Nevşehir Hacı Bektaş Veli University Course Catalogue

Information Of Programmes

FACULTY OF LETTERS & SCIENCE / MAT203 - MATHEMATICS

Code: MAT203 Course Title: GENERAL TOPOLOGY I Theoretical+Practice: 4+0 ECTS: 6
Year/Semester of Study 2 / Fall Semester
Level of Course 1st Cycle Degree Programme
Type of Course Compulsory
Department MATHEMATICS
Pre-requisities and Co-requisites None
Mode of Delivery Face to Face
Teaching Period 14 Weeks
Name of Lecturer SAMED ÖZKAN (ozkans@nevsehir.edu.tr)
Name of Lecturer(s)
Language of Instruction Turkish
Work Placement(s) None
Objectives of the Course
The aim of the course is to teach some basic concepts in Topology, to create the ability of Mathematical idea and commend, to help to gain the basic topological knowledge and ability for their later educations.

Learning Outcomes PO MME
The students who succeeded in this course:
LO-1 Can define the concepts of topological space, open set and closed set. Can build a topological structure on a set. PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts.
PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data.
Examination
LO-2 Can find interior, exterior, boundary, closure and accumulation points of a set. PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts.
PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data.
Examination
LO-3 Can define the concepts of base and subbase. Can generate a topology from base or subbase. Can examine the convergence of sequences in topological spaces. PO-1 Have the ability to conceptualize the events and facts related to the field of mathematics such as Analysis, Geometry and Algebra with the help of the scientific methods and techniques and can define these concepts.
PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data.
Examination
LO-4 Can define the concepts of continuous, open, closed maps and homeomorphism. PO-2 Have the knowledge to critize, analyze, and evaluate the correctness, reliability, and validity of mathematical data.
Examination
PO: Programme Outcomes
MME:Method of measurement & Evaluation

Course Contents
Fundamental Concepts, Metric Spaces, Topological Spaces, Usual Topology of Real Numbers, Neighborhoods, Open and Closed Sets, Interior, Exterior, Boundary, Closure and Accumulation Points, Subspaces, Bases and Subbases, Sequences and Convergence in Topological Spaces, Continuity, Open and Closed Functions, Homeomorphisms and Topological Properties.
Weekly Course Content
Week Subject Learning Activities and Teaching Methods
1 Fundamental Concepts Lecturing
2 Fundamental Concepts Lecturing
3 Metric Spaces Lecturing
4 Topological Spaces Lecturing
5 Usual Topology of Real Numbers Lecturing
6 Neighborhoods Lecturing
7 Open and Closed Sets Lecturing
8 mid-term exam
9 Interior, Exterior, Boundary, Closure and Accumulation Points Lecturing
10 Subspaces Lecturing
11 Bases and Subbases Lecturing
12 Sequences and Convergence in Topological Spaces Lecturing
13 Continuity Lecturing
14 Open and Closed Functions Lecturing
15 Homeomorphisms and Topological Properties Lecturing
16 final exam
Recommend Course Book / Supplementary Book/Reading
1 O. Mucuk, Topoloji ve Kategori, Nobel Yayın, Ankara, 2010.
2 Ş. Yüksel, Genel Topoloji, Selçuk Üniversitesi, Konya, 2002.
3 M. Koçak, Genel Topolojiye Giriş ve Çözümlü Alıştırmalar, Kampüs Yayıncılık, Eskişehir, 2011.
4 S. Lipschutz, General Topology, Schaum’s Outline Series, New York, 1965.
Required Course instruments and materials

Assessment Methods
Type of Assessment Week Hours Weight(%)
mid-term exam 8 2 40
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project
8.Term Paper
9.Project
final exam 16 2 60

Student Work Load
Type of Work Weekly Hours Number of Weeks Work Load
Weekly Course Hours (Theoretical+Practice) 4 14 56
Outside Class
       a) Reading 4 14 56
       b) Search in internet/Library 2 14 28
       c) Performance Project 0
       d) Prepare a workshop/Presentation/Report 0
       e) Term paper/Project 0
Oral Examination 0
Quiz 0
Laboratory exam 0
Own study for mid-term exam 4 4 16
mid-term exam 2 1 2
Own study for final exam 5 4 20
final exam 2 1 2
0
0
Total work load; 180