An Introduction to Set Theory MAT1103b

Course content:

Fundamental notions of Set Theory. Basic properties of operations on sets. Cartesian products.

Unions and untersections of families of sets.

Ordering relations (minimal and maximal elements, least upper bounds and greatest lower bounds). Linear orderings. Partially ordered sets.

Cardinal numbers. Cantor theorem. Cantor-Bernstein theorem. Continuum hypothesis. Ordinal numbers. Zermelo-Fraenkel axioms of set theory.

Mathematical induction.

Recurrence equations. Methods of solving linear homogeneous recurrence equations with constant coefficients.

Learning outcomes:
Students should be acquainted with basic notions and facts of set theory.