Set Theory I
| Title | ΘΕΩΡΙΑ ΣΥΝΟΛΩΝ Ι / Set Theory I |
| Code | 0132 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Spring |
| Common | Yes |
| Status | Active |
| Course ID | 40000301 |
Programme of Study: Merikīs Foítīsīs (2014-sīmera)
Registered students: 1
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| KORMOS | Elective Courses belonging to the selected specialization | Spring | - | 5.5 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 59
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | 6 | 3 | 5.5 |
| Academic Year | 2025 – 2026 |
| Class Period | Spring |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600276396
|
Type Of Offer
- Disciplinary Course
Course Type 2021
Specialization / Direction
Course Type 2011-2015
Knowledge Deepening / Consolidation
Mode of Delivery
- Face to face
- Distance learning
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600276396
- eLearning (Moodle): https://elearning.auth.gr/course/view.php?id=15169
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Examination)
Prerequisites
Required Courses
- 0102Α Introduction to Algebra and Number Theory
General Prerequisites
Knowledge of basic proof techniques and basic operations on sets.
General Competences
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Adapt to new situations
- Make decisions
- Work autonomously
- Advance free, creative and causative thinking
Course Content (Syllabus)
Basic (naive) set theory, equinumerous sets, Cantor's theorems, Theorem of Cantor-Bernstein, Continuum Hypothesis, Russell's paradox.
Axiomatic set theory (ZF and ZFC), axiomatic foundation of Natural numbers, Integers, Rationals and Reals.
Partial Orders, Total Orders and Well Orders and properties of Well-Ordered sets.
Ordinal numbers, Transfinite Induction.
Cardinal numbers, Alephs and basic Cardinal Arithmetic.
Axiom of Choice (AC), Statements equivalent to the AC, Zorn's Lemma.
(If time permits) Konig's Lemma.
Keywords
Set Theory, Oridnal Numbers, Cardinal Numbers, Well Ordered Sets, Axiom of Choice
Educational Material Types
- Notes
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Communication with Students
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ✓ | |||
| Reading Assigment | 122 | ✓ | ✓ | ✓ | |
| Exams | 4 | ✓ | ✓ | ||
| Total | 165 |
Student Assessment
Description
Two midterm exams and a final exam will be given.
Student Assessment methods
- Written Exam with Short Answer Questions (Formative, Summative)
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Assignment (Formative, Summative)
- Performance / Staging (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
- Σημειώσεις στη Συνολοθεωρία, Γ. Μοσχοβάκης, Εκδόσεις Δουβίτσας, 1993.
- ΑΦΕΛΗΣ ΣΥΝΟΛΟΘΕΩΡΙΑ, Paul Halmos, Εκδόσεις Εκκρεμές,
Κωδικός Βιβλίου στον Εύδοξο: 77108962
- Αξιωματική Θεωρία Συνόλων, Κ. Κάλφα, Εκδόσεις Ζήτη, 1990
Last Update
23-10-2025
