| CODE | 108961 |
|---|---|
| ACADEMIC YEAR | 2023/2024 |
| CREDITS |
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| SCIENTIFIC DISCIPLINARY SECTOR | MAT/01 |
| TEACHING LOCATION |
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| SEMESTER | 2° Semester |
| TEACHING MATERIALS | AULAWEB |
The course introduce set theory as foundational theory for mathematics. Then it presents some subjects peculiar to the theory, like ordinal and cardinal arithmetic, and provides some applications of them to algebra, topology, and analysis.
Main goal of the course is to introduce and analyse the set theoretic constructions and their mathematical applications.
At the end of the course, students will be able to deal with basic set theoretic operations, recognise the applicazions of set theoretic principles like the axiom of choince, be familiar with the concepts of order type of a well order and cardinality, and apply set-theoretic methods to various mathematical problems.
Familiarity with basic mathematical notions from algebra, analysis, and topology.
Class lectures.
1. Review of the notion of a set and of basic set theoretic operations
2. Construction of number sets
3. The axiomatisation of set theory
4. The axiom of choice and its equivalents
5. Ordinals, cardinals, and their arithmetic
6. Descriptive set theory
7. Applications
The instructor notes will be available. Other useful references are:
D.W. Cunningham, Set theory, Cambridge University Press 2016.
K. Hrbacek, T. Jech, Introduction to set theory, Dekker 1999.
D. Goldrei, Classic set theory, Chapman & Hall 1996.
Office hours: By appointment.
Office hours: by appointment
RICCARDO CAMERLO (President)
GIUSEPPE ROSOLINI (President)
All class schedules are posted on the EasyAcademy portal.
Written exam. The written exam can be partially or totally replace by exercises proposed during lectures.
Students with DSA certification («specific learning disabilities»), disability or other special educational needs are advised to contact the teacher at the beginning of the course to establish on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.
The evaluation of the written test or the exercises takes into account the correctedness of the solution, the clarity of the exposition, and the rigour of the arguments.