Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
GROUP THEORY MAT 536 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Yüksek Lisans Dersin Türü SECMELI Dersin Koordinatörü Doç.Dr. MURAT GÜZELTEPE Dersi Verenler Doç.Dr. MURAT GÜZELTEPE Dersin Yardımcıları Dersin Kategorisi Dersin Amacı To introduce subject of base abstract algebra Dersin İçeriği Algebraic structure, Groups
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - Students will have acquired a sound understanding of the classification of finitely generated abelian groups. 1 - 4 - 15 - A - C - 2 - Students will have acquired knowledge of some fundamental results and techniques from the theory of finite groups. 1 - 4 - 15 - A - C - 3 - Students will have acquired knowledge of group actions on sets, simple groups. 1 - 4 - 15 - A - C - 4 - Students will have acquired knowledge of Sylow’s theorems. 1 - 4 - 15 - A - C - 5 - Students will have acquired knowledge of various applications of Sylow’s theorems. 1 - 4 - 15 - A - C - 6 - Students will have developed an appreciation of the homeomorphism and isomorphism theorems for groups. 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 consepts
2 Axioms of group
3 Subgroups and cyclic groups
4 Normal subgroups
5 Quotient sets, quotient groups
6 Homomorphism
7 Isomorphism, automorphism
8 Permutation group
9 Direct sum
10 Structure of finite abelian groups
11 Sylow theorems
12 Resolvable groups
13 P-group. Normal series
14 General linear group

Ders Notu
Ders Kaynakları

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 Student follows the current journals in his/her field and puts forward problems. X
2 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
3 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
4 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
5 Student determines the problems to be solved within his/her field and if necessary takes the lead.
6 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field.
7 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters
8 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research.
9 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
10 Student follows the current journals in his/her field and puts forward problems. X
11 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
12 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
13 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
14 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
15 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
16 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
17 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
18 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
19 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
20 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. 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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