COURSE SYLLABUS

RIEMANN SURFACES II

1	Course Title:	RIEMANN SURFACES II
2	Course Code:	MAT6104
3	Type of Course:	Optional
4	Level of Course:	Third Cycle
5	Year of Study:	1
6	Semester:	2
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 the sheaf of germs of meromorphic functions, Riemann surfaces of algebraic functions.;
2	Learns orientable and non-orientable Riemann surfaces.;
3	Learns compact Riemann surfaces and their genus.;
4	Learns automorphisms of Riemann surfaces and conformal equivalences of Riemann surfaces.;
5	Learns covering surfaces of Riemann surfaces, differentials of second order, surface integrals.;
6	Learns harmonic and analytic differentials.;
7	Learns Hilbert spaces of differentials, the existence theorem of harmonic and analytic differentials.;

22	Course Content:

Week	Theoretical	Practical
1	The sheaf of germs of meromorphic functions, Riemann surfaces of algebraic functions
2	Orientable and non-orientable Riemann surfaces and their properties
3	Compact Riemann surfaces and their genus
4	Automorphisms of Riemann surfaces and conformal equivalences of Riemann surfaces
5	Covering surfaces of Riemann surfaces, differentials of second order, surface integrals
6	Harmonic and analytic differentials and their properties
7	Harmonic and analytic differentials, Hilbert spaces of differentials and their properties
8	The existence theorem of harmonic and analytic differentials, the Riemann-Roch theorem
9	Construction Riemann surfaces of logarithm function and its properties
10	Construction Riemann surfaces of polynomial and root functions and their properties
11	Riemann surfaces of algebraic functions and their properties
12	Conformal equivalences of Riemann surfaces
13	Automorphisms of Riemann surfaces and their properties.
14	Conformal equivalence of tori and covering surfaces of Riemann surfaces and their 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