Syllabus
Algebraic structures: groups, cyclic groups, factorization, the homomorphism theorem. Ring, ideal. Field of fractions.
Divisibility in integral domains.
Irracionality. Real numbers (Dedekind, fundamental sequences, axiomatization, decimal numbers). Algebraic and transcendent numbers.
Complex numbers, extensions of the complex numbers set (quaternions, octonions).
Cardinalities of number systems.
Means (arithmetic, geometric, harmonic).
Algebraic equations and inequalities: linear, quadratic, cubic. Vieta's formulas, solvability of algraic equations in radicals. Diophantine equatioins (linear, Pell's).
Annotation
Introductory course devoted to the elements of arithmetics and algebra, especially to basic results on number systems, operations, sequences, and elementary functions.