1	Course Title:	ALGEBRAIC TOPOLOGY II
2	Course Code:	MAT4078
3	Type of Course:	Optional
4	Level of Course:	First Cycle
5	Year of Study:	4
6	Semester:	8
7	ECTS Credits Allocated:	6
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 the concept of homotopy and its properties.; 2 Learns the homotopy relation and the homotopy theory of equivalence relation.; 3 Learns the fundamental groups.; 4 Learns free groups and Seifert-Van Kampen theorem.; 5 Learns covering spaces and their classification.; 6 Learns the homology theory and homology groups.;

22	Course Content:

Week	Theoretical	Practical
1	The concept of homotopy and its properties
2	The homotopy relation and its properties.
3	The fundamental groups and its applications, the fundamental groups of some surfaces
4	Free groups and their properties
5	The Seifert-Van Kampen theorem and its applications.
6	Covering spaces and classification of covering spaces
7	The lifting of curves to covering spaces, and its applications.
8	The covering space maps and their properties
9	The basic concepts of the theory of homotopy
10	The homology groups and their properties
11	The relations between fundamental group and first homology group.
12	The homomorphisms of continuous functions and their properties.
13	Exact homology sequences and their properties
14	The homology groups of compact 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	4	56
Homeworks, Performances	0	0	0
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	1	21	21
Others	14	2	28
Final Exams	1	31	31
Total WorkLoad			178
Total workload/ 30 hr			5,93
ECTS Credit of the Course			6

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