Syllabus
Statement, variable and constant. Truth values.
Equivalent statements, tautology, contradiction. Quantifiers.
Negation. Operations with statements.
Intuitive approach to sets. Equality of sets, inclusion.
Basic operations with sets. Subsets and their systems.
Decomposition of a set. Number sets: Natural numebrs and mathematics induction; integers, divisibility in the set of integers; real and complex numbers, their line and plane representations. Binary relations over a set and their properties, esp. equivalence and order.
Mappings of sets and their properties. Binary operations on a set and their basic properties. Basic algebraic structures (group, number field) and their properties.
Algebraic equality and inequality. Algebraic equation and inequation, their solvability and solution in simpler cases.
Annotation
The basic course covering the basic elements necessary for further mathematics courses.