Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
COMPLEX MANİFOLDS I MAT 627 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Doktora Dersin Türü SECMELI Dersin Koordinatörü Doç.Dr. MAHMUT AKYİĞİT Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Dersin Amacı The complex structures and manifolds course aims to give the fundamental knowledge for the studies of graduate students who study at topology, algebra and geometry branch. Dersin İçeriği Riemann manifolds, Complex vector fields, Complex structures, complex torsion, Complex coordinate system, Holomorphic function holomorphic map, Holomorphic forms and vector fields, Holomorphic line bundles, Complex manifolds: definition and examples, Holomorphic functions on complex manifolds, Complex submanifolds, Almost complex manifolds nijenhuis tensor, Complex tangent vector infinitezimal otomorfizm, Compact complex manifold, The examples of complex manifolds
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/she learns concept of Riemann manifolds 1 - 2 - 4 - 10 - 15 - A - C - 2 - He/she defines complex structures 1 - 2 - 4 - 10 - 14 - 15 - A - C - 3 - He/she learns holomorphic fonctions 1 - 2 - 4 - 10 - 14 - 15 - A - C - 4 - He/she realizes complex manifolds 1 - 2 - 4 - 10 - 14 - 15 - A - C - 5 - He/she establishes between the Riemann manifold and complex manifolds 1 - 2 - 4 - 10 - 14 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 4:Drilland Practice 10:Brain Storming 14:Self Study 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
14 The examples of complex manifolds
13 Compact complex manifold
12 Complex tangent vector infinitezimal otomorfizm
11 Almost complex manifolds nijenhuis tensor,
10 Complex submanifolds
9 Holomorphic functions on complex manifolds
8 Complex manifolds: definition and examples
7 Holomorphic line bundles
6 Holomorphic forms and vector fields
5 Holomorphic function and holomorphic map
4 Complex coordinate system
3 Complex structures and complex torsion
2 Complex vector fields
1 Riemann manifolds

#### Kaynaklar

Ders Notu 1.) Daniel Huybrechts, Complex geometry, Springer, 1965.
2.) Kunihiko Kodaira, Complex manifold and deformation of complex structures, Springer, 1981.
Ders Kaynakları

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
KisaSinav 1 10
Odev 1 10
Odev 2 10
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 10 10
Quiz 1 10 10
Assignment 2 16 32
Final examination 1 10 10
Toplam İş Yükü 158
Toplam İş Yükü /25(s) 6.32
Dersin AKTS Kredisi 6.32
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