COURSE SYLLABUS

METRIC SPACES

1	Course Title:	METRIC SPACES
2	Course Code:	MAT2028
3	Type of Course:	Compulsory
4	Level of Course:	First Cycle
5	Year of Study:	2
6	Semester:	4
7	ECTS Credits Allocated:	4
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
10	Laboratory (hour/week) :	0
11	Prerequisites:	None
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Doç. Dr. AYSUN YURTTAŞ GÜNEŞ
16	Course Lecturers:	Doç. Dr. Yeliz KARA ŞEN
17	Contactinformation of the Course Coordinator:	Uludag University, Art and Science Faculty Department of Mathematics, 16059 Görükle Bursa-TURKEY 0 224 294 17 69/ ayurttas@uludag.edu.tr
18	Website:
19	Objective of the Course:	The aim of the course is to make the students gain the basic subjects of the metric sapaces and normed spaces. The goals are to teach the metric spaces, normed spaces and topological spaces, their examples and properties. To teach the related notions and results so that the students can make their applications, and let them know about the historical background of the topics.
20	Contribution of the Course to Professional Development	Students have the necessary equipment about toplogy courses in undergraduate education.

Learning Outcomes:

1	Learns metric spaces, normed spaces, topology and topological spaces. ;
2	Learns the interior, the exterior, the boundary and the closure of a set in metric, normed and topological spaces. ;
3	Learns sequences and convergence of the sequences in the metric and normed sapaces.;
4	Learns continuity of functions in metric and normed spaces. ;
5	Learns complete metric spaces.;

22	Course Content:

Week	Theoretical	Practical
1	Metric spaces, their properties and examples.
2	Normed spaces, their properties and examples.
3	Open and closed sets in metric and the normed spaces.
4	Accumulation and closure points of metric and normed spaces.
5	Sequences and their convergence in metric and normed spaces.
6	Submetric and subnormed spaces, their properties and examples.
7	Continuity and uniform continuity in metric and normed spaces.
8	Midterm exam.
9	Equivalent metrics and their properties.
10	Complete metric spaces and their properties.
11	The completions of metric spaces.
12	Topological spaces, their properties and examples.
13	Open and closed sets in topological spaces.
14	Accumulation and closure points of topological spaces.

23	Textbooks, References and/or Other Materials:	[1] Topoloji, O. Bizim [2] Topoloji, O. Mucuk [3] Genel topoloji, N. Yıldız [4] Topology, J. Munkers
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	40
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	60
Total	2	100
Contribution of Term (Year) Learning Activities to Success Grade		40
Contribution of Final Exam to Success Grade		60
Total		100
Measurement and Evaluation Techniques Used in the Course	The system of relative evaluation is applied.
Information

ECTS / WORK LOAD TABLE

CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High