Title

  • Advanced Topics in Mathematics and Natural Sciences

Courses

  • Mathematics methods of biosciences III (Lectures and Excercises)
  • Mathematical biology (Lectures)

Responsible person

Contents

This module is dedicated to the mathematical and biological foundations for the advanced study of bioinformatics and genome research. In `Mathematical methods of biosciences III', selected topics of Fourier analysis (in particular Fourier series and Fourier transform) and stochastics (in particular stochastic processes: Poisson process, Markov chains in continuous time) are presented.

In `Mathematical biology', a selection of fundamental models in biology will be presented. Some of them belong to the core of genome research (like the Luria-Delbrueck experiment, the coalescent process, and geometric models for DNA), others build the bridge to biophysics (like the Hodgkin-Huxley model for the action potential) and biochemistry (kinetic models for (bio)chemical reactions). The mathematical methods used are stochastics, differential equations, discrete mathematics, and geometry.

Skills

Students learn to understand and apply the  named mathematical concepts, and they get to know a representative selection of mathematical models for biological, biochemical and biophysical processes. Furthermore, emphasis is on the modelling aspect, that is, the translation of the real-life process into a suitable idealisation and mathematical formulation.

Number of achievements

2 graded examinations

Forms of examination

  • Winter and summer term: a Portfolio of Exercises (Pass: 50% of the achievable points, individual demonstration of exercises) and written test (90-120 min) or oral examination(20-30 min). The exercises as part of this portfolio will usually be handed out weekly. The Written test or oral exam are about the Lectures and Exercises.

Conditions for ECTS acquisition

Participation in the Exercises and passing of the Portfolio: 5 ECTS each

Workload and ECTS

Mathematics methods of biosciences III: 150 h
Mathematical biology: 150 h

Total: 10 ECTS

Prerequisites

Mathematics for Computer Scientists I and II, Mathematical methods of biosciences I and II

Type and usability

Module for the Master's course

  • Bioinformatics and Genome Research
  • Naturwissenschaftliche Informatik (Additional Basics or Advanced Natural Sciences)

Duration

Winter term: Mathematics methods of biosciences III
Summer term: Mathematical biology
every year