Mathematics for data science - Einzelansicht

After the course the students will be familiar with the fundamental concepts of data science. The participants can analyse given data sets with respect to dimensionality reduction and clustering. They also know the basic structure of neural networks and support vector machines to solve classification tasks. The participants know relevant methods from linear algebra and optimization and can apply these techniques. This embraces the design of appropriate algorithms and the implementation of different numerical methods to solve the corresponding problems. 

R.A. Horn, C. R. Johnson Matrix Analysis, Cambridge Univ. Press 2013

D.A Simovici. Mathematical Analysis For Machine Learning And Data Mining-World Scientific, 2018.  M.P. Deisenroth, A. A. Faisal, C. S. Ong, Mathematics for Machine Learning. Cambridge University Press 2021. D.A Simovici. Linear Algebra Tools for Data Mining. World Scientific, 2013. C.C. Aggarwal. Neural networks and deep learning: a textbook. Springer 2018.

Examples of complex dynamics. Models for dynamical systems in continuous and discrete time. Computer simulation. Control and Feedback. Stability, stabilization, and Lyapunov functions. Coupled systems: Disturbance or Cooperation? Networks of systems. Consensus. Synchronization.   

The topics will be presented in a lecture, deepened by exercises. Some of the exercise include computer programming and simulation.

B. Sc.; Analysis and Linear Algebra at Bachelor level, knowledge of Matlab or Python

1 written exam

“Complex dynamics”

                120 min (100%) / SuSe + WiSe