Mathematics (English) Preview
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code:

MATH322

Course Name:

Ring Theory

Semester:

Spring

Course Credits:

ECTS

Language of instruction:

English

Course Condition:

Does the Course Require Work Experience?:

Type of course:

Compulsory Courses

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator:

Prof. Dr. SELÇUK DEMİR

Course Lecturer(s):

Prof. Dr. Şükrü Yalçınkaya

Course Assistants:

Course Objective and Content

Course Objectives:

The aim of the course is to learn the fundamentals of the introductory ring and field theory which are the basic concepts in algebra.

Course Content:

The content of the course consists of rings, integral domains, fields, ideals, factor rings, prime and maximal ideals, homomorphisms of rings, rings of quotients, localisation, Euclidean woman, principal ideal domain, unique factorisation domain, rings of polynomials, factorisation of polynomials, field extensions, splitting and separable fields, finite fields and ruler and compasss constructions.

Learning Outcomes

The students who have succeeded in this course;
1) Understand rings, integral domains and fields
2) Understand ideals, homomorphisms and quotient rings.
3) Understand Euclidean domains, principal ideal domains, unique factorization domains
4) Understand field extensions
5) Understand the finite fields

Course Flow Plan

Week	Subject	Related Preparation
1)	Rings, integral domains, fields
2)	Ideals, factor rings
3)	Prime and maximal ideals
4)	Homomorphisms, Homomorphism theorems
5)	Euclidean domain, Principal ideal domain, Unique factorisation domains
6)	Rings of quotients and localisation
7)	Rings of polynomials, factorisation of polynomials
8)	Midterm Exam
9)	Field extensions
10)	Algebraic extensions
11)	Splitting fields
12)	Separable fields
13)	Finite fields
14)	Ruler and compass constructions

Sources

Course Notes / Textbooks:	John B. Fraleigh and Neal Brand - “A First Course in Abstract Algebra”
References:	Lecture notes

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4	5
Program Outcomes
1) Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.
2) Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3) Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.
4) Have the ability to think analytically and use the time effectively in the process of deduction.
5) Have the ability to search the literature, understand and interpret scientific articles.
6) Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7) Have the ability to work efficiently in interdisciplinary teams.
8) Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9) Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10) Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.
11) Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.	2
2)	Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3)	Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.
4)	Have the ability to think analytically and use the time effectively in the process of deduction.	3
5)	Have the ability to search the literature, understand and interpret scientific articles.
6)	Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7)	Have the ability to work efficiently in interdisciplinary teams.
8)	Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9)	Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10)	Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.	3
11)	Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.	3

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Midterms	1	% 40
Final	1	% 60
total		% 100
PERCENTAGE OF SEMESTER WORK		% 40
PERCENTAGE OF FINAL WORK		% 60
total		% 100

Workload and ECTS Credit Calculation

Activities	Number of Activities	Preparation for the Activity	Spent for the Activity Itself	Completing the Activity Requirements	Workload
Course Hours	13	0	3		39
Study Hours Out of Class	13	0	3		39
Midterms	1	0	15		15
Final	1	0	25		25
Total Workload					118