Advanced course in foundations of mathematics
Scientific Disciplinary Sector (SSD)
MAT/01 - MATHEMATICAL LOGIC
Secondo semestre dal Mar 6, 2023 al Jun 16, 2023.
This monographic course introduces advanced topics in the area of the foundations of mathematics and discusses their repercussions in mathematical practice. The specific arguments are detailed in the programme. At the end of this course the student will know advanced topics related to the foundations of mathematics. The student will be able to reflect upon their interactions with other disciplines of mathematics and beyond; to produce rigorous argumentations and proofs; and to read related articles and monographs, including advanced ones.
Prerequisites and basic notions
Bachelor's degree in mathematics (pure, applied, ...). Alternatively, a bachelor's degree in some related subject (computer science, statistics, ...) if the emphasis of the studies was put on formal and mathematical methods.
Introduction to Zermelo-Fraenkel style axiomatic set theory, with attention to constructive aspects and transfinite methods (ordinal numbers, axiom of choice, etc.).
Gödel's incompleteness theorems and their repercussion on Hilbert's programme, with elements of computability theory (recursive functions and predicates, etc.).
Visualizza la bibliografia con Leganto, strumento che il Sistema Bibliotecario mette a disposizione per recuperare i testi in programma d'esame in modo semplice e innovativo.
All lectures will be held in lecture hall. Additional homework exercises will be assigned and partially discussed at lectures.
Learning assessment procedures
The exam consists of a single oral exam with open questions and marks out of thirty. Exam methods are not differentiated between attending and non-attending students.
The exam aims to verify the student's full maturity about proof techniques and the ability to read and understand advanced topics of the foundations of mathematics.
Criteria for the composition of the final grade
The final grade consists of the outcome of the sole oral exam.