2016/2017

2018/2019

DM270

MAT/04 (COMPLEMENTARY MATHEMATICS)

DEPARTMENT OF MATHEMATICS "FELICE CASORATI"

MATHEMATICS

PERCORSO COMUNE

3°

2nd semester (04/03/2019 - 14/06/2019)

6

48 lesson hours

Italian

WRITTEN AND ORAL TEST

ANTONINI SAMUELE (titolare) - 6 ECTS

Sequences, numerical series, limits, classical numerical sets

The course aims to offer an analysis on the mathematical method, on the classical and modern axiomatic systems, on the meta-theoretical issues arisen in the 20th century, and on the attempts to solve the problem of foundations of mathematics.

Axiomatic method: primitive notions and axioms. Meta-theoretical issues in modern axiomatic systems: consistency, independence, completeness.
Peano Arithmetic: independence of axioms; definition by induction; addition, multiplication and order.
Cantorian set theory: comparing of infinite sets, countable and uncountable sets. Cantor's Theorem.
Paradoxes and crisis of foundations. Frege and the Russell's antinomy. Foundational programmes: logicism, intuitionism, formalism.
Zermelo-Fraenkel set theory. Construction of number sets: integer, rational, real numbers through Dedekind's cuts and through Cauchy's sequences.

Lectures and discussions on the theoretical part and on the solution of problems and exercises.

- Borga, M., Palladino, D. oltre il mito della crisi: fondamenti e filosofia della matematica nel 20 secolo. Brescia, La scuola, 1997.

- Fiori, C., Invernizzi, S. Numeri reali. Pitagora, 1999.

- Teacher's notes

Written and oral examination, with the goal of evaluate the knowledge of the topics presented during the course. The access at the oral examination is possible only after a positive evaluation of the written examination.

Written and oral examination, with the goal of evaluate the knowledge of the topics presented during the course. The access at the oral examination is possible only after a positive evaluation of the written examination.