1. Propositional and predicate logic: proposition, compound proposition, propositional form, propositional formula, quantifiers, negation, language of mathematics. 2. Axiomatic systam of mathematics: axiom, mathematical definition, mathematical theorem (logical implication), types of proofs of mathematical theorems. 3. Basics of set theory and binary relations: set and its definition, relations between sets, operations with sets; relation and its graphical representation, selected properties of relations, equivalence relation, arrangement relation. 4. Number fields: natural, whole, rational, irrational and real numbers (motivation for expanding the field of natural numbers and outlines of the principle of constructions); operations with them, absolute value, supremum, infimum. Prime numbers, divisibility, decompositions, greatest common divisor, least common multiple (Euclid's algorithm). 5. Number systems: types of number systems, expression of the natural number in the number system, abbreviated and extended notation. Number notation conversions between systems with different bases (grouping, successive division algorithm), numerical operations in systems with different bases. 6. Algebraic expressions and their modifications: powers with a rational exponent and operations with them. Polynomials (definition and operations with polynomials), algebraic formulas. Logarithms (definition and operations with logarithms). Modifications of algebraic expressions. 7. Elementary functions: (linear, linear curve, quadratic, power, exponential, logarithmic and trigonometric functions) overview of definitions of elementary functions, their graphs and properties. Polynomial and rational functions, power functions with a rational exponent, parametric systems of functions, cyclometric functions. Transformation of graphs of functions, functions with absolute value. 8. Equations and inequalities: definition of concepts (equation, equality, domain of an equation, domain of a variable, equivalent adjustments), solution of individual types of equations and inequalities, numerical and graphical solutions, equations and inequalities with absolute value (linear, quadratic, equations and inequalities with parameters) . Irrational equations, more demanding exponential, logarithmic and trigonometric equations and inequalities even with an absolute value and their systems. 9. Systems of equations and inequalities: definition of terms, systems of linear equations with two and three unknowns, matrix notation and discussion of solvability, systems of linear inequalities. Selected systems of equations (logarithmic, exponential, irrational). 10. Combinatorics and probability: definition of basic concepts of combinatorics and probability (combinatorial rules of sum and product, variation, permutation of combination, random experiment, random phenomenon, opposite phenomenon), classical definition of probability. 11. Basics of statistics: statistical set, its classification, frequency, graphical representation, characteristics of statistical set arithmetic, weighted, harmonic, geometric mean, median, mode, range of variation, deviations from mean values. 12. Complex numbers: domain of complex numbers, Gauss plane, algebraic and geometric form of a complex number, operations with complex numbers, absolute value, Moivre's theorem and its use, solution of a quadratic equation in the domain of complex numbers, binomial equations. 13. Systematization of knowledge. Evaluation of the semester, credits.
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