20410619 - ME430 - FOUNDATIONS AND HISTORY OF MATHEMATICAL ANALYSIS

Revisiting the fundamental structures and concepts of mathematical analysis from a historical and critical point of view, also in light of the specific learning objectives of upper secondary school. Knowing how to design learning units on central themes for mathematical analysis in the context of a school course.

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Programme

The following key topics will be revisited in depth and introduced from a historical point of view:
1. R and its fundamental subsets
2. Concept of limit and notable limits
3. Series
4. Continuous functions
5. Derivability and monotonicity
6. Second derivative and convexity
7. Elementary analytic functions (exponential, trigonometric functions and their inverses)
8. Integrals and areas
9. The Fundamental Theorem of Calculus
10. Complex numbers

Other course objectives
Analysis of fundamental school evaluation moments such as the tests/problems/questionnaires of the State Exam and the Invalsi tests.
Discussion of ministerial guidelines.

Core Documentation

E. Giusti, Analisi Matematica 1
E. Giusti Piccola storia del calcolo infinitesimale dall'antichità al Novecento

Type of delivery of the course

5 hours of frontal teaching a week live remote lesson and recording of the lesson itself.

Attendance

not compulsory

Type of evaluation

written test with exercise and subsequent oral test