Combinatorics:

- Binomial coefficients,
- applications (e.g. complete brackets),
- sieve formula, application: counting prime numbers,
- counting mappings, words,
- counting injective mappings, permutations,
- counting surjective mappings, applications (e.g. partitions of sets), equivalence relations,
- partitions of numbers,
- multisets,
- equivalence classes of mappings.

Stochastics:

- probability spaces,
- discrete distributions (e.g. binomial, Poisson),
- continuous distributions (e.g. normal, exponential),
- conditional probability, Bayesian formula, independence,
- random variables, expected value and variance,
- independence of random variables, covariance and correlation,
- applications (for example, runtime analysis of Mergesort and Quicksort),
- Markov inequality, Hoeffding inequality,
- weak and strong law of large numbers,
- central limit theorem,
- Markov chains, hidden Markov models,
- Monte Carlo simulation, simulation of distributions, application (e.g. Monte Carlo ray tracing).

Statistics:

- estimating parameters,
- confidence interval,
- testing hypotheses,
- tests for expected value,
- adaptation test, independence test,
- application (e.g. pseudo-random numbers),
- linear regression.