Syllabus
(1) Úvod – co je matematika (2) Přirozená čísla (3) Dělitelnost, Základní věta aritmetiky (4) Celá, racionální a reálná čísla (5) Komplexní čísla (6) Množiny (7) Logika (8) Relace (9) Funkce, zobrazení (10) Operace (11) Algebraické struktury (12) Shrnutí a závěr
Annotation
The course is devoted to basic mathematical concepts (and related skills), on which lower and upper secondary mathematics is based. Knowledge of these concepts is assumed in all other mathematical subjects.
SYLABUS:
Sets, statements, proofs. Propositional and predicate calculus.
Sessions on a set, representation.
Binary operations, basic algebraic structures (group, field of integrity, solid).
Numerical fields, axioms and models. Natural numbers, Pean axioms, induction, number systems.
Real numbers, extended real numbers, supremum and infimum. Intervals, subsets of real numbers.
Complex numbers.
Real functions. Definition field and field of values, restrictions. Folding, inverse functions.
Operations between functions. Linear transformation of function graphs. Simplicity, limitations and limitations.
Monotony in point and interval, convexity and concavity. Parity and periodicity.