysis and algebra with specialised training in numerical methods, scientific computing and algorithm design. Early years are typically devoted to core graduate courses such as real analysis, functional analysis, and advanced linear algebra alongside specialised classes in numerical analysis, partial differential equations, numerical linear algebra, approximation theory, and scientific computing. Students also take electives drawn from computer science, statistics, and engineering to support interdisciplinary research.
Beyond formal courses, the programme emphasises independent study, research seminars and reading courses tailored to your dissertation topic. You will work closely with a research advisor to develop and execute an original research project, usually culminating in a written dissertation and an oral defence. Common research areas include numerical solution of PDEs, computational linear algebra, high-performance scientific computing, uncertainty quantification, optimisation, and computational aspects of inverse problems and data assimilation.
Training also covers practical skills such as software development for scientific computing, use of high-performance computing resources, reproducible numerical experimentation, and the communication of technical results through publications and conference presentations. Teaching experience is typically available through graduate teaching assistantships.
Applicants should hold a strong undergraduate degree in mathematics or a closely related field; many applicants also hold a master’s degree. A solid grounding in undergraduate real analysis, linear algebra, differential equations and basic numerical analysis is expected. Prior coursework in advanced calculus, probability and computational methods is advantageous.
Application materials usually include academic transcripts, a statement of purpose describing research interests and fit with faculty, a curriculum vitae, and letters of recommendation from academic or professional referees. International applicants must demonstrate English proficiency according to the university’s requirements. Competence in programming and familiarity with numerical computing environments will strengthen an application.
Graduates with a PhD in Computational Mathematics pursue a wide range of careers. Many continue in academic research and teaching at universities and research institutes. Others join national laboratories or research centres working on large-scale simulation, modelling and data assimilation projects. In the private sector, alumni find roles in quantitative finance, data science, machine learning, software development for scientific computing, engineering simulation, and industries that require advanced numerical modelling such as energy, aerospace and pharmaceuticals.
The combination of theoretical training and practical computational skills also prepares graduates for leadership roles in interdisciplinary teams, research & development groups, and technology start-ups where rigorous numerical methods and high-performance computing are central.
Indiana University Bloomington has a long-established Department of Mathematics that offers a collaborative environment for both pure and applied research. The department’s faculty include researchers active in computational and applied mathematics, enabling students to find supervision in a variety of numerical and algorithmic areas. Interdisciplinary collaboration is encouraged across campus with departments such as computer science, statistics, engineering and the sciences.
PhD students benefit from access to campus computing resources and support for high-performance computing, as well as from a vibrant seminar and colloquium programme that brings national and international researchers to campus. Graduate teaching and research assistantships provide financial support and professional development. The Bloomington campus offers a strong academic community and opportunities to engage in collaborative projects that bridge theory, computation and application.
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