Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
COMMUTATIVE ALGEBRA MAT 608 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 basic abstract algebra. Dersin İçeriği Algebraic structures, Commutative structures
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - Students will be able to demonstrate facility in dealing with polynomials in one and more variables. 1 - 4 - 15 - A - C - 2 - Students will be able to demonstrate understanding of some basic ideal structure of polynomial rings. 1 - 4 - 15 - A - C - 3 - Students will be able to demonstrate appreciation of the subtleties of factorisation into prime and irreducible elements. 1 - 4 - 15 - A - C - 4 - Students will be able to demonstrate ability to relate polynomials to other algebraic structures. 1 - 4 - 15 - A - C - 5 - Students will be able to demonstrate ability to compute generating sets. 1 - 4 - 15 - A - C - 6 - Students will be able to demonstrate ability to solve problems relating to the factorisation of polynomials, irreducible polynomials and extension fields. 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 Rings
2 Ideals
3 Pime and maximal ideals
4 Homomorphism
5 Principal ideals domains
6 Unique factorization domain
7 Factorization over polynomial rings
8 Chain conditions
9 Primary ideals
10 Primary ideals
11 Primary decompositions
12 Artinian rings
13 Noetharian rings
14 Noetharian rings

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 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
3 Student completes the missing or limited knowledge by using the scientific methods. X
4 Student completes the missing or limited knowledge by using the scientific methods. X
5 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
6 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
7 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
8 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
9 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
10 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
11 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
12 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
13 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
14 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
15 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
16 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
17 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
18 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
19 Student follows the necessary technological developments in his/her field, and s/he uses them. X
20 Student follows the necessary technological developments in his/her field, and s/he uses them. X
21 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
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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