1. Conceptual bases of mathematics: primitive concepts in arithmetic, geometry, probability; the idea of ​​demonstration; mathematics, philosophy and scientific knowledge.
2. The discrete and the continuous. Euclidean geometry, natural numbers, the real line. Conceptual, epistemological, linguistic and didactic nodes of teaching and learning mathematics.
3. Mathematics in culture: the social and economic role of mathematics, mathematics in education, the community
international mathematics.