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| MATL7163 | Riemann Surfaces | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Third Cycle | | Status | Elective | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | -- | | Co-Lecturer | Assoc.Prof.Dr. Bahadır Özgür Güler | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | To understand Riemann surfaces, holomorphic funcitons and covering properties. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | learn some further analysis in Riemann surfaces | | | | PO - 2 : | apply these concepts to advanced problems | | | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), PO : Learning Outcome | | |
| Covering spaces, the fundamental group, analytic continuation, algebraic functions, differential forms, integration of differential forms, Linear differential Equations, cohomology groups, Finiteness Theorem, Exact Cohomology Sequence, Riemann-Roch Theorem, Serre Duality Theorem, Harmonic Differential Forms, Abels Theorem, Jacori İnversion Problem
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Kohomology groups,Finite theorem | | | Week 2 | Riemann Rouch theorem, Serre Dual theorem | | | Week 3 | Harmonic differential forms | | | Week 4 | Abel theorem,Jacobi inversion problem | | | Week 5 | Dirichlet boundary value problem | | | Week 6 | Countable topology,Weyl lemma | | | Week 7 | Countable topology,Weyl lemma | | | Week 8 | Runge approximation theory | | | Week 9 | Midterm | | | Week 10 | Mittag-Leffler and Weierstrass theorems | | | Week 11 | Mittag-Leffler and Weierstrass theorems | | | Week 12 | Riemann transformation theorems | | | Week 13 | Riemann transformation theorems | | | Week 14 | Riemann Hilbert problem | | | Week 15 | Riemann Hilbert problem | | | Week 16 | End-of-term exam | | | |
| 1 | Orster, F. 1981; Lectures on Riemann Surfaces, Springer Verlag, New York | | | |
| 1 | Ahlfors, L.W. Sario, L. 1960; Riemann Surfaces, Princeton University Press | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 11/04/2017 | 2 | 30 | | Quiz | 11 | 25/04/2017 | 1 | 30 | | End-of-term exam | 16 | 05/06/2017 | 2 | 40 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 14 | 42 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Arasınav için hazırlık | 4 | 8 | 32 | | Arasınav | 2 | 1 | 2 | | Ödev | 4 | 9 | 36 | | Kısa sınav | 1 | 1 | 1 | | Dönem sonu sınavı için hazırlık | 5 | 8 | 40 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 225 |
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