Elementary Mathematics from an Advanced Standpoint 1

The course aims to offer a historical and epistemological reading of some central topics in mathematics — conics, algebra, trigonometry, functions, number systems and logic — from the perspective of Felix Klein's Elementary Mathematics from a Higher Standpoint. The course seeks to show how mathematical concepts and methods have developed over time through changes in language, representation and levels of abstraction, connecting elementary content with more general theoretical structures. A multicultural perspective on mathematical thought will also be emphasized, with attention to the plurality of traditions, contexts and historical contributions involved in the construction of mathematics.

By the end of the course, students will be able to interpret elementary mathematical content from a higher standpoint, in the perspective of Felix Klein, identifying its theoretical structure and level of abstraction. They will also be able to recognize the historical and conceptual evolution of the main topics covered, with attention to the plurality of traditions and contexts in which mathematical thought has developed.