12826 - Mathematical Data Science Modulübersicht

Module Number: 12826
Module Title:Mathematical Data Science
  Mathematische Grundlagen der Data Science
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. Hartmann, Carsten
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: On special announcement
Credits: 8
Learning Outcome:After successfully completing the module, students have deepened their knowledge of stochastics acquired in the basic modules. They know the  mathematical and statistical methods from data analysis. They have acquired basic skills for in-depth modules in stochastics or optimization. They have gained experience  in doing independent research.
Contents:Choice of the following topics
  • Concentration of random vectors in high dimensions
  • Concentration inequalities
  • Linear and nonlinear principal component analysis (PCA)
  • Random matrices
  • Sparse recovery (compressed sensing) and LASSO regression
  • Introduction to statistical learning
  • Kernel methods and Gaussian processes
  • Applications in signal and image processing, random networks, …
Recommended Prerequisites:Knowledge of the content of the modules
  • 11103 : Analysis I
  • 11104 : Analysis II
  • 11101 : Lineare Algebra und analytische Geometrie I
  • 11217 : Wahrscheinlichkeitstheorie
or very good knowledge of the content of the modules
  • 11113: Mathematics IT-2 (Linear Algebra)
  • 11213: Mathematics IT-3 (Analysis)
  • as well as of the content one of the modules
    - 11917 : Mathematik W-3 (Statistik)
    - 11926 : Statistik für Anwender
    - 11212 : Statistics
Mandatory Prerequisites:None
Forms of Teaching and Proportion:
  • Lecture / 4 Hours per Week per Semester
  • Exercise / 2 Hours per Week per Semester
  • Self organised studies / 150 Hours
Teaching Materials and Literature:
  • C.M. Bishop. Pattern Recognition and Machine Learning. Springer, 2006.
  • D.P. Dubhashi, A. Panconesi. Concentration of Measure for the Analysis of Randomized Algorithms, Cambridge University Press, 2009.
  • R. van Handel. Probability in High Dimension. Lecture Notes, Princeton University, 2016. 
  • R. Vershynin. High-Dimensional Probability: An Introduction with Applications in Data Science, Cambridge University Press, 2018
Module Examination:Prerequisite + Final Module Examination (MAP)
Assessment Mode for Module Examination:Prerequisite:
  • Successful completion of a semester project
Final module examination:
  • Project presentation, 45 min.
Evaluation of Module Examination:Performance Verification – graded
Limited Number of Participants:None
Part of the Study Programme:
  • Master (research-oriented) / Angewandte Mathematik / PO 2019
  • Master (research-oriented) / Artificial Intelligence / PO 2022
  • Abschluss im Ausland / Betriebswirtschaftslehre / keine PO
  • Master (research-oriented) / Environmental and Resource Management / PO 2011 - 2. SÄ 2017
  • Master (research-oriented) - Double Degree / Environmental and Resource Management / PO 2021
  • Master (research-oriented) / Environmental and Resource Management / PO 2021
  • Bachelor (research-oriented) / Informatik / PO 2008 - 1. SÄ 2017
  • Master (research-oriented) / Informatik / PO 2008 - 2. SÄ 2017
  • Master (research-oriented) / Informations- und Medientechnik / PO 2017
  • Master (research-oriented) / Künstliche Intelligenz Technologie / PO 2022
  • Bachelor (research-oriented) / Mathematik / PO 2019
  • Master (research-oriented) / Physics / PO 2021
  • Bachelor (research-oriented) / Wirtschaftsmathematik / PO 2019 - SÄ 2021
Remarks:
  • Study programme Angewandte Mathematik M.Sc.: Compulsory elective module in complex „Stochastics“ or in complex „Optimization “
  • Study programme Mathematik B.Sc.: Compulsory elective module in complex „Specialisation“, in limited extend 
  • Study programme Wirtschaftsmathematik B.Sc.: Compulsory elective module in complex „Specialisation“, in limited extend
  • Study programme  Informatik B.Sc.: Compulsory elective module in  „Applied Mathematics“ or in field of application „Mathematics“
  • Study programme  Informatik M.Sc.: Compulsory elective module in „Mathematics“ or in field of application „Mathematics“
  • Study programme  Informations- und Medientechnik M.Sc.: compulsory elective module in „Fundamental Methods“
  • Study programme Physics M.Sc.: Compulsory elective module in complex „Minor Subject“
Module Components:
  • Lecture: Mathematical Data Science
  • Accompanying exercise
Components to be offered in the Current Semester:
  • no assignment