Mathematical logic

Mathematical statement and statement formula, logic conjunctive, tautology, inference rules (modus ponens, generalization rule), mathematical proof.

Relations

Binary relations, relation qualities, (partial) ordering, equivalence, equivalence classes.

Diagram and its representation

Key terms (peak, edge, sub-diagram, sequence, path, circle), (non)oriented diagram, diagram isomorphism, (non)continuous diagrams.

Euler diagrams and tree diagrams

Closed Euler diagram, tree diagram, diagram frame, diagram algorithm examples.

Linear equation sets

Matrix representation of a set, gradient form, Gauss elimination, regressive substitution.

Arithmetic vectors and matrices

Gigit vectors, matrix, matrix multiplication, transposed matrix, square matrix, inverse matrix, matrix determinant, Crammer’s rule for solving sets.

Vector and linear space

Abstract vector space, vector operations, linear combinations, linear dependence and independence, bases, dimensions, matrix rank, Frobenius theorem.

Finite prime bodies

Solving equations in these bodies, RSA algorithm.

Linear representation

Defining linear representation, its matrix, basis change, proper numbers and vectors, applications.

Scalar product

Scalar product, orthonormal basis, singular matrix decomposition, vector product and its application to analytical geometry.

Linear programming task

Types of assignments, mathematical model formulation, key terms, graphical solution, possibilities of ending, interpretation.

Simplex method

Distinguishing the single-phase and biphasic simplex method, interpretation of the single-phase method (the use of a simplex chart), optimization test. Relation between simplex method and matrix calculation.