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