Set theory:
Sets, subsets, operations with sets:
union,intersection, difference, symmetric difference,
Cartesian product and disjoint union.
Functions: graph of a function.
Composition; injections,
surjections, bijections, inverse function.
Computing cardinals:
Cardinality of Cartesian product, union.
Cardinality of all functions from a set to another set.
Cardinality of all injective, surjective
bijective functions from a set to another set.
Infinite sets, finite sets.
Countable sets,
properties, examples (Z, Q).
R is not countable. R, RxR, RxRxR have the same cardinal.
Operations with cardinal numbers.
Cantor-Bernstein theorem.
Relations:
Equivalence relations,
partitions, quotient set; examples,
parallelism, similarity of triangles.
Order relations, min, max, inf, sup; linear order.
Examples: N, Z, R, P(A). Well ordered sets and induction.
Inductively ordered sets and Zorn’s lemma.
Mathematical logic:
Propositional Calculus.
Truth tables. Predicate Calculus.