Level 0
The topics at this level are usually taught somewhere before university.
Calculus
- Limits
- Derivatives
- Integration
- Partial derivatives
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
- Matrix rank
- The determinant
- Matrix inverse
- Eigenvalues and -vectors
- Singular value decomposition
- Pseudo-inverse
- Quadratics
- Abstract linear algebra
Level 2
Topics generally covered in the later parts of BSc programs.
General
- Axiomatic set theory
- Numbers revisited
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 no longer covered in organized educational formats, but rather in research articles or materials aimed at working scientists.
Information theory
- Kolmogorov complexity