Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
INTRODUCTION TO ALGEBRA IME 309 5 3 + 1 4 7
 Dersin Dili Türkçe Dersin Seviyesi Lisans Dersin Türü ZORUNLU Dersin Koordinatörü Dr.Öğr.Üyesi ERCAN MASAL Dersi Verenler Dr.Öğr.Üyesi ERCAN MASAL Dersin Yardımcıları Res.Assist.Mithat TAKUNYACI Dersin Kategorisi Alanına Uygun Öğretim Dersin Amacı To give detailed information to students of elementary education about binary operations which are on many fields of mathematics. To introduce algebraic structure as group, subgroup, ring, subring, ideal which set up a theoretical substructure of especially linear algebra by the help of binary operations and give main group, varieties of subgroup Dersin İçeriği Binary operations, definition of group, subgroups, permutation groups, homomorphism, cyclic groups, residue classes, normal subgroups, quotient groups, definition of ring, subrings, ideals.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - Explain detailed information about binary operations, show properties of a given operatione 1 - 4 - A - C - 2 - Define subgroup and theorems related subgroup and apply them to problems. 1 - 4 - A - C - 3 - Explain the definition of rank of a element and solve the problems related rank. 1 - 4 - A - C - 4 - Explain theorem of normal subgroup and demonstrate a subgroup is whether normal subgroup or not. 1 - 4 - A - C - 5 - Explain definition of group homeomorphism, express theorem of isomorphism. Demonstrate core of a homeomorphism. Solve the problems related homeomorphism 1 - 4 - A - C - 6 - Express the concept of ring, demonstrate that algebraic structure is whether ring or not 1 - 4 - A - C -
 Öğretim Yöntemleri: 1:Lecture 4:Drilland Practice Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Binary operation and concept of group
2 Examples of group
3 Theorems of subgroup and their applications
4 Cyclic groups and their applications
5 Rank of a element and its applications, dihedral group
6 Residue class, Lagrange Theorem and quotient group
7 Normal subgroups and their applications
8 Group homeomorphism and theores of isomorphism
9 Mid – Term Exam
10 Applications of homeomorphism
11 Permutation groups
12 Ring and its applications
13 Subring and ideals
14 Ring homeomorphism

Ders Notu
Ders Kaynakları

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 60
KisaSinav 1 15
Odev 1 10
KisaSinav 2 15
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 4 64
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 10 10
Quiz 2 3 6
Assignment 1 20 20
Performance Task (Laboratory) 1 30 30
Toplam İş Yükü 178
Toplam İş Yükü /25(s) 7.12
Dersin AKTS Kredisi 7.12
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