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Studies & Degrees in Computational Methods

Computational methods are the mathematical and programming techniques used to solve scientific and technical problems on a computer: numerical analysis, algorithms, simulation and the handling of large data sets. As a field of study it usually appears under the names scientific computing, computational science or computational science and engineering. Carnegie Mellon University (CMU) defines scientific computing, "sometimes called computational science", as the application of high-performance computers and modern computational technologies to problems in the sciences and engineering.

The Technische Universität München (TUM) describes the field as one that brings together applied mathematics, especially numerical analysis, computer science, and scientific or engineering applications. Its purpose is practical. According to TUM, numerical simulations supplement experiments and make it possible to examine systems that would be too time-consuming, expensive or dangerous to study by experiment alone.

What students learn

TUM lists the skills that detailed simulations require: mathematical modelling, numerical analysis, efficient algorithms, computer architecture, software design and implementation, validation, and visualisation of results. A typical programme therefore combines three blocks:

  • mathematics: numerical methods, differential equations, linear algebra, statistics
  • computing: programming, parallel and high-performance computing, data structures, machine learning
  • an application area, such as physics, mechanics, fluid dynamics, biology or finance

The application area gives each programme its character. The master's degree in Numerical Methods in Engineering of the Universitat Politècnica de Catalunya (UPC) trains students in computational mechanics, with subjects such as finite elements and numerical methods for partial differential equations. At CMU, the B.S. in Computational Biology includes a course on computational methods for biological modelling and simulation.

Qualifications and levels

  • Bachelor's level. Computational methods are rarely a first degree on their own. Students normally meet them inside a degree in mathematics, physics, computer science or engineering, or as an added option. CMU, for example, offers a minor in Scientific Computing whose curriculum spans the natural sciences, mathematics, programming and research. Degrees that apply computation to one science also exist: the CMU B.S. in Computational Biology requires a minimum of 360 units under the university's own unit system.
  • Master's level. This is where most specialised programmes are found. The M.Sc. in Computational Science and Engineering at TUM takes four semesters of full-time study and has 120 ECTS credits. The M.Sc. in Computational Mechanics at the Universität Duisburg-Essen also lasts four semesters and has 120 credits. The UPC master's degree has 120 ECTS credits over two academic years; UPC states that it no longer admits new students for 2026-27 and has been reformulated as the master's degree in Computational and Data-Assisted Engineering (CODE). In Spain, official master's degrees have 60, 90 or 120 ECTS credits under Royal Decree 822/2021.
  • Doctorate. Research in numerical methods and simulation continues at PhD level. UPC notes that the scientific training of its master's degree also allows graduates to go on to a doctoral degree.

Master's programmes are aimed at graduates of technical degrees. TUM addresses its programme to engineering, science or mathematics graduates and selects candidates through an aptitude assessment.

Where to study computational methods

SpainExchange lists 11 active schools for this subject: three in Spain, two in the United States, two in Germany, and one each in Australia, Bermuda, Switzerland and Sweden. They include the Universidad Autónoma de Madrid, the Universitat Politècnica de Catalunya, Carnegie Mellon University, the Technische Universität München, the Universität Duisburg-Essen, ETH Zurich, Uppsala Universitet and the Australian National University.

English is common at master's level: both the TUM programme and the UPC master's degree are taught in English. This is not a general rule, so the language of instruction should be checked for each programme, together with the language certificate asked for at admission.

Costs differ widely between countries and between resident and international students. As one example, TUM states that tuition fees for international students from third countries are 6,000 euros per semester for this programme (checked in October 2026), and that many international students can have them waived or receive scholarships.

Careers

Graduates work wherever problems are solved by calculation and simulation: engineering and technology companies, research laboratories, software development, data analysis, finance and universities. Typical roles are simulation engineer, numerical analyst, research software developer and data scientist.

Official statistics do not treat computational methods as a separate occupation, but two related groups give an indication for the United States. The Bureau of Labor Statistics (BLS) describes mathematicians and statisticians as professionals who analyse data and apply computational techniques to solve problems, and projects their employment to grow 10 percent from 2025 to 2035. For computer and information research scientists it projects growth of 22 percent over the same period. BLS adds that both groups typically need at least a master's degree.

Frequently asked questions

Can I study computational methods as a bachelor's degree?

Rarely as a degree of its own. It is usually part of a degree in mathematics, physics, computer science or engineering, or a minor such as the Scientific Computing minor at Carnegie Mellon University. Specialised programmes are mostly master's degrees.

What background do I need for a master's degree?

A first degree in engineering, science or mathematics is the usual requirement; TUM, for example, addresses its programme to graduates of those fields. Programming experience and a solid base in calculus and linear algebra are needed from the first semester.

How long does a master's degree take?

The programmes at TUM and at the Universität Duisburg-Essen take four semesters and have 120 credits. In Spain, official master's degrees have 60, 90 or 120 ECTS credits.

Are these programmes taught in English?

Often, but not always. The TUM master's degree is taught in English, and so is the UPC master's degree in Numerical Methods in Engineering. Check the language of instruction of each programme before applying.