Level 0

The topics at this level are usually taught somewhere before university.

General

Terminology

Calculus

Linear algebra

  • Basic linear algebra
  • Dot products
  • Matrix multiplication

Level 1

These are topics covered in the early years of most BSc programs.

General

Calculus

  • Taylor series

Linear algebra

Level 2

Topics generally covered in the later parts of BSc programs.

General

Linear algebra

  • The spectral theorem
  • The fundamental theorem of algebra

Level 3

Topics generally covered in MSc programs.

Information theory

  • Entropy
  • Mutual information
  • Kulback Leibler divergence

Machine learning

  • Group convolutions
  • The graph Laplacian

Level 4

Topics that are usually not covered in university courses, but rather in research articles or materials aimed at working scientists.

Information theory

  • Kolmogorov complexity