MT015 Advanced Differential Geometry

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

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

Update Time: 09.05.2024 11:37