TÜRKÇE
ENGLISH
Information
| Unit | INSTITUTE OF NATURAL AND APPLIED SCIENCES |
| MATHEMATICS (MASTER) (WITH THESIS) | |
| Code | MT521 |
| Name | Introduction to Differential Geometry |
| Term | 2018-2019 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 |
The current term course schedule has not been prepared yet.
|
Course Goal / Objective
To teach the concept of differentiable manifolds and submanifolds. To teach the concept of vector field on a diferentiable manifold and Lie groups
Course Content
Differentiability for functions of several variables, vector fields on open subsets of an Euclidean space, the rank of a mapping, Definition of differentiable manifolds and examples, Rank of a differentiable function defined on a differentiable manifold, immersions and submersions, submanifolds, Lie groups and vector fields
Course Precondition
Resources
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows the concept of differentiable manifold and gives some examples |
| LO02 | Makes some analysis on differentiable manifolds |
| LO03 | Knows the concept of submanifold |
| LO04 | Knows the concept of a Lie group |
| LO05 | Can investigate actions of a Lie group on a differentiable manifold |
| LO06 | Can investigate actions of a Lie group on a differentiable manifold |
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. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in his area of expertise and other areas of mathematics. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | |
| 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. | 5 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | 5 |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | |
| 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. | 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. | 4 |
| 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 | Topological manifolds | Read the relevant sections in the textbook and solve problems | |
| 2 | Analysis on the functions of several variables | Read the relevant sections in the textbook and solve problems | |
| 3 | Differentiable manifolds | Read the relevant sections in the textbook and solve problems | |
| 4 | Differentiable manifolds | Read the relevant sections in the textbook and solve problems | |
| 5 | Differentiable functions | Read the relevant sections in the textbook and solve problems | |
| 6 | The rank of a mapping | Read the relevant sections in the textbook and solve problems | |
| 7 | Submanifolds of a differentiable manifold | Read the relevant sections in the textbook and solve problems | |
| 8 | Mid-Term Exam | Review the topics discussed in the lecture notes and source | |
| 9 | Submanifolds of a differentiable manifold | Read the relevant sections in the textbook and solve problems | |
| 10 | Lie groups | Read the relevant sections in the textbook and solve problems | |
| 11 | Actions of a Lie group on a manifold | Read the relevant sections in the textbook and solve problems | |
| 12 | Actions of a Lie group on a manifold | Read the relevant sections in the textbook and solve problems | |
| 13 | The tangent space at a point of a manifold and tangent bundle | Read the relevant sections in the textbook and solve problems | |
| 14 | Vector fields on Manifolds | Read the relevant sections in the textbook and solve problems | |
| 15 | One parameter groups acting on a manifold | Read the relevant sections in the textbook and solve problems | |
| 16 | Term Exams | Review the topics discussed in the lecture notes and source | |
| 17 | Term Exams | Review the topics discussed in the lecture notes and source |
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 | ||