Complements of Mathematics

Lecture Register

Academic year 2023/2024
Lecturer Andrea Carlo Giuseppe Mennucci, Luigi Ambrosio, Alessandra Caraceni, Giulio Bresciani

Lecture

  • 04 Oct 2023 (2h 00m)

    Luigi Ambrosio - Course (teaching activity) - Face to face

    Propositional calculus and first basic elements of set theory

  • 10 Oct 2023 (2h 00m)

    Luigi Ambrosio - Course (teaching activity) - Face to face

    Functional relations, axiom of infinity and of good foundation, Von Neumann's construction of natural numbers

  • 10 Oct 2023 (2h 00m)

    Alessandra Caraceni - Course (teaching activity) - Face to face

    Esercitazione 1

  • 13 Oct 2023 (2h 00m)

    Luigi Ambrosio - Course (teaching activity) - Face to face

    Natural numbers are well ordered. Recursive constructions, sequences. Cardinality, Cantor-Bernstein theorem

  • 17 Oct 2023 (2h 00m)

    Luigi Ambrosio - Course (teaching activity) - Face to face

    Solutions to problems in basic set theory and cardinality, using Cantor-Bernstein

  • 19 Oct 2023 (2h 00m)

    Alessandra Caraceni - Course (teaching activity) - Face to face

    Esercitazione 2

  • 24 Oct 2023 (1h 00m)

    Luigi Ambrosio - Course (teaching activity) - Face to face

    Well ordered sets, Equivalent formulations of the axiom of choice, Proof of Zermelo theorem, transfinite induction

  • 26 Oct 2023 (2h 00m)

    Alessandra Caraceni - Course (teaching activity) - Face to face

    Esercitazione 3

  • 31 Oct 2023 (2h 00m)

    Alessandra Caraceni - Course (teaching activity) - Face to face

    Esercitazione 4

  • 02 Nov 2023 (2h 00m)

    Luigi Ambrosio - Course (teaching activity) - Face to face

    Proof of Zorn's lemma, construction of relative integers and rationals, axiomatization of fields

  • 07 Nov 2023 (2h 00m)

    Alessandra Caraceni - Course (teaching activity) - Face to face

    Esercitazione 5

  • 09 Nov 2023 (2h 00m)

    Luigi Ambrosio - Course (teaching activity) - Face to face

    Ordered and Archimedean fields. Characterization of the set of real numbers, up to isomorphisms, among complete ordered fields

  • 15 Nov 2023 (2h 00m)

    Luigi Ambrosio - Course (teaching activity) - Face to face

    Basic definitions and results on limits of sequences: Bolzano-Weierstrass, Cauchy criterion, upper and lower limits, subsequences

  • 16 Nov 2023 (2h 00m)

    Alessandra Caraceni - Course (teaching activity) - Face to face

    Esercitazione 6

  • 21 Nov 2023 (2h 00m)

    Alessandra Caraceni - Course (teaching activity) - Face to face

    Esercitazione 7

  • 23 Nov 2023 (2h 00m)

    Luigi Ambrosio - Course (teaching activity) - Face to face

    Ordini di infinito e di infinitesimo, teorema di Stolz-Cesaro, convergenza delle medie

  • 28 Nov 2023 (2h 00m)

    Alessandra Caraceni - Course (teaching activity) - Face to face

    Esercitazione 8

  • 30 Nov 2023 (2h 00m)

    Luigi Ambrosio - Course (teaching activity) - Face to face

    Limits on filtered ordered sets, cofinal families, summations and series, absolute versus unconditional convergence

  • 08 Dec 2023 (2h 00m)

    Luigi Ambrosio - Course (teaching activity) - Face to face

    Second Cesaro Lemma, Partial summations, Cauchy product

  • 12 Dec 2023 (1h 00m)

    Luigi Ambrosio - Course (teaching activity) - Face to face

    Exercises on summable series, Dirichlet criterion and discrete-continuous analogies

  • 14 Dec 2023 (2h 00m)

    Alessandra Caraceni - Course (teaching activity) - Face to face

    Esercitazione 9

  • 06 Feb 2024 (2h 00m)

    Giulio Bresciani - Course (teaching activity) - Face to face

    Esercitazione di preparazione compitino.

  • 13 Feb 2024 (2h 00m)

    Giulio Bresciani - Course (teaching activity) - Face to face

    Struttura euclidea di R^n. Topologia di R^n. Spazi topologici. Parte interna e chiusura. Esempi.

  • 15 Feb 2024 (2h 00m)

    Giulio Bresciani - Course (teaching activity) - Online

    Frontiera e insieme derivato. Esercizi su concetti topologici di base. R è connesso.

  • 22 Feb 2024 (2h 00m)

    Giulio Bresciani - Course (teaching activity) - Face to face

    Esercizi su spazi topologici connessi, distanza da un sottoinsieme di R^n, funzioni continue su chiusi e limitati hanno max e min, insiemi perfetti in R^n.

  • 29 Feb 2024 (2h 00m)

    Giulio Bresciani - Course (teaching activity) - Face to face

    Esercizi su funzioni continue, uniformemente continue, omeomorfismi, isometrie.

  • 07 Mar 2024 (2h 00m)

    Alessandra Caraceni - Course (teaching activity) - Face to face

    Esercitazione topologia

  • 14 Mar 2024 (2h 00m)

    Alessandra Caraceni - Course (teaching activity) - Face to face

    Esercitazione topologia 2

  • 04 Apr 2024 (2h 00m)

    Giulio Bresciani - Course (teaching activity) - Face to face

    Esercizi su teorema di Baire, proprietà di separazione, funzioni Lipscithz.

  • 11 Apr 2024 (2h 00m)

    Giulio Bresciani - Course (teaching activity) - Face to face

    Esercizi su convergenza puntuale e uniforme, lemma di Dini, spazi di Banach non hanno dimensione numerabile.

  • 18 Apr 2024 (2h 00m)

    Giulio Bresciani - Course (teaching activity) - Face to face

    Continuità puntuale e uniforme, Ascoli-Arzelà, funzioni analitiche, spazi normati di dimensione infinita

  • 02 May 2024 (2h 00m)

    Giulio Bresciani - Course (teaching activity) - Face to face

    Didattica integrativa. Campi vettoriali chiusi e potenziali.

  • 07 May 2024 (2h 00m)

    Giulio Bresciani - Course (teaching activity) - Face to face

    Didattica integrativa. Esercizi su calcolo in più variabili. Equazioni differenziali ordinarie. Variabili separabili ed equazioni lineari.