MS in Industrial Mathematics and Data Analysis 

at University of Bremen, Bremen

Besides the formal prerequisites for application, the following knowledge and skills must be available regarding the subsequent Bachelor studies:

• Experience in programming: python, Matlab, R, or something equivalent
• Sound knowledge in real analysis, multivariate calculus, and linear algebra (matrix theory)
• Ordinary differential equations: Peano’s theorem, Picard-Lindelöf’s theorem
• Lebesgue integration: L_p spaces, Lebesgue's dominated convergence theorem
• Functional analysis: Banach and Hilbert spaces, linear operators, weak convergence
• Probability theory: random variables, probability distributions, law of large numbers
• Numerical mathematics:
  • Linear systems: LU decomposition, iterative solvers (conjugate gradients)
  • Nonlinear equations and systems: Banach fixed-point theorem, Newton’s method
  • Interpolation and extrapolation
  • Numerical integration: Newton-Cotes formulas, Gaussian quadrature
  • Ordinary differential equations: Runge-Kutta methods
  • Approximation of derivatives by finite differences

The main requirements are as follows:

• a Bachelor's degree or other comparable undergraduate degree, with a minimum of 180 ECTS points
• proof, typically via the transcript of records, of at least 90 ECTS points in mathematics during the undergraduate degree programme
• proof of at least 24 ECTS points in a technical application subject or in computer science