COURSE SYLLABUS

RIEMANN SURFACES I

1	Course Title:	RIEMANN SURFACES I
2	Course Code:	MAT6103
3	Type of Course:	Optional
4	Level of Course:	Third Cycle
5	Year of Study:	1
6	Semester:	1
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 57 / obizim@uludag.edu.tr
18	Website:
19	Objective of the Course:	The aim of the course is to give basic properties of the theory of the Riemann surfaces. So have the ability conduct original research for future studies.
20	Contribution of the Course to Professional Development

Learning Outcomes:

1	Learns algebraic functions, meromorphic functions and analytic functions.;
2	Learns topological spaces, topological transformation groups and manifolds.;
3	Learns elliptic functions and periodic functions.;
4	Learns general properties of elliptic functions.;
5	Learns analytic and meromorphic continuation.;
6	Learns the Monodromy theorem, fundamental group, branch point and monodromy group.;
7	Learns Riemann surfaces and Riemann surfaces of some special functions.;

22	Course Content:

Week	Theoretical	Practical
1	Algebraic functions, meromorphic functions and analytic functions and their properties.
2	Topological spaces, topological transformation groups and manifolds and their properties.
3	Elliptic functions, periodic and double periodic functions, lattices and fundamental regions.
4	Topological properties of elliptic functions.
5	Uniform and normal convergence of function series and sequences and their properties.
6	Weierstrass Pi function and its properties.
7	The field of elliptic functions and its properties.
8	The construction of elliptic functions with given properties.
9	Topological properties of double periodic elliptic functions.
10	Meromorphic, analytic and mero-morphic continuation along a path and their properties.
11	Analytic continuation with power series.
12	Regular and singüler points and their properties, the Monodromy theorem and its properties.
13	The fundamental group and its properties.
14	The Riemann surfaces and its properties.

23	Textbooks, References and/or Other Materials:	[1] Introduction to Riemann Surfaces, G. Springer, [2] 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

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