Sets and infinity

The course is offered as a freestanding course.

Successful completion of at least 7.5 credits in logic or mathematics, or the equivalent.

The course treats naive set theory primarily from a mathematical perspective, but with elements of philosophical and historical aspects.

After introducing the background to the emergence of set theory, the principle of extensionality is introduced as the fundamental property of sets. The focus of the course is to reduce arithmetic and mathematical analysis to set theory and thus provide a foundation for mathematics. Via set theory, we develop a precise understanding of the concept of infinity in mathematics.

The course ends with a discussion of Russell's paradox and how set theory can be given a stable foundation through logical axiomatization.

On successful completion of the course the student will be able to:

Knowledge and understanding

• explain the central concepts and constructions of naive set theory,
• explain how the concept of infinity can be treated with set-theoretic methods,
• explain the need to axiomatize set theory, against the background of paradoxes in naive set theory,

Competence and skills

• define basic mathematical concepts (relations, functions, etc.) within the framework of set theory,
• within the framework of set theory, define different number systems and basic arithmetic from the natural numbers,
• formulate and outline proofs of the most important results in the course,

Judgement and approach

• demonstrate familiarity with set theory as a foundation for mathematics.

The course is taught remotely in the form of recorded lectures followed by online quizzes. There may be scheduled online lessons.

Language of instruction: English

Each module is examined individually through either a written assignment or an oral exam. Marking teacher may request supplementation of the examined student performance.

If a student who has been failed twice for the same examination element wishes to change examiner before the next examination session, such a request is to be granted unless there are specific reasons to the contrary (Chapter 6 Section 22 HF).

If a student has received a certificate of disability study support from the University of Gothenburg with a recommendation of adapted examination and/or adapted forms of assessment, an examiner may decide, if this is consistent with the course’s intended learning outcomes and provided that no unreasonable resources would be needed, to grant the student adapted examination and/or adapted forms of assessment.

If a course has been discontinued or undergone major changes, the student must be offered at least two examination sessions in addition to ordinary examination sessions. These sessions are to be spread over a period of at least one year but no more than two years after the course has been discontinued/changed. The same applies to placement and internship (VFU) except that this is restricted to only one further examination session.

If a student has been notified that they fulfil the requirements for being a student at Riksidrottsuniversitetet (RIU student), to combine elite sports activities with studies, the examiner is entitled to decide on adaptation of examinations if this is done in accordance with the Local rules regarding RIU students at the University of Gothenburg.

The grading scale for the course comprises: Pass with Distinction (VG), Pass (G) and Fail (U). The grading scale for modules 1 and 2 comprises: Pass (G) and Fail (U). The grading scale for modules 3, 4 and 5 comprises: Pass with Distinction (VG), Pass (G) and Fail (U).

For the grade VG on the entire course, VG is required on modules 3, 4 and 5, and G on the remaining parts.

Students who are currently taking the course or have completed it will be given the opportunity to express their views and share their experiences in an anonymous course evaluation. A compilation of the course evaluation and the course coordinator's reflections on it will be made available to the students within reasonable time after the end of the course. The next time the course is taught the compilation and any measures based on it will be presented to the students.

The course requires access to a computer (or equivalent) with internet connection, video camera and microphone.

The course may not be included in the degree together with the course LOG010 or LOG011.