Focus on Technomathematics in the master's program in Applied Mathematics

Mathematical methods are used in many modern technical products and processes. For example, communication networks and the protocols running on them are represented by graph-theoretic structures and algorithms, while chemical, biological as well as engineering processes are often described by systems of differential equations. The material behavior of components is modeled by partial differential equations; engineering logistics is no longer possible without solving large integer optimization problems. Graph-theoretical methods based on differential equations and calculus of variations as well as optimization methods are also used in image processing and imaging; furthermore, methods from statistics and data analysis, numerics and harmonic analysis and approximation theory are used there. Thus, in technomathematics one studies mathematical methods that find their application in many technical problems.

The following overview shows examples of what is hidden behind some frequently occurring technical buzzwords in everyday life:

Technical keyword

Everyday applications

heat conduction

building services, insulation, CPU cooling

electromagnetic waves

mobile communications, satellite communications, aircraft engineering

mechanical waves

material strength, earthquake detection, seismic imaging

fluid dynamics

wastewater treatment, turbine engineering, oil production, weather simulation

population dynamics

population growth, spread of diseases

Graph theory

networks: road traffic, utility routes, data traffic, internet

waves and radiation

medical imaging: CT, X-ray, mamography

Celestial mechanics

planet motions, space probes, space stations

Virtual Reality

computer games, animation, visual effects

Technomathematicians first translate a problem into the language of mathematics, that is, into formulas and equations. This translation is a crucial step in the development process, because the better the model reflects reality, the more precise the results will be in the end. A mathematical model is often time-saving and cost-efficient compared to time-consuming and sometimes unfeasible practical experiments. The computational solution thus obtained on the basis of mathematical analyses and simulations is translated back into reality by the technomathematicians and checked to what extent the results reflect reality.

The detailed typical work steps of technomathematicians can be described as follows:

  1. Mathematical model building: Translation into the language of mathematics; finding an approach.
  2. First model analysis: plausibility of the model; if necessary simplification of the model
  3. Deeper model analysis: solvability of the model and uniqueness of the solution; model properties
  4. Model discretization and computer implementation: computability and simulation
  5. Analysis of the discretization: convergence statements
  6. If necessary, comparison of results with laboratory experiments
  7. Conclusions from analysis and simulation to reality

At the interface between mathematics and technology, technomathematicians therefore need a sound basic and specialized knowledge of mathematics as well as a good understanding of technology. In addition, knowledge of computer science, especially programming, is required. Technomathematicians are in great demand in research and development departments in industry as a link between mathematics and engineering.

The Technomathematics emphasis in the Master's Degree program in Applied Mathematics

The requirement for designation of the Technomathematics concentration is met if three elective modules, one project seminar, and the master's thesis from this concentration have been completed. Among others, the following elective modules assigned to Technomathematics are offered on a recurring basis:


from Mathematics:

introduction to finite methods, finite methods in applications, inverse problems, mathematical methods of strength theory, queueing theory, event time and reliability analysis, numerical methods of data and signal processing.

from Photonics and Machine Vision:

system theory of image processing, algorithms of image processing, system theory of optics, computer vision, robot vision, application and development of optical systems, microoptics

from Mechanical Engineering:

engineering mechanics 2, engineering mechanics 3, fluid mechanics, machine dynamics, control engineering, multibody systems and structural dynamics.