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Studies & Degrees in Analysis and Scientific Computing

Analysis and scientific computing is the part of applied mathematics that turns problems from science and engineering into equations and then solves those equations on a computer. Analysis supplies the theory: calculus, differential equations and the study of how well an approximate solution matches the true one. Scientific computing supplies the methods: numerical algorithms, programming and the use of parallel computers. Many universities teach the same field under the names computational science and engineering, numerical mathematics or applied mathematics.

TU Wien (Vienna University of Technology) describes computational science and engineering as a field that integrates numerical mathematics and computer science with the natural sciences and engineering to make efficient computer simulations possible. Applications range from fluid flow and acoustics to electronics, solid mechanics, chemistry and materials science.

What students learn

  • Mathematical analysis, linear algebra and ordinary and partial differential equations
  • Numerical methods: how to discretise an equation, solve large systems and estimate the error
  • Programming in languages such as C, C++, Fortran or Python, and algorithms and data structures
  • High-performance computing, from single workstations to computing clusters and supercomputers
  • Modelling in one or more application areas of physics or engineering

Qualifications and levels

The subject is seldom a bachelor's degree of its own. Students normally start with mathematics, physics, computer science or engineering and specialise at master's level.

  • Bachelor's degree. At TU Wien the bachelor's programme in Technical Mathematics takes six semesters and 180 ECTS credits, is taught in German and leads to a Bachelor of Science. There is no selection procedure, but applicants must complete a study preparation and reflection phase before admission.
  • Master's degree. TU Wien's master's programme in Computational Science and Engineering takes four semesters and 120 ECTS credits and is taught in English. Three compulsory modules (Computer Science, Scientific Computing and Applied Mathematics) are followed by a specialisation in fields such as computational fluid dynamics and acoustics, computational electronics, or computational chemistry and materials science, and by a thesis. The degree awarded is Diplom-Ingenieur (Dipl.-Ing.), which the university describes as internationally comparable with a Master of Science. The master's programme in Technical Mathematics, also four semesters and 120 ECTS credits, is taught in German and offers a specialisation in applied mathematics focused on modelling with differential equations and numerical simulation.
  • Doctorate. Research in analysis, numerical methods and simulation continues in doctoral programmes.

For comparison, official degrees in Spain are a bachelor's degree (grado) of 240 ECTS credits followed by a master's degree of 60, 90 or 120 ECTS credits.

Admission

Admission to the TU Wien master's in Computational Science and Engineering is possible with an eligible bachelor's degree from an accredited institution in Austria or abroad. A degree counts as eligible if it includes at least 30 ECTS credits of informatics and mathematics, including one programming language, linear algebra and calculus. For the master's in Technical Mathematics, the university may ask for supplementary examinations of up to 30 ECTS credits to make up for differences in previous study.

Where to study it

SpainExchange lists one active school under this subject: Vienna University of Technology (TU Wien), in Austria. Its Institute of Analysis and Scientific Computing, part of the Faculty of Mathematics and Geoinformation, has 19 research groups and more than 60 scientific staff, and teaches more than 150 courses per academic year. The institute also coordinates the master's in Computational Science and Engineering.

Language is the main practical point. The English-taught master's is open to students without German, while the bachelor's and the master's in Technical Mathematics require German. Similar programmes exist in other countries under the names listed above, so search for those as well.

Careers

Graduates work where simulation replaces or supports experiments: research institutes, engineering and software companies, and university research. TU Wien states that its graduates can pursue careers in applied research at universities, at non-university research institutions and in industry, including the development of simulation software for engineering and science.

The US Bureau of Labor Statistics groups this work with mathematicians and statisticians, who apply mathematical theories and techniques to practical problems in business, engineering and the sciences. They typically need at least a master's degree, and their employment is projected to grow 10 percent from 2025 to 2035.

Frequently asked questions

Is scientific computing the same as computer science?

No. Computer science studies computing itself. Scientific computing uses computers to solve mathematical models from physics, chemistry and engineering, and needs much more mathematics, especially analysis and numerical methods.

What background do I need for a master's in this field?

A bachelor's degree in mathematics, physics, computer science or engineering. TU Wien asks for at least 30 ECTS credits covering programming, linear algebra and calculus.

Can I study it in English?

Yes at master's level: the Computational Science and Engineering master's at TU Wien is taught in English. The bachelor's and master's programmes in Technical Mathematics there are taught in German.

How long does it take?

At TU Wien, six semesters for the bachelor's degree (180 ECTS credits) and four semesters for the master's degree (120 ECTS credits).