MAT5006 TopologyBahçeşehir UniversityDegree Programs APPLIED MATHEMATICS (TURKISH, NON-THESIS)General Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
APPLIED MATHEMATICS (TURKISH, NON-THESIS)
Master TR-NQF-HE: Level 7 QF-EHEA: Second Cycle EQF-LLL: Level 7

Course Introduction and Application Information

Course Code Course Name Semester Theoretical Practical Credit ECTS
MAT5006 Topology Fall 3 0 3 8
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction: Turkish
Type of course: Departmental Elective
Course Level:
Mode of Delivery: Face to face
Course Coordinator : Assoc. Prof. ATABEY KAYGUN
Recommended Optional Program Components: None
Course Objectives: The aim of this lesson is to give the fundamental concepts of general topology and the methods of proof. Also, the other aim is to give information about metric and topological properties of mathematical concepts in metric spaces that are important for the mathematics science.

Learning Outcomes

The students who have succeeded in this course;
1) He/She defines the basic concepts of metric space,
2) He/She decides whether arbitrary functions are metrics or not,
3) He/She adapts knowledge of functions theory and analysis to metric space,
4) He/She proves and interprets the basic theorems in metric space,
5) He/She defines basic concepts of topology which are the bases of theoretical courses,
6) He/She decides whether structure on an arbitrary set are topology or not,
7) He/She adapts knowledge of functions theory and analysis to topologic space,
8) He/She proves and interprets the fundamental theorems by using properties of topologic space,
9) He/She solves problem by using topology,
10) He/She develops the culture of mathematic by gaining abstract thinking ability.

Course Content

1 Metric spaces, submetric spaces, isometries
2 Open and closed disks, spheres, diameters
3 Topology of metric spaces
4 Sequences and continuity in metric spaces
5 Topological structure and open sets in topological spaces closed sets and properties of the family of closed subsets in topological spaces, neighborhoods of a point and fundamental systems of neighborhoods
6 Bases and subbases of a topology
7 Systems of open neighborhoods
8 Equality of topologies and comparison of topologies
9 Contact and limit points of a set in the topologic space
10 Interior point and interior of a set, closure point and closure of a set
11 The frontier of a subset, dense, nowhere dense, somewhere dense subsets of topological spaces
12 Continuity of functions in a topological space and homeomorphisms
13 Sequences in the topological space and limit of a sequence, T2
14 Subspaces, finite products of topological spaces

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Metric spaces, submetric spaces, isometries
2) Open and closed disks, spheres, diameters
3) Topology of metric spaces
4) Sequences and continuity in metric spaces
5) Topological structure and open sets in topological spaces closed sets and properties of the family of closed subsets in topological spaces, neighborhoods of a point and fundamental systems of neighborhoods
6) Bases and subbases of a topology
7) Systems of open neighborhoods
8) Equality of topologies and comparison of topologies
9) Equality of topologies and comparison of topologies
10) Contact and limit points of a set in the topologic space
11) Interior point and interior of a set, closure point and closure of a set
12) The frontier of a subset, dense, nowhere dense, somewhere dense subsets of topological spaces
13) Continuity of functions in a topological space and homeomorphisms
14) Sequences in the topological space and limit of a sequence, T2 Subspaces, finite products of topological spaces

Sources

Course Notes / Textbooks: 1. Gürkanlı A. Turan, Genel Topoloji, Samsun, 1993.
References: 1. Lipschutz, S., General Topology, Schaum Publishing Co., 1965
2. Özdamar, E., Görgülü A., Alp, A., Genel topoloji, Uludağ Üni. Yayınları, 1999.
3. Aslım, G., Genel topoloji, İzmir, Ege Üniversitesi, 1988

Evaluation System

Semester Requirements Number of Activities Level of Contribution
Homework Assignments 1 % 20
Midterms 1 % 30
Final 1 % 50
Total % 100
PERCENTAGE OF SEMESTER WORK % 50
PERCENTAGE OF FINAL WORK % 50
Total % 100

ECTS / Workload Table

Activities Number of Activities Duration (Hours) Workload
Course Hours 14 3 42
Study Hours Out of Class 14 5 70
Homework Assignments 1 20 20
Midterms 1 30 30
Final 1 38 38
Total Workload 200

Contribution of Learning Outcomes to Programme Outcomes

No Effect 1 Lowest 2 Low 3 Average 4 High 5 Highest
           
Program Outcomes Level of Contribution
1) Ability to assimilate mathematic related concepts and associate these concepts with each other.
2) Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization.
3) Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques.
4) Ability to make individual and team work on issues related to working and social life.
5) Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball.
6) Ability to use mathematical knowledge in technology.
7) To apply mathematical principles to real world problems.
8) Ability to use the approaches and knowledge of other disciplines in Mathematics.
9) Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary.
10) To apply mathematical principles to real world problems.
11) To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.
12) To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself.