Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
This information is intended exclusively for students already enrolled in this course.If you are a new student interested in enrolling, you can find information about the course of study on the course page:
Laurea magistrale in Mathematics - Enrollment from 2025/2026The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
| Modules | Credits | TAF | SSD |
|---|
| Modules | Credits | TAF | SSD |
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| Modules | Credits | TAF | SSD |
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1 module between the following1 module between the following 3 modules among the followingLegend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Advanced course in foundations of mathematics (2020/2021)
Teaching code
4S001104
Academic staff
Coordinator
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/01 - MATHEMATICAL LOGIC
Period
II semestre dal Mar 1, 2021 al Jun 11, 2021.
Learning outcomes
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.
Program
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.).
| Author | Title | Publishing house | Year | ISBN | Notes |
|---|---|---|---|---|---|
| Peter Smith | An Introduction to Gödel's Theorems (Edizione 2) | Cambridge University Press | 2013 | 9781107606753 | |
| Torkel Franzén | Gödel's Theorem: An Incomplete Guide to its Use and Abuse. | A K Peters, Ltd. | 2005 | 1-56881-238-8 | |
| Riccardo Bruni | Kurt Gödel, un profilo. | Carocci | 2015 | 9788843075133 | |
| Abrusci, Vito Michele & Tortora de Falco, Lorenzo | Logica. Volume 2 - Incompletezza, teoria assiomatica degli insiemi. | Springer | 2018 | 978-88-470-3967-4 | |
| Shoenfield, Joseph R. | Mathematical Logic. (Edizione 2) | Association for Symbolic Logic & A K Peters | 2001 | 1-56881-135-7 | |
| Peter Aczel, Michael Rathjen | Notes on Constructive Set Theory | 2010 | |||
| Yiannis N. Moschovakis | Notes on Set Theory | Springer | 1994 | 978-1-4757-4155-1 | |
| Peter Cameron | Sets, Logic and Categories | Springer | 1998 | 978-1-4471-0589-3 | |
| Kenneth Kunen | The Foundations of Mathematics (Edizione 2) | College Publications | 2012 | 978-1-904987-14-7 |
Examination Methods
Single oral exam with open questions and grades out of 30. The exam modalities are equal for attending and non-attending students.
The exam's objective is to verify the full maturity about proof techniques and the ability to read and comprehend advanced arguments of the foundations of mathematics.
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.
