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Modulbeschreibung - Detailansicht

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Moduldetails
Mathematische Modelle in der Biologie
Fakultät für Mathematik
TUMAFMA
9
1
1
MA3601
Zuordnungen zu SPO-Versionen
Lehrveranstaltungen und Prüfungsveranstaltungen
Beschreibungen
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Allgemeine Daten (Modulhandbuch)
Master
Einsemestrig
Wintersemester
Englisch
Arbeitsaufwand (Work Load)
270
90
180
Studien- und Prüfungsleistungen
The module examination is based on a written exam (60-90 minutes) or an oral exam (20-30 minutes). Students have to understand basic analytic, stochastic and discrete structures to model biological systems and can evaluate the connection of different results related to different model approaches. They are able to choose the appropriate models.
N
J
Beschreibung
MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra and Discrete Structures 1, MA1102 Linear Algebra and Discrete Structures 2, MA1401 Introduction to Probability Theory
Bachelor 2019: MA0001 Analysis 1, MA0002 Analysis 2, MA0004 Linear Algebra 1, MA0005 Linear Algebra 2 and Discrete Structures, MA0009 Introduction to Probability Theory and Statistics
After successful completion of the module, the student is able to evaluate the connection of different results related to different model approaches (stochastic/deterministic, discrete/continuous) and to choose the appropriate level for the description of the system under observation. Furthermore they are able to formulate mathematical models for biological systems on the basis of analytic, stochastic or discrete mathematical structures.
Introduction in theory and application of dynamical systems and stochastic processes: linear compartmental models, Markov-chains, Galton-Watson processes, birth-death-processes, population models, spatial models and age structured models.
The emphasis of the module is to teach the understanding of the importance for different model approaches for one single biological system.
lecture, exercise course, self-study assignments
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.
blackboard
J.D. Murray, Mathematical Biology. Springer-Verlag, 3rd ed. in 2 vols.:
Mathematical Biology: I. An Introduction, 2002;
Mathematical Biology: II. Spatial Models and Biomedical Applications, 2003;
P. Jagers: Branching Processes With Biological Applications. Wiley, London 1975
Modulverantwortliche*r
Johannes Müller (johannes.mueller@mytum.de)