Kocaeli University / European Credit Transfer System (ECTS)

Name of Lecturer(s)

Assistant Prof. Dr. Ayşe Arzu ARI

Learning Outcomes of the Course Unit
Program Competencies-Learning Outcomes Relation

Learning Outcomes of the Course Unit

1) It has detailed knowledge of binary operationsand shows the properties it provides whengiven a transaction
2) Defines the concept of group.
3) Explains the theorems about subgroup and subgroup
4) Displays the end groups by table.
5) Applies basic theorems about cyclic groups.
6) Solves problems related to the rank of an element.
7) Dihedral has information about groups andexamples.
8) The remaining class implements the conceptof chapter groups and their basic theorems.
9) Solve exercises related to normal subgroup.
10) Solve exercises related to grouphomomorphisms.
11) Solve exercises about permutation groups.
12) It solves the exercises on the concept of the ring.
13) Solves the exercises related to the lower ringand ideal.
14) Explains the concept of ring homomorphism.

Program Competencies-Learning Outcomes Relation

Program Competencies

Learning Outcomes

High

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

Abstract Mathematics

Course Contents

Binary operations, group definition and basic properties, subgroups, permutation groups,cyclic groups, smooth n-gen symmetry group, cyclic permutations, single and doublepermutations, homomorphisms, Kosets and Lagrange theorems, isomorphism theorems,rings, sub-rings and ideals, prime and maximal ideals, ring homomorphisms, arithmeticin rings, polynomial rings, objects; Burnside theorem and its applications, p-groups andrelated theorems, A n simplicity for n> 4.

Weekly Schedule

1) Introduction to Algebra
2) Basic Concepts and Definitions of Group Theory
3) Groups elementary features
4) Subgroups
5) Turnover Groups
6) Side sets and Lagrange's Theorem
7) General review and practice
8) Midterm
9) Normal Subgroups and Quotient Groups
10) Homomorphisms
11) Ring Concept and basic characteristics
12) Completeness Regions and Sub-Rings
13) Fields
14) Ideal and Quotient Rings
15) Some special Idaels and Characterizations
16) General review and practice

Planned Learning Activities and Teaching Methods

1) Lecture
2) Question-Answer

Assessment Methods and Criteria

Contribution of Midterm Examination to Course Grade	30%
Contribution of Final Examination to Course Grade	70%
Total	100%

Language of Instruction

Turkish

Work Placement(s)

Not Required

Course Unit Title	Course Unit Code	Type of Course Unit	Level of Course Unit	Year of Study	Semester	ECTS Credits
Abstract Algebra	IMO208	Compulsory	Bachelor's degree	2	Spring	4