Data Science Lab, University of Bern, 2025
Prepared by Dr. Mykhailo Vladymyrov.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License
Summary¶
Main content is currently provided solely as interactive live discussion. We look at a few of more commonly used mathematical concepts in Data Science, such as vector spaces, probability & distributions, frequency domain, and differential calculus. Specifically, we look at those form the perspective of Data Science, and how they can be used in practice to and how we can think of them in a more intuitive way.
These notebooks are primarily for running the visualizations and the exercises.
To keep track of the topics suggested for the discussion, in this notebook is also given this list of topics:
linear algebra (with DL in mind) - vector space:
vectors - linearity, basis, “good” basis, freedom of parametrization,
dot products - length and direction, mse
projection
matrices as list of vectors, mat mul, rotation
(O) basis change, pca
metric space - MSE
tensors
statistical distributions
distributions: uniform, normal, etc;
metrics: mean std mode, momenta space, AuC = 1
distributions proximity: Entropy, KL distance, Wasserstein distance
likelihood
number of samples in the dataset and model performance
frequency domain
sine, cosine
Fourier transform
trends
differential calculus:
slope
equilibrium - 4 types of zero
how to calculate the slope in practice
and how to use it