Foundations of mathematics I (2020/2021)

Course code
Name of lecturer
Peter Michael Schuster
Peter Michael Schuster
Number of ECTS credits allocated
Academic sector
Language of instruction
I semestre dal Oct 1, 2020 al Jan 29, 2021.

Lesson timetable

Go to lesson schedule

Learning outcomes

The course is an introduction into the fundamental methods and concepts of mathematics, especially into the method of proof and the language of sets.

At the end of the course the student will be expected to demonstrate that s/he has attained adequate skills in synthesis and abstraction, as well as the ability to recognize and produce rigorous proofs and to formalize and solve moderately difficult problems related to the topics of the course.


With the exception of some optional exercise classes, the entire course will be held in lecture hall. At the same time all hours will be available online.

Contents of the course:

Propositions and predicates
Connectives and quantifiers
Sets, elements, subsets
The axiomatic-deductive method
Mathematical terminology
Proof techniques
Relations and functions
Families and sequences
The Peano axioms
Number systems
Transfinite methods

Reference books
Author Title Publisher Year ISBN Note
Day, Martin An Introduction to Proofs and the Mathematical Vernacular. 2015
Silvana Franciosi, Francesco De Giovanni Elementi di algebra Aracne 1995 8879990241 Per Fondamenti della matematica: le prime parti del libro
Velleman, Daniel J. How to Prove It: A Structured Approach (Edizione 2) Cambridge University Press 2006 978-0-521-67599-4
Cantini, Andrea & Minari, Pierluigi Introduzione alla logica : linguaggio, significato, argomentazione. (Edizione 1) Le Monnier 2009 978-88-00-86098-7
C. Toffalori, S. Leonesi Matematica, miracoli e paradossi Mondadori 2007 9788842420934 Da acccompagnare certi argomenti del corso.
Ebbinghaus, H.-D., Hermes, H., Hirzebruch, F., Koecher, M., Mainzer, K., Neukirch, J., Prestel, A., Remmert, R. Numbers Springer 1991 978-0-387-97497-2 Per questo corso, piuttosto i primi due capitoli.
Halmos, Paul Teoria elementare degli insiemi (Edizione 4) Feltrinelli 1981

Assessment methods and criteria

Single written exam with open questions and grades out of 30. The exam modalities are equal for attending and non-attending students.

The assessment methods may be subject to change as the development of the situation demands. The distance modality will anyway be guaranteed for all students who require this in the academic year 2020-21.