Propositional logic. Propositional calculus.

Sets, set operations, relations, functions. Cardinality of sets, countable sets, uncountable sets. Elementary number sets. Integers and rationals. Induction principle.

More on functions: injective and surjective functions, invertible functions, image and pre-image.

The set of real numbers. Separation axiom, Dedekind cuts. Infimum and supremum. Archimedean property.  Complex numbers: cartesian and trigonetric form, basic properties, powers, complex roots, fundamental theorem of algebra.

Sequences of real numbers: monotone sequences, convergence of a sequence, subsequences, limsup and liminf of a sequence, Bolzano-Weierstrass theorem.

Introduction to functions of real numbers. Elementary functions: exponential and logarithmic function, trigonometric functions, irrational functions. Monotone functions.

The topology of real numbers: intervals, half lines, open sets, closed sets. The topology of the Euclidean space Rn: balls, open and closed sets. Compact sets in the Euclidean space.