1	Course Title:	ALGEBRAIC TOPOLOGY I
2	Course Code:	MAT4077
3	Type of Course:	Optional
4	Level of Course:	First Cycle
5	Year of Study:	4
6	Semester:	7
7	ECTS Credits Allocated:	5
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:	Prof. Dr. OSMAN BİZİM
16	Course Lecturers:	Prof. Dr. Osman Bizim
17	Contactinformation of the Course Coordinator:	Uludağ Üniversitesi, Fen-Edebiyat Fakültesi Matematik Bölümü, Görükle Bursa-TÜRKİYE 0 224 294 17 50 / obizim@uludag.edu.tr
18	Website:
19	Objective of the Course:	The aim of this course to give the basic principals of algebraic topology.
20	Contribution of the Course to Professional Development

21

Learning Outcomes:

1 Learns topological groups and their properties.; 2 Learns group action on a space.; 3 Learns Brower-fixed point theorem and its applications.; 4 Learns categories and functors.; 5 Learns the path, the path-connected topological spaces and local path connected topological spaces.; 6 Learns the basic concepts of algebraic toplogy.;

22	Course Content:

Week	Theoretical	Practical
1	Topological Groups and their properties
2	The acts of a group on a topological group and its properties
3	The Brower-fixed point theorem and its applications
4	Categories
5	Functors
6	The path in the topological spaces and their properties
7	The connected and path-connected topological spaces and the relations between them
8	The local path connected topological spaces and its applications
9	Two dimensional manifolds and their properties
10	Orientable and nonorientable surfaces and their properties
11	Connected two dimensional manifolds and their properties
12	The classification theorem of compact surfaces and their properties
13	Triangulation of compact surfaces
14	The Euler caracteristic of surfaces

23	Textbooks, References and/or Other Materials:	1. W. S. Massey, A Basic Course in Algebraic Toplogy, Springer-Verlag, 1991. 2. M.J. Greenberg, J.R. Harper, Algebraic Topolgy, A First Course, Addison-Wesley, 1981. 3. J. Munkres, Topology, Prentice-Hill, 2.Ed. 2000.
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
Information

25

ECTS / WORK LOAD TABLE

Activites	NUMBER	TIME [Hour]	Total WorkLoad [Hour]
Theoretical	14	3	42
Practicals/Labs	0	0	0
Self Study and Preparation	14	2	28
Homeworks, Performances	0	0	0
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	1	20	20
Others	14	2	28
Final Exams	1	32	32
Total WorkLoad			150
Total workload/ 30 hr			5
ECTS Credit of the Course			5

26	CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
PQ1 PQ2 PQ3 PQ4 PQ5 PQ6 PQ7 PQ8 PQ9 PQ10 LO1 5 5 5 5 5 5 5 5 5 5 LO2 5 5 5 5 5 5 5 5 5 5 LO3 5 5 5 5 5 5 5 5 5 5 LO4 5 5 5 5 5 5 5 5 5 5 LO5 5 5 5 5 5 5 5 5 5 5 LO6 5 5 5 5 5 5 5 5 5 5

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High