1	Course Title:	OTOMORF FUNCTIONS I
2	Course Code:	MAT5209
3	Type of Course:	Optional
4	Level of Course:	Second Cycle
5	Year of Study:	1
6	Semester:	1
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 57 / obizim@uludag.edu.tr
18	Website:
19	Objective of the Course:	The aim of the course is to introduce automorphic functions by using the student’s undergraduate background on the theory of complex analysis. The basic concepts of the theory of automorphic functions will be given.
20	Contribution of the Course to Professional Development

21

Learning Outcomes:

1 Learns the linear transformations and their basic properties. ; 2 Learns the fixed points of the transformations and geometric classification of transformations.; 3 Learns groups of linear transformations and their basic properties.; 4 Learns discontinuous groups and their fundamental regions.; 5 Learns finite groups and their generating transformations.; 6 Learns ordinary and parabolic cycles, and function groups.; 7 Learns automorphic functions and their basic properties.;

22	Course Content:

Week	Theoretical	Practical
1	The linear transformations and their basic properties
2	The fixed points of the transformations and basic properties
3	The linear transformations and the circles
4	Inversion in a circle and properties
5	Geometric classification of linear transformations
6	Isometry circles and properties
7	groups of linear transformations and their basic properties
8	Discontinuous groups and their properties
9	Fundamental regions of discontinuous groups and their properties
10	Isometry circles of discontinuous groups and their properties
11	Finite groups and their properties and generating transformations
12	Cyclic transformation groups and their basic properties,
13	Ordinary and parabolic cycles and their properties,
14	Automorphic functions and their properties

23	Textbooks, References and/or Other Materials:	[1] Automorphic Functions, L. Ford, [2] Complex Analysis, L. Ahlfors, [3] Complex Functions, G. A. Jones, D. Singerman
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	0	0
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	100
Total	1	100
Contribution of Term (Year) Learning Activities to Success Grade		0
Contribution of Final Exam to Success Grade		100
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	5	70
Homeworks, Performances	0	0	0
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	0	0	0
Others	14	5	70
Final Exams	1	43	43
Total WorkLoad			225
Total workload/ 30 hr			7,5
ECTS Credit of the Course			7,5

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 LO7 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