## 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