Syllabus
Revision of basic concept related to algebraic structures
Peano arithmetic: Natural numbers as an algebraic structure, Positional representation of natural numbers
Construction of the whole numbers system. Embedding of semigroups into groups
Construction of the field of rational numbers; Positional representation of rational numbers
Construction of the field of real numbers
Construction of the field of complex numbers; geometrical model of the field of complex numbers.
Basic properties of groups. Lagrange Theorem, quotient groups. Group homomorphisms.
Basic properties of rings.
Annotation
The course covers two domains of algebra and theoretical arithmetic useful for lower and upper secondary mathematics teachers. It deals with the construction of number systems (natural, whole, rational, real and complex numbers), and broadens and deepens the knowledge that students gained during their previous study.
The second part covers algebraic structures focusing mainly on the structures with one and two binary operations. Knowledge of structures that students gained in previous courses is generalised and broadened.