Course Name Code Semester T+U Hours Credit ECTS
Algebra IME 307 5 2 + 0 2 2
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level Bachelor's Degree
Course Type Compulsory
Course Coordinator Dr.Öğr.Üyesi ERCAN MASAL
Course Lecturers Dr.Öğr.Üyesi ERCAN MASAL,
Course Assistants

Res. Assist. Emine Nur BİLGİÇ

Course Category Available Basic Education in the Field
Course Objective

The objective of this class is to teach algebraic stuctures such that groups, rings and fields and to work on the relations between them.

Course Content

Binary operations; definition of algebraic groups and its basic properties; subgroups; permutation groups; cyclic groups; symmetry group of regular polygons; cyclic permutations; odd and even permutations; homomorphisms; Cosets and Lagrange theorem; isomorphism theorems; an action of a group on a set; rings, sub rings and ideals; prime and maximal ideals; homomorphisms on rings; arithmetics on rings; polynomial rins; Burnside theorem and its applications; fields; p-groups and related theorems.

# Course Learning Outcomes Teaching Methods Assessment Methods
1 Student knows group structures and proves important theorems related to group structures Lecture, Drilland Practice, Testing,
2 Student observes the pros of equivalency of two algebraic structures by understanding the isomorphism theorems Lecture, Drilland Practice, Testing,
3 Student knows the notions of cosets and normal subspaces Lecture, Drilland Practice, Testing,
4 Student understands the notion of rings Lecture, Drilland Practice, Testing,
5 Student knows homomorphisms on rings. Lecture, Drilland Practice, Testing,
Week Course Topics Preliminary Preparation
1 Preliminaries, Binary Operations
2 Groups
3 Subgroups
4 Permutation groups
5 Dihedral Groups and Symmetry Groups
6 Cyclic Permutations
7 Even and odd permutations and homomorphisms
8 İsomorphism and isomorphism theorems
9 Midterm
10 Cosets and Lagrange Theorem
11 An action of a group on a set
12 Rings, Subrings, and Ideals
13 Ring homomorphisms and operations on rings
14 Rings of polynomials and fields
Resources
Course Notes
Course Resources

Örneklerle Soyut Cebir, Fethi Çallıalp, Birsen Yayınevi

Cebire Giriş, Ahmet Arıkan-Sait Halıcıoğlu, Palme Yayınevi

Order Program Outcomes Level of Contribution
1 2 3 4 5
1 X
2 X
3 X
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 60
1. Kısa Sınav 15
1. Ödev 10
2. Kısa Sınav 15
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 2 32
Hours for off-the-classroom study (Pre-study, practice) 16 1 16
Mid-terms 1 3 3
Quiz 2 2 4
Assignment 1 2 2
Final examination 1 5 5
Total Workload 62
Total Workload / 25 (Hours) 2.48
dersAKTSKredisi 2