Syllabus
- Natural numbers. The path from natural numbers to integers. Operations and their properties. Ordering and its properties. Divisibility. The basic theorem of arithmetic.
- The path from integers to rational numbers. Operations and their properties. Ordering and its properties. Decimal expansions.
- Incommensurability, irrationality. The path to real numbers. Decimal expansions. Ordering. Real axis.
- Arithmetic, geometric and harmonic mean.
- Calculating with letters. Algebraic expressions and their transformations. Algebraic formulas and their geometric interpretation.
- Linear equations and their geometric meaning. Quadratic equations and their solvability. Vièta's formulas.
- Complex numbers as pairs of real numbers, their algebraic and geometric form. Derivation of trigonometric formulas. Gaussian numbers. Dual numbers.
Annotation
An introductory course and seminar whose aim is to provide a firm foundation for arithmetic and algebra. It focuses especially on number sets, operations, ordering, and linear and quadratic equations.