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| Unit | INSTITUTE OF NATURAL AND APPLIED SCIENCES |
| MATHEMATICS (MASTER) (WITH THESIS) | |
| Code | MT503 |
| Name | General Topology |
| Term | 2024-2025 Academic Year |
| Term | Fall |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ALİ ARSLAN ÖZKURT |
| Course Instructor |
Prof. Dr. ALİ ARSLAN ÖZKURT
(Güz)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course to provide information about countability in topological spaces, product spaces, weak topologies, embedding, homeomorphism, convergence, separation axioms and compactness .
Course Content
Countability in topological spaces, product spaces, embedding theorems, convergence, separation axioms, compactness,
Course Precondition
Pre-requisites None
Resources
S. Willard : General Topology
Notes
J. Dgundji : General Topology
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Defines first and second countable spaces |
| LO02 | Comprehends Product topology, weak topology and embedding theorems |
| LO03 | Understands convergence of a sequence, the net and filter in topological spaces, |
| LO04 | Establishes a relationship between convergence in analysis and topology. |
| LO05 | Can define Hausdorff, regular and normal spaces |
| LO06 | Understands the compact space and comprehends basic theorems about compact spaces. |
| LO07 | Understands the relationship between compactness and convergence. |
| LO08 | Improves the ability of abstract thinking. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in his area of expertise and other areas of mathematics. | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 3 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | 3 |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education. | 4 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have knowledge of a foreign language at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. | 4 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Review of some topological concepts. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Sub-base and the concept of neighborhood. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Sub-base and the concept of neighborhood 2 | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | First and Second countable spaces | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Product spaces and weak topologies | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Separable spaces and Embedding Theorems. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Convergence of sequences, Sequential continuity | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Nets and Convergence. Filters and convergence. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | T0 and T1-spaces. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | T2 (Hausdorff), regular, T3-spaces. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Completely regular, normal spaces and Jone's Lemma. and T4-spaces. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Tychonoff spaces and T4 spaces | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | The compactness andthe finite intersection property, and the relationship between the compactness and convergence. Heine-Borel Theorem. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Fundamental properties of compact spaces and Heine-Borel Theorem. | Read the relevant sections in the textbook and solve problems | Öğretim Yöntemleri: Anlatım, Tartışma |
| 16 | Term Exams | Topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
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 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||