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Information
| Code | MT015 |
| Name | Advanced Differential Geometry |
| Term | 2024-2025 Academic Year |
| Semester | . Semester |
| 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 | Doç. Dr. NERGİZ POYRAZ |
Course Goal / Objective
To teach the general properties of curves and surfaces in three dimensional Euclidean space and manifolds.
Course Content
Curves in 3-dimensional Euclidean space, examples of some curves, 1-forms, differential forms, the structural equations, isometries, surfaces in 3-dimensional Euclidena space, regular surfaces, mappings of surfaces, topological properties of surfaces, manifolds.
Course Precondition
None
Resources
1. H. H. Hacısalihoğlu, Yüksek Diferensiyel Geometri’ ye Giriş, Fırat Ünv. Fen Fak. 1980.
Notes
1. H. H. Hacısalihoğlu, Yüksek Diferensiyel Geometri’ ye Giriş, Fırat Ünv. Fen Fak. 1980.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | 1. Express the general properties of curves in 3-dimensional Euclidean space. |
| LO02 | 2. Will be able to express general properties of 1-forms and differential forms. |
| LO03 | 3. Define the concepts of regular surface and orientable surface. |
| LO04 | 4. Will be able to define transformations between surfaces. |
| LO05 | 5. Define the basic information about surfaces and manifolds. |
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. | 2 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 1 |
| 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. | 5 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | |
| 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. | 4 |
| 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. | |
| 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. | 3 |
| 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. | 5 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Curves in 3-dimensional Euclidean space, some | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | 1-forms | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Differential forms | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Roof areas, connection forms | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Structure equations | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Isometries | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Orientation | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Pages related to the subject in the source books | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Surfaces in 3-dimensional Euclidean space | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | regular surfaces | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Orientable surfaces | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Transformations between surfaces | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Manifolds | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Topological properties of surfaces | Pages related to the subject in the source books | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Topological properties of surfaces 1 | Pages related to the subject in the source books | Ölçme Yöntemleri: Yazılı Sınav |
| 16 | Term Exams | Pages related to the subject in the source books | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Pages related to the subject in the source books | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 13 | 3 | 39 |
| Out of Class Study (Preliminary Work, Practice) | 13 | 5 | 65 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 3 | 5 | 15 |
| Mid-term Exams (Written, Oral, etc.) | 0 | 0 | 0 |
| Final Exam | 1 | 25 | 25 |
| Total Workload (Hour) | 144 | ||
| Total Workload / 25 (h) | 5,76 | ||
| ECTS | 6 ECTS | ||