MSc Computational and Applied Mathematics (CAM)

This master’s degree focuses on modern applied mathematics and scientific computing, aimed at students who want to use rigorous mathematical analysis or computational methods to predict phenomena or to optimise processes in science and engineering. In the early phase of the programme you build a solid foundation in mathematical modelling, applied analysis and high-performance computing, and learn to derive models while evaluating their assumptions and limitations.

From the second semester onward you specialise by choosing two of three fields: Modelling and Applied Analysis; Numerical Analysis and Simulation; and Optimisation. The compulsory elective courses (all taught in English) mirror the mathematical research at Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU). Course topics range from modelling, PDE analysis and numerical simulation in continuum mechanics (for example transport in complex multiphase flows and fluid–structure interaction), to multiscale analysis and mathematics for the life sciences, as well as many areas of mathematical optimisation such as shape optimisation, optimisation with PDEs and discrete optimisation.

The study plan also allows you to take additional master’s modules from across the university, so you can pursue interests beyond mathematics or deepen complementary skills. This combination of theory, numerical methods and high-performance computing prepares you for research projects, thesis work and careers or further study in computational science, engineering and applied mathematics.

Key features / requirements

• Language of instruction: English (all mandatory elective courses are taught in English)
• Initial curriculum: strong grounding in mathematical modelling, applied analysis and high-performance computing
• Specialisation: choose two of the three tracks — Modelling & Applied Analysis; Numerical Analysis & Simulation; Optimisation
• Course topics reflect FAU research: PDE modelling and analysis, numerical simulation in continuum mechanics, multiscale analysis, life-science mathematics, shape/PDE/discrete optimisation
• Flexibility to take master’s modules from elsewhere at the university to broaden or complement your studies
• Programme website: https://studium.math.fau.de/cam

This MSc is built around rigorous mathematical modelling and high-performance computation, taught across four semesters. In the first two semesters all students take two courses in modelling and analysis of continuum mechanics (15 ECTS), two courses on programming techniques and architectures for supercomputers (15 ECTS), plus a hands-on practical course in modelling, simulation and optimisation (5 ECTS). These core modules develop the ability to translate physical and engineering problems into mathematical models, analyse their properties, implement scalable numerical solvers, and run large-scale simulations efficiently.

Beyond the core, students select CAM-specific mandatory electives (40 ECTS) across the first three semesters and may add 15 ECTS of freely chosen Master’s-level courses from the university to broaden or deepen their profile. The fourth semester is devoted to the Master’s phase (30 ECTS): after preparation in a Master’s seminar, you carry out an individual research project and write the Master’s thesis within six months, finishing with a colloquium presentation. Each student is assigned a mentor from the Department of Mathematics who helps design a personalised study plan aligned with academic and career goals.

Curriculum at a glance (concise requirements)

• Core modelling & analysis (continuum mechanics): 15 ECTS (two courses) — semesters 1–2
• Programming techniques / supercomputer architectures: 15 ECTS (two courses) — semesters 1–2
• Practical course in modelling, simulation & optimisation: 5 ECTS — semesters 1–2
• CAM mandatory electives: 40 ECTS — semesters 1–3
• Free-choice Master’s courses (any university Master’s portfolio): 15 ECTS — semesters 1–3
• Master’s phase (seminar, thesis, colloquium): 30 ECTS — semester 4 (thesis completed within six months)

Key learning outcomes

• Formulate and analyse continuum-mechanics models with rigorous mathematical tools.
• Design, implement and optimise numerical algorithms for large-scale simulations on high-performance computing platforms.
• Apply simulation and optimisation techniques in practical, project-based contexts.
• Conduct independent research, document results in a Master’s thesis, and communicate findings in a scientific colloquium.

For the full module catalogue and detailed course descriptions, consult the official course webpage: https://studium.math.fau.de/cam

Graduates acquire a combination of theoretical and practical skills—mathematical modelling, numerical simulation, optimisation and high‑performance computing—suitable for careers in R&D, engineering firms, computational science teams, software companies, finance and data‑driven industries. The programme also provides a solid foundation for doctoral studies in applied mathematics, scientific computing or related interdisciplinary fields.

The strong emphasis on practical HPC skills and research experience (Master’s project) makes alumni attractive to employers seeking specialists who can design and implement scalable computational methods for complex engineering and scientific problems.