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Information
| Code | MTS301 |
| Name | Set Theory |
| Term | 2024-2025 Academic Year |
| Semester | 5. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. YILMAZ DURĞUN |
| Course Instructor |
Prof. Dr. YILMAZ DURĞUN
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
Aim of this course is that explains basic notions of “naive” set theory (cardinalities, ordered sets, transfinite induction, ordinals).
Course Content
Sets, cardinality, equinumerous sets, countable sets, Cantor–Bernstein theorem, Cantor's theorem, functions, operations on cardinals, ordered sets, equivalence relations and orderings, isomorphisms, well-orderings, well-ordered sets, transfinite induction, Zermelo's theorem, Zorn's lemma and its applications are the topics covered in this course.
Course Precondition
None
Resources
Kümeler Teorisine Giriş, Prof. Dr. Nurettin Ergun
Notes
Basic Set Theory, A. Shen, N. K.Vereshchagin
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | They learn to form precise definitions. |
| LO02 | They develop a solid understanding of fundamental concepts in set theory. |
| LO03 | They improve their problem-solving skills. |
| LO04 | They learn to analyze complex problems. |
| LO05 | Set theory, encourages students to think abstractly and generalize concepts. |
| LO06 | They learn to identify patterns and commonalities across different mathematical structures. |
| LO07 | They enhance their ability to solve problems in various contexts. |
| LO08 | They learn to construct logical arguments. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 4 |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrates the ability to express the basic theories of mathematics accurately both in writing and orally. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 4 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 4 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Comprehends at least one of the computer programming languages. | 3 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 3 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | |
| PLO19 | Bilgi - Kuramsal, Olgusal | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | 3 |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Basic definitions and theorems about sets | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | Cardinality concept and its properties | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | Equal cardinalities | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | Countable set | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 5 | Cantor–Bernstein Theore | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 6 | Cantor’s Theore | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Functions and basic properties of functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Operations on cardinals | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Equivalence relations and orderings | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | Isomorphisms | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 12 | Well-founded orderings | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Well-ordered sets | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | Transfinite induction | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Zermelo’s Theorem, Zorn’s Lemma and its application | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 16 | Term Exams | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review the topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 6 | 84 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 2 | 1 | 2 |
| Mid-term Exams (Written, Oral, etc.) | 2 | 2 | 4 |
| Final Exam | 1 | 2 | 2 |
| Total Workload (Hour) | 134 | ||
| Total Workload / 25 (h) | 5,36 | ||
| ECTS | 5 ECTS | ||