MT0026 Riemann Geometry

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

Information

Code MT0026
Name Riemann 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 differantiable manifolds, tensors, immersion and imbeddindgs.

Course Content

Differentiable manifolds, Tangent Spaces, Vector Fields, Lie operator, Topology of Manifolds, Riemannian metrics, Riemannian Connections, Geodesics, Curvature tensor and Sectional Curvature, Tensor on Manifolds.

Course Precondition

None

Resources

Manfredo Perdigao do Carmo , Riemann Geometri , Birkhauser, 1992 W. M. Boothby, Diferansiyellenebilir manifoldlar ve Rimann Geometriye Giriş, Elsevier, 2003.

Notes

Manfredo Perdigao do Carmo , Riemann Geometri , Birkhauser, 1992


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Knows the concept of differentiable manifold, gives examples.
LO02 Learns the concepts of Immersion and Imbedding.
LO03 Learn vector fields, Lie bracket operator concepts.
LO04 Learns the concepts of affine connection and Riemann connection.
LO05 Learns the concepts of curvature tensor and cross-sectional curvature.
LO06 Learns the concepts of Ricci curvature and scalar curvature.
LO07 Knows the general properties of tensors.


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. 4
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. 2
PLO04 Bilgi - Kuramsal, Olgusal Has basic knowledge in all areas of mathematics. 5
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. 4
PLO06 Bilgi - Kuramsal, Olgusal Effectively uses the technical equipment needed to express mathematics. 2
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.
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. 2
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. 5
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.
PLO13 Yetkinlikler - Öğrenme Yetkinliği Adheres to the ethical rules required by its scientific title 5


Week Plan

Week Topic Preparation Methods
1 Differentiable manifolds Pages related to the subject in the source books Öğretim Yöntemleri:
Anlatım, Tartışma
2 Tangent spaces Pages related to the subject in the source books Öğretim Yöntemleri:
Anlatım, Tartışma
3 Immersion and Imbeddings and examples Pages related to the subject in the source books Öğretim Yöntemleri:
Anlatım, Tartışma
4 Orientation in manifolds Pages related to the subject in the source books Öğretim Yöntemleri:
Anlatım, Tartışma
5 Vector fields, Lie bracket operator Pages related to the subject in the source books Öğretim Yöntemleri:
Anlatım, Tartışma
6 Topology of manifolds Pages related to the subject in the source books Öğretim Yöntemleri:
Anlatım, Tartışma
7 Riemann metrics Pages related to the subject in the source books Öğretim Yöntemleri:
Anlatım, Tartışma
8 Mid-Term Exam All topics covered up to week 7 in recommended resources Ölçme Yöntemleri:
Yazılı Sınav
9 Affine and Riemann connections Pages related to the subject in the source books Öğretim Yöntemleri:
Anlatım, Tartışma
10 geodesics Pages related to the subject in the source books Öğretim Yöntemleri:
Anlatım, Tartışma
11 Convex neighborhoods Pages related to the subject in the source books Öğretim Yöntemleri:
Anlatım, Tartışma
12 Curvature tensor and cross-sectional curvature Pages related to the subject in the source books Öğretim Yöntemleri:
Anlatım, Tartışma
13 Ricci curvature and scalar curvature Pages related to the subject in the source books Öğretim Yöntemleri:
Anlatım, Tartışma
14 Tensors on manifolds Pages related to the subject in the source books Öğretim Yöntemleri:
Anlatım, Tartışma
15 Tensors on manifolds 1 Pages related to the subject in the source books Öğretim Yöntemleri:
Anlatım, Tartışma
16 Term Exams All topics covered in recommended resources Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams All topics covered in recommended resources 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