• Basic information
• Learning outcomes
• Contents
• Assessment
• Workload

Learning outcomes

Upon successful completion of this course, students will be able to:

1. Obtain a detail knowledge of algebraic structures, rings, ideals and their properties.

   Contribution to Program Outcomes

   1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
   2. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
   3. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
   4. Exhibiting professional and ethical responsibility.

   Method of assessment

   1. Written exam
   2. Homework assignment
2. Furthermore, to be familiar with algebraic field extensions and Galois theory.

   Contribution to Program Outcomes

   1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
   2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

   Method of assessment

   1. Written exam
   2. Homework assignment
3. Finally, to be able to do some calculations and applications of prementioned subjects.

   Contribution to Program Outcomes

   1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
   2. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

   Method of assessment

   1. Written exam
   2. Homework assignment

Contents
Week 1:	Rings. Basic properties of rings.
Week 2:	Subrings. Characteristic of a ring. Examples.
Week 3:	Ideals. Finitely generated ideals. Principal ideal ring.
Week 4:	Quotient rings. Ring homomorphisms.
Week 5:	The Isomorphism Theorem.
Week 6:	The Correspondence Theorem. Midterm I.
Week 7:	Sum and direct sum of ideals. Minimal, prime, and maximal ideals.
Week 8:	Some applications of prime and maximal ideals.
Week 9:	Nilpotent ideals. Irreducible and prime elements of a ring.
Week 10:	Principal ideal domain. Unique factorization domain.
Week 11:	Euclidean domain. Midterm II.
Week 12:	İrreducible polynomials and Eisenstein criterion.
Week 13:	Algebraic extension of a field.
Week 14:	Splitting field of a polynomial. Algebraic number field.
Week 15*:	-
Week 16*:	Final Exam.
Textbooks and materials:	Basic Abstract Algebra, P.B. Bhattacharya, S. K. Jain, S. R. Nagpaul, ISBN-13: 978-0521466295 ISBN-10: Edition: 2nd. ed. 1994, Cambridge University Press.
Recommended readings:	Abstract Algebra, D.S.Dummit, R.M.Foote, ISBN-13: 978-0471433347 ISBN-10: 0471433349 Edition: 3rd
	* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

Assessment
Method of assessment	Week number	Weight (%)
Mid-terms:	6,11	50
Other in-term studies:	0	0
Project:	0	0
Homework:	3,5,7,9,11	10
Quiz:	0	0
Final exam:	16	40
	Total weight:	(%)

Workload
Activity	Duration (Hours per week)	Total number of weeks	Total hours in term
Courses (Face-to-face teaching):	3	14
Own studies outside class:	3	14
Practice, Recitation:	0	0
Homework:	5	5
Term project:	0	0
Term project presentation:	0	0
Quiz:	0	0
Own study for mid-term exam:	10	2
Mid-term:	4	2
Personal studies for final exam:	10	1
Final exam:	2	1
		Total workload:
		Total ECTS credits:	*
	* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)