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

Learning outcomes

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

1. Become familiar and hopefully adapt at simple proof techniques.

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
   4. Acquire scientific knowledge and work independently
   5. Work effectively in multi-disciplinary research teams
   6. Design and conduct research projects independently
   7. Develop mathematical, communicative, problem-solving, brainstorming skills.
   8. Effectively express his/her research ideas and findings both orally and in writing
   9. Defend research outcomes at seminars and conferences.
   10. Demonstrating professional and ethical responsibility.

   Method of assessment

   1. Written exam
   2. Homework assignment
   3. Seminar/presentation
2. Develop critical thinking abilities

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
   4. Acquire scientific knowledge and work independently
   5. Design and conduct research projects independently
   6. Develop mathematical, communicative, problem-solving, brainstorming skills.
   7. Effectively express his/her research ideas and findings both orally and in writing
   8. Defend research outcomes at seminars and conferences.
   9. Demonstrating professional and ethical responsibility.

   Method of assessment

   1. Written exam
   2. Homework assignment
   3. Seminar/presentation
3. Develop problem-solving and brainstorming abilities

   Contribution to Program Outcomes

   1. Define and manipulate advanced concepts of Mathematics
   2. Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
   3. Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
   4. Acquire scientific knowledge and work independently
   5. Design and conduct research projects independently
   6. Develop mathematical, communicative, problem-solving, brainstorming skills.
   7. Effectively express his/her research ideas and findings both orally and in writing
   8. Defend research outcomes at seminars and conferences.
   9. Write progress reports clearly on the basis of published documents, thesis, etc
   10. Demonstrating professional and ethical responsibility.

   Method of assessment

   1. Written exam
   2. Homework assignment
   3. Seminar/presentation

Contents
Week 1:	Rings
Week 2:	Ideals
Week 3:	Modules
Week 4:	Tensor product
Week 5:	Rings of fractions
Week 6:	Modules of fractions.
Week 7:	Primary decomposition.
Week 8:	Integral dependence and valuations. Midterm Exam.
Week 9:	Chain conditions
Week 10:	Noetherian rings
Week 11:	Artin rings
Week 12:	Discrete valuation rings
Week 13:	Dedekind domains
Week 14:	Completions
Week 15*:	-
Week 16*:	Final Exam.
Textbooks and materials:	Introduction to Commutative Algebra, M.F. Atiyah, I.G. Macdonald
Recommended readings:	Introduction to Commutative Algebra, M.F. Atiyah, I.G. Macdonald
	* 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:	8	30
Other in-term studies:		0
Project:		0
Homework:	2,3,4,5,6,9,10,11,12,14	30
Quiz:		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:	5	14
Practice, Recitation:	0	0
Homework:	5	10
Term project:	0	2
Term project presentation:	0	1
Quiz:	0	0
Own study for mid-term exam:	10	1
Mid-term:	2	1
Personal studies for final exam:	15	1
Final exam:	3	1
		Total workload:
		Total ECTS credits:	*
	* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)