Repetition of linear algebra

Vector spaces, matrices and systems of linear equations, norms.

Eigenvalues of the matrix

Characteristic polynomial, eigenvalues and their calculation, definite and semi-definite matrices.

Matrix decompositions - decompositions of matrices

Choleského, QR decomposition, SVD decomposition.

Introduction to optimization tasks

Introduction to the general optimization problem, demonstration of linear and quadratic programming.

Combinatorics and graphs

Repetition of concepts from combinatorics and graphs, corresponding characteristics and algorithms for their determination.

Complexity of algorithms

Algorithmic complexity, definition of classes P and NP, basic examples of algorithms and their complexity, Cook's theorem and its consequences.

Solving complex problems

Examples of problems and their approximation, method of branches and boundaries, local search and more.

Approximation solution of relaxation problems

Introduction to information theory

Introduction to information theory, random variable, random process, Markov chain, measure of information and entropy.

Combined quantities

Combined degree of entropy and information, mutual information and its determination, conditional mutual information.

Autoregression model

Definition of autoregression model and its use, error of autoregression model.

Causality

Granger causality, conditional mutual information, introduction to Bayesian networks.