|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 Coordinator||Prof.Dr. Ali Arslan ÖZKURT|
To teach the students the basic concepts in general topology, continuity and homeomorphisms in topological spaces and to give basic properties of metric spaces.
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's Contribution To Program|
|No||Program Learning Outcomes||Contribution|
Is able to prove Mathematical facts encountered in secondary school.
Recognizes the importance of basic notions in Algebra, Analysis and Topology
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
Is able to express basic theories of mathematics properly and correctly both written and verbally
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
Expresses clearly the relationship between objects while constructing a model
Draws mathematical models such as formulas, graphs and tables and explains them
Is able to mathematically reorganize, analyze and model problems encountered.
Knows at least one computer programming language
Uses effective scientific methods and appropriate technologies to solve problems
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
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
Knows programming techniques and is able to write a computer program
Is able to do mathematics both individually and in a group.
|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|
|Textbook||1. An introduction to metric and topological spaces, Author. W.A.Sutherland|
2. Genel Topoloji, Author: Ali Bülbül