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Syllabus ( MATH 525 )


   Basic information
Course title: Commutative Algebra
Course code: MATH 525
Lecturer: Assist. Prof. Altan ERDOĞAN
ECTS credits: 7.5
GTU credits: 3 (3+0+0)
Year, Semester: 2016, Fall and Spring
Level of course: Second Cycle (Master's)
Type of course: Area Elective
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: Linear Algebra
Professional practice: No
Purpose of the course: To understand the structures of modules over commutative rings
   Learning outcomes Up

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 Up
Week 1: Rings
Week 2: Ideals
Week 3: Modules
Week 4: Tensor product
Week 5: Rings and modules of fractions
Week 6: Primary decomposition
Week 7: Integral dependence and valuations
Week 8: Midterm
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*: Review
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 Up
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 Up
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)
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