Preparatory course in Mathematics, WS 2024

Proposed content and its ordering of the course:

Number fields: natural numbers, integers, rational numbers, real numbers. Work with fractions.

Algebraic expressions: powers, roots and their manipulations.

Logarithms, exponentials. absolute value. Domain of definition.

Linear and quadratic functions; Equations, equations with parameter. Inequalities: linear, quadratic, with power or square root, with absolute values. Inequalities in product form.

Goniometric functions. Equations, inequalities.

Sequences and series: arithmetic sequence, geometric sequence, sum of a geometric series, sum of the first n terms of an arithmetic or geometric series.

Combinatorics: permutations, combinations and combinations with repetition, binomial theorem in problem solving,

Probability, statistics: probability of random phenomena, independence of phenomena, conditional probability.

Complex numbers, notation in another number system.

Systems of equations and inequalities. Equations: with percentages, with square roots, goniometric, with absolute values. Linear and quadratic.

Analytic geometry: point and vector coordinates, line in plane (general equation, parametric form), angle and scalar product, vector product, planes and half-planes, conics.

Statement logic: conjunction, disjunction, implication, equivalence, negation.