Ders Bilgileri

Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
HOMOLOGICAL ALGEBRA MAT 609 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Doktora Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. MEHMET ÖZEN Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Dersin Amacı To introduce subject of base abstract algebra Dersin İçeriği Algebraic structure, homological algebra
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - Students will have learnt the most important notions of homological algebra. 1 - 4 - 15 - A - C - 2 - Students will have learnt the basic methods of homological algebra. 1 - 4 - 15 - A - C - 3 - Students will have discussed such topics as chain complexes and spectral sequences. 1 - 4 - 15 - A - C - 4 - Students will have done applications to subjects such as cohomology of groups and Hochschild cohomology of algebras. 1 - 4 - 15 - A - C - 5 - Students will have acquired an intoduction to classical homological algebra which provides a link with the modern approach via derived categories. 1 - 4 - 15 - A - C - 6 - Students will have learnt about modules such as projective, injection, and free modules. 1 - 4 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 4:Drilland Practice 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

Ders Akışı

Hafta Konular ÖnHazırlık
1 Basic concepts
2 Modules
3 Submodules
4 Homomorphism
5 Homological structure
6 Complete sequences
7 Complete sequences
8 Projective modules
9 Injection modules
10 Generator, base
11 Free modules
12 Free moduless
13 Tensor product
14 Tensor product

Ders Notu
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
12 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
13 Student completes the missing or limited knowledge by using the scientific methods. X
14 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
15 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
16 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
17 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
18 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
19 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
20 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
21 Student follows the necessary technological developments in his/her field, and s/he uses them. X

Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
KisaSinav 1 10
KisaSinav 2 10
Odev 1 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 20 20
Quiz 2 1 2
Assignment 1 15 15
Final examination 1 25 25
Toplam İş Yükü 158
Toplam İş Yükü /25(s) 6.32
Dersin AKTS Kredisi 6.32
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