Mathematics as a logical system. The number system, especially Peano's axioms for the natural numbers and Dedekinds construction of the real numbers. Cardinality. Basic set theory. Groups, rings, fields, linear spaces. Metric spaces, convergence, continuity, compactness, connections. Contractions and fix point theorems with applications. Analysis, in particular in R and Rⁿ: The definition of the elementary functions and the derivation of their properties. Advanced study of differential and integral calculus. The concept of area and volume.
An independent work within an area from the current mathematical literature.