13639 - Mathematical Foundations of Data Science Modulübersicht

Module Number: 13639
Module Title:Mathematical Foundations of Data Science
  Mathematische Grundlagen der Datenwissenschaft
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: Every winter semester
Credits: 8
Learning Outcome:After completing the course, the students are able to apply statistical learning methods to justify conclusions drawn from data. They are familiar with fundamental properties, assumptions, limitations of the considered methods and their derivation.
Contents:
  • Linear Regression
  • Empirical Risk Minimization
  • Model Assessment and Model Selection
  • Bias-Variance Decomposition 
  • Bayesian Decision Theory 
  • Naïve Bayes Classifier 
  • Linear Classifiers
Recommended Prerequisites:Good command of basic linear algebra, analysis and probability theory is recommended, e.g. as taught in the modules
  • 11103: Analysis I
  • 11104: Analysis II
  • 11101: Lineare Algebra und analytische Geometrie I
  • 11217: Wahrscheinlichkeitstheorie
    or 11917: Mathematik W-3 (Statistik)
    or 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:
  • Trevor Hastie, Robert Tibshirani, Jerome Friedman: The elements of statistical learning: data mining, inference, and prediction. Springer, 2009.
  • Philippe Rigollet, Jan-Christian Hütter: High-Dimensional Statistics, Lecture Notes, MIT, 2023. 
  • Stefan Richter. Statistical analysis of machine learning algorithms, Lecture Notes, Universität Heidelberg, 2020.
Module Examination:Prerequisite + Final Module Examination (MAP)
Assessment Mode for Module Examination:Prerequisite:
  • successful completion of a homework

Final module examination:

  • written exam, 90 min.
Evaluation of Module Examination:Performance Verification – graded
Limited Number of Participants:None
Part of the Study Programme:
  • Master (research-oriented) / Mathematical Data Science / PO 2025
Remarks:
  • Study programme Mathematical Data Science M.Sc.: Mandatory module
Module Components:
  • Lecture: Mathematical Foundations of Data Science
  • Accompanying exercises
  • Related examination
Components to be offered in the Current Semester:
  • no assignment