MT342 Topology

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

Information

Code MT342
Name Topology
Semester 6. Semester
Duration (T+A) 3-0 (T-A) (17 Week)
ECTS 5 ECTS
National Credit 3 National Credit
Teaching Language Türkçe
Level Lisans Dersi
Type Normal
Mode of study Yüz Yüze Öğretim
Catalog Information Coordinator Prof. Dr. YILMAZ DURĞUN


Course Goal

To teach the students the basic concepts in general topology, continuity and homeomorphisms in topological spaces and to give basic properties of metric spaces.

Course Content

Definition of topology, interior, exterior, boundary and derived set of a set in a topological space, bases, Hausdorff spaces and product spaces, continuity and homeomorphisms and metric spaces.

Course Precondition

none

Resources

1. Genel Topoloji, Yazar: Ali Bülbül

Notes

An introduction to metric and topological spaces, Author. W.A.Sutherland


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Can decide whether a given structure a topology on a set
LO02 Can determine the continuity of a function on a topological space
LO03 They realize that there is no difference between topological spaces which are equivalent under homeomorphisms
LO04 Can apply some arguments in analysis to topological spaces
LO05 Can define metric spaces and state some basic concepts in metric spaces
LO06 Can show that every metric space is a topological space
LO07 Can find interior, closure, exterior and boundary of a set in a topological space
LO08 Can explain and prove of the basic theorems in topology and use them for solving mathematical problems


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. 4
PLO02 Bilgi - Kuramsal, Olgusal Understands importance of basic consepts of Algebra, Analaysis and Topology. 3
PLO03 Yetkinlikler - Öğrenme Yetkinliği Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. 4
PLO04 Bilgi - Kuramsal, Olgusal Demonstrate the ability to express the basic theories of mathematics both correctly. 5
PLO05 Bilgi - Kuramsal, Olgusal Understands the relationship between the different fields of mathematics and its relation to other disciplines. 4
PLO06 Bilgi - Kuramsal, Olgusal Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. 5
PLO07 Bilgi - Kuramsal, Olgusal Comprehend and explain mathematical models such as formulas, graphs, tables and schema. 4
PLO08 Bilgi - Kuramsal, Olgusal Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. 4
PLO09 Bilgi - Kuramsal, Olgusal Comprehends at least one of the computer programming languages. 5
PLO10 Bilgi - Kuramsal, Olgusal Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. 3
PLO11 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians 4
PLO12 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. 4
PLO13 Yetkinlikler - Öğrenme Yetkinliği Understands the programming techniques and shows the ability to do programming.
PLO14 Yetkinlikler - Öğrenme Yetkinliği Demonstrates the ability to study mathematics both independently and as a group. 3
PLO15 Bilgi - Kuramsal, Olgusal Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study.
PLO16 Bilgi - Kuramsal, Olgusal Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications.
PLO17 Bilgi - Kuramsal, Olgusal It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability.
PLO18 Bilgi - Kuramsal, Olgusal Gains the ability to use information technologies effectively for contemporary mathematical applications.
PLO19 Bilgi - Kuramsal, Olgusal Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields.
PLO20 Bilgi - Kuramsal, Olgusal Gains the consciousness of prefesional ethics and responsibility.


Week Plan

Week Topic Preparation Methods
1 Professional and ethical responsibility Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
2 Definition of topological space, Topology of the real line, open and closed sets Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
3 Closure and properties of closure Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
4 Interior, exterior and boundary of a set in a topological space Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
5 Relative topology and properties Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
6 Topologies induced by functions Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
7 Bases and Neighbourhood bases Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
8 Mid-Term Exam Review of the topics discussed in the lecture notes and sources Öğretim Yöntemleri:
Tartışma
9 Product topology and some examples Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
10 Continuity and continuity at a point Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
11 Some examples about continuity and homeomorphisms Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım
12 Properties of homeomorphisms and some examples Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
13 Hausdorff spaces and their properties Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
14 Metric spaces and some properties Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
15 Continuity in metric spaces and some examples Review of the relevant pages from sources Öğretim Yöntemleri:
Anlatım, Tartışma
16 Term Exams Review of the topics discussed in the lecture notes and sources Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Review of the topics discussed in the lecture notes and sources Ölçme Yöntemleri:
Yazılı Sınav


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 3 42
Assesment Related Works
Homeworks, Projects, Others 0 0 0
Mid-term Exams (Written, Oral, etc.) 1 12 12
Final Exam 1 18 18
Total Workload (Hour) 114
Total Workload / 25 (h) 4,56
ECTS 5 ECTS