Syllabus ( MATH 519 )
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Basic information
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| Course title: |
Module Theory I |
| Course code: |
MATH 519 |
| Lecturer: |
Assoc. Prof. Dr. Ayten KOÇ
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| ECTS credits: |
7.5 |
| GTU credits: |
3 (3+0+0) |
| Year, Semester: |
1/2, Fall and Spring |
| Level of course: |
Second Cycle (Master's) |
| Type of course: |
Area Elective
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| Language of instruction: |
English
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| Mode of delivery: |
Face to face
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| Pre- and co-requisites: |
none |
| Professional practice: |
No |
| Purpose of the course: |
To teach the structure of modules over noncommutative rings |
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Learning outcomes
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Upon successful completion of this course, students will be able to:
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Explan the structure of modules
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Review the literature critically pertaining to his/her research projects, and connect the earlier literature to his/her own results
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Work effectively in multi-disciplinary research teams
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Develop mathematical, communicative, problem-solving, brainstorming skills.
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Defend research outcomes at seminars and conferences.
Method of assessment
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Written exam
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Develop awareness for simple and semisimple modules
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
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Acquire scientific knowledge and work independently
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Develop mathematical, communicative, problem-solving, brainstorming skills.
Method of assessment
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Written exam
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Homework assignment
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Identify Artin and Noether modules
Contribution to Program Outcomes
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Define and manipulate advanced concepts of Mathematics
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Relate mathematics to other disciplines and develop mathematical models for multidisciplinary problems
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Acquire scientific knowledge and work independently
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Develop mathematical, communicative, problem-solving, brainstorming skills.
Method of assessment
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Written exam
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Contents
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| Week 1: |
Rings |
| Week 2: |
Modules and submodules |
| Week 3: |
Module homomorphisms |
| Week 4: |
Categories of modules and exact sequences |
| Week 5: |
Direct summands |
| Week 6: |
Direct sums and products of modules |
| Week 7: |
Generating and cogenerating. |
| Week 8: |
Midterm exam |
| Week 9: |
Simple and semisimple modules |
| Week 10: |
Finitely generated modules and chain conditions |
| Week 11: |
Series of modules: Modules of finite composition lenght |
| Week 12: |
Indecomposable decompositions of modules |
| Week 13: |
Noetherian and Artinian modules |
| Week 14: |
Noetherian and Artinian modules |
| Week 15*: |
General review |
| Week 16*: |
Final exam |
| Textbooks and materials: |
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| Recommended readings: |
1. F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Second Edition, 13, Springer-Verlag, New York, 1992.
2. A. Facchini, Module Theory. Endomorphism rings and direct sum decompositions in some classes of modules,
Progress in Math. 167, Birkhauser Verlag, Basel, 1998.
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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Assessment
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| Method of assessment |
Week number |
Weight (%) |
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| Mid-terms: |
8 |
40 |
| Other in-term studies: |
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0 |
| Project: |
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0 |
| Homework: |
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0 |
| Quiz: |
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0 |
| Final exam: |
16 |
60 |
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Total weight: |
(%) |
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Workload
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| Activity |
Duration (Hours per week) |
Total number of weeks |
Total hours in term |
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| Courses (Face-to-face teaching): |
3 |
14 |
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| Own studies outside class: |
4 |
14 |
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| Practice, Recitation: |
0 |
0 |
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| Homework: |
6 |
10 |
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| Term project: |
0 |
0 |
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| Term project presentation: |
0 |
0 |
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| Quiz: |
0 |
0 |
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| Own study for mid-term exam: |
10 |
1 |
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| Mid-term: |
1 |
1 |
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| Personal studies for final exam: |
15 |
1 |
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| Final exam: |
2 |
1 |
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Total workload: |
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Total ECTS credits: |
* |
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* ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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