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Studies & Degrees in Scientific Computing

Scientific computing is the use of mathematical models and computers to solve problems in science and engineering that cannot be solved by hand. Numerical analysis is its mathematical core: the design and study of algorithms that give approximate but reliable answers to equations. Together they make it possible to simulate the weather, the air flow around an aircraft, a chemical reaction or a financial market. The field is also known as computational science.

Students learn three things at once: mathematics (linear algebra, differential equations, approximation and optimisation), programming for large computations, and the science or engineering field in which the methods are applied. The Computational Modeling and Simulation programme of the University of Pittsburgh shows this mix. Its students take courses in numerical methods, computer science and scientific computing, and also meet the requirements of a traditional discipline such as physics, chemistry, bioengineering, economics or mathematics.

Qualifications and levels

Scientific computing is mainly a graduate subject. Undergraduates usually reach it through a degree in mathematics, computer science, physics or engineering that includes numerical courses.

  • Bachelor's degree. A mathematics degree usually includes calculus, differential equations and linear and abstract algebra; numerical analysis and programming courses build on these. In Spain an official bachelor's degree (grado) has 240 ECTS credits.
  • Master's degree. The University of California San Diego runs Computational Science, Mathematics and Engineering (CSME), a campus-wide interdisciplinary M.S. and Ph.D. programme. Its stand-alone M.S. is meant for scientists and engineers who want specialised training in computational science but do not plan a doctorate. The University of California, Davis offers an M.S. in Applied Mathematics. Official master's degrees in Spain have 60, 90 or 120 ECTS credits.
  • PhD. At the University of Pittsburgh, the Department of Mathematics offers Master of Arts, Master of Science and Doctor of Philosophy degrees, and numerical analysis and scientific computing is one of its research areas. The university also has a separate Computational Modeling and Simulation PhD programme. At UC San Diego the CSME Ph.D. is integrated into the doctoral programmes of the participating departments. UC Davis offers a Ph.D. in Mathematics or Applied Mathematics.

Where to study it

SpainExchange lists three active schools for scientific computing, all in the United States: the University of Pittsburgh in Pennsylvania, and the University of California San Diego (La Jolla) and the University of California, Davis in California. Teaching is in English.

Admission works differently in each programme. At Pittsburgh, applicants to the Computational Modeling and Simulation PhD apply through one of three schools, depending on their area of concentration, and the application deadline is 15 January. At UC San Diego the M.S. and the Ph.D. have separate application and admission procedures. UC Davis describes admission to all its mathematics graduate programmes as competitive and highly selective.

When comparing programmes, look at the computing resources students can use, the fields of application on offer and the home department of the degree. Pittsburgh, for example, states that its students use the university's Center for Research Computing, and its mathematics department lists research in large-scale scientific computing and supercomputing, computational fluid dynamics and turbulence.

Careers

Graduates work as computational scientists, numerical analysts, simulation engineers, research software engineers and data scientists. Employers include research laboratories, universities, engineering and energy companies, finance and the technology sector.

The US Bureau of Labor Statistics has no separate category for this field. It projects employment of mathematicians and statisticians to grow 10 percent from 2025 to 2035, and employment of computer and information research scientists to grow 22 percent in the same period. Both groups typically need at least a master's degree, which matches the graduate focus of the programmes above.

Frequently asked questions

What is the difference between numerical analysis and scientific computing?

Numerical analysis is the mathematics of approximation algorithms: how accurate, stable and fast they are. Scientific computing applies those algorithms on computers to real problems in science and engineering. Most programmes teach both.

Can I study scientific computing as a bachelor's degree?

Usually not as a separate degree. Most students take a bachelor's degree in mathematics, computer science, physics or engineering and specialise at master's or PhD level, as in the programmes of the three universities listed here.

Do I need to know programming before I start?

Programming is part of the training, and graduate programmes expect a solid base in mathematics and some computing experience. Ask each programme for its exact prerequisites.

Where can I study scientific computing?

SpainExchange lists the University of Pittsburgh, the University of California San Diego and the University of California, Davis. All three teach it at graduate level and in English.