COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Topology * MT   342 6 3 3 5

Prerequisites and co-requisites
Recommended Optional Programme Components None

Language of Instruction Turkish
Course Level First Cycle Programmes (Bachelor's Degree)
Course Type
Course Coordinator Prof.Dr. Ali Arslan ÖZKURT
Instructors
Prof.Dr.ALİ ARSLAN ÖZKURT1. Öğretim Grup:A
Prof.Dr.ALİ ARSLAN ÖZKURT2. Öğretim Grup:A
 
Assistants
Goals
To teach the students the basic concepts in general topology, continuity and homeomorphisms in topological spaces and to give basic properties of metric spaces.
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.

Learning Outcomes
-


Course's Contribution To Program
NoProgram Learning OutcomesContribution
12345
1
Is able to prove Mathematical facts encountered in secondary school.
X
2
Recognizes the importance of basic notions in Algebra, Analysis and Topology
X
3
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
X
4
Is able to express basic theories of mathematics properly and correctly both written and verbally
X
5
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
X
6
Expresses clearly the relationship between objects while constructing a model
X
7
Draws mathematical models such as formulas, graphs and tables and explains them
X
8
Is able to mathematically reorganize, analyze and model problems encountered.
X
9
Knows at least one computer programming language
10
Uses effective scientific methods and appropriate technologies to solve problems
X
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
12
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields
13
Knows programming techniques and is able to write a computer program
14
Is able to do mathematics both individually and in a group.
X

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
1 Review of some basic concepts and definition of topological space Review of the relevant pages from sources
2 Topology of the real line, open and closed sets Review of the relevant pages from sources
3 Closure and properties of closure Review of the relevant pages from sources
4 Interior, exterior and boundary of a set in a topological space Review of the relevant pages from sources
5 Relative topology and properties Review of the relevant pages from sources
6 Topologies induced by functions Review of the relevant pages from sources
7 Bases and Neighbourhood bases Review of the relevant pages from sources
8 Mid-term exam Review of the topics discussed in the lecture notes and sources
9 Product topology and some examples Review of the relevant pages from sources
10 Continuity and continuity at a point Review of the relevant pages from sources
11 Some examples about continuity and homeomorphisms Review of the relevant pages from sources
12 Properties of homeomorphisms and some examples Review of the relevant pages from sources
13 Hausdorff spaces and their properties Review of the relevant pages from sources
14 Metric spaces and some properties Review of the relevant pages from sources
15 Continuity in metric spaces and some examples Review of the relevant pages from sources
16-17 Final exam Review of the topics discussed in the lecture notes and sources

Recommended or Required Reading
Textbook1. An introduction to metric and topological spaces, Author. W.A.Sutherland
2. Genel Topoloji, Author: Ali Bülbül
Additional Resources