Mathematical Foundations of Data Science

This interactive resource companion supports the Mathematics of Data Science course taught at the University of Vienna, exploring core mathematical foundations essential for modern data science tools and methods. The course emphasizes both theoretical understanding and practical implementation of key algorithms.

Course Modules

The course revolves around six foundational topics, and the interactive demonstrations were crafted accordingly.

Machine Numbers

Floating point systems · Machine precision

Data Compression

Huffman coding · DCT · JPEG standard

Image Processing

Edge detection · Denoising · Enhancement

High-Dimensional Analysis

Concentration phenomena · JL Lemma

Dimensionality Reduction

SVD · PCA · Kernel methods

Learning & Clustering

SVM · Graph cuts · Validation

About This Project

This project leverages:

  • Python to implement mathematical concepts
  • Gradio to construct explorative user interface over the pure Python implementation of concepts
  • Pyodide to hydrate the Gradio user interfaces written in Python inside your browser using WebAssembly
  • Quarto to generate this website from the Jupyter Notebook sources

flowchart LR
  A[Jupyter Notebook Written] --> B[Quarto Rendering Process Run]
  B --> C[Custom Quarto Notebook Filter Processes Source Notebook]
  C --> D[Gradio-lite HTML Added]
  D --> E[HTML File with Gradio-lite Bundle Generated]