Teaching: Data Science: Numerische Methoden (lecture+exercises)

Overview

• 4 SWS (2h lecture + 2h exercises), credits: 6
• See StudIP for details on time and place.
• The lecture is held in hybrid format, i.e. it can be attended in person or online and recordings will be made available. Interactive participation in the lecture is strongly encouraged.
• The solution to the weekly exercise sheets will be discussed in hybrid sessions.
• There will be the option for a weekly in-person discussion session where students are encouraged to ask questions.
• Lanuguage: German (English optional)

Target audience / what to expect?

This lecture will provide a basic overview on numerical methods for modern data science. This will cover aspect such as complexity and numerical stability. We will usualy skip proofs and focus on intuition and practical relevance. It is aimed at students of computer science and data science at the bachelor level. A preliminary requirement is a basic understanding of linear algebra and (finite-dimensional) analysis. As we will closely follow the lecture material with computational examples, familiary with scientific computing environments will help. For this we will rely mostly on Python. All examples can be run on the GWDG jupyter cloud.

Tentative list of topics

• algorithms on graphs (shortest path, spanning tree)
• efficient and numericaly stable solution of linear systems, matrix decompositions, fast Fourier transform
• numerical optimization (gradient descent, Newton's method, stochastic methods, linear programming, automatic differentiation)
• basic notions of space and time complexity analysis

Literature

(This list will be expanded)

• Cormen et al.: Introduction to Algorithms, MIT Press
• P. Deuflhard, A. Hohmann: Numerical Analysis in Modern Scientific Computing, Springer
• J. Nocedal, S. J. Wright: Numerical Optimization, Springer