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| Course Description |
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| Course Name |
: |
Module Theory |
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| Course Code |
: |
MT 418 |
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| Course Type |
: |
Optional |
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| Level of Course |
: |
First Cycle |
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| Year of Study |
: |
4 |
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| Course Semester |
: |
Spring (16 Weeks) |
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| ECTS |
: |
5 |
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| Name of Lecturer(s) |
: |
Asst.Prof.Dr. ZEYNEP YAPTI ÖZKURT
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| Learning Outcomes of the Course |
: |
Knows the definition of modules and their properties.
Knows the definitions and properties of submodules, quotient modules and homomorphisms.
Knows the structure of finitely generated and free modules.
Understands the decomposition theorems.
Makes applications on finite abelian groups.
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| Mode of Delivery |
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Face-to-Face |
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| Prerequisites and Co-Prerequisites |
: |
None |
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| Recommended Optional Programme Components |
: |
None |
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| Aim(s) of Course |
: |
Understand the definitions and basic theorems of modules, learn the properties of finitely generated and free modules, make applications on finite abelian groups. |
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| Course Contents |
: |
Modules, submodules and quotient modules. Homomorphisms. direct sums, finitely generated modules, torsion submodules, free modules. Hilbert Basis Theorem. Submodules of free modules. Decomposition theorems. Finitely generated abelian groups. |
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| Language of Instruction |
: |
Turkish |
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| Work Place |
: |
Faculty of Science Annex Classrooms |
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Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
|
1 |
Definition of modules and proporties |
Required readings |
Lecture and Discussion |
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2 |
sub modules |
Required readings |
Lecture and Discussion |
|
3 |
Homeomorphisms and quotient modules |
Required readings |
Lecture and Discussion |
|
4 |
Direct sums |
Required readings |
Lecture and Discussion |
|
5 |
Finite generated modules |
Required readings |
Lecture and Discussion |
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6 |
Torsion modules |
Required readings |
Lecture and Discussion |
|
7 |
Free modules |
Required readings |
Lecture and Discussion |
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8 |
Midterm exam |
Review and problem solving |
written exam |
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9 |
Free modules |
Required readings |
Lecture and Discussion |
|
10 |
Quotient rings and maximal ideals |
Required readings |
Lecture and Discussion |
|
11 |
Hilbert bases theorem |
Required readings |
Lecture and Discussion |
|
12 |
Submodules of free modules |
Required readings |
Lecture and Discussion |
|
13 |
Decomposition theorems |
Required readings |
Lecture and Discussion |
|
14 |
Finitely generated abelian groups |
Required readings |
Lecture and Discussion |
|
15 |
Exercises |
Required readings |
Lecture and Discussion |
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16/17 |
Final exam |
Review and problem solving |
written examination |
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Required Course Resources |
| Resource Type | Resource Name |
| Recommended Course Material(s) |
 Rings, Modules and Linear algebra, B. Hartley and T.O. Hawkes
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| |
| Required Course Material(s) | |
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Assessment Methods and Assessment Criteria |
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Semester/Year Assessments |
Number |
Contribution Percentage |
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Mid-term Exams (Written, Oral, etc.) |
1 |
100 |
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Homeworks/Projects/Others |
0 |
0 |
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Total |
100 |
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Rate of Semester/Year Assessments to Success |
40 |
| |
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Final Assessments
|
100 |
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Rate of Final Assessments to Success
|
60 |
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Total |
100 |
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| Contribution of the Course to Key Learning Outcomes |
| # | Key Learning Outcome | Contribution* |
|
1 |
Is able to prove Mathematical facts encountered in secondary school. |
4 |
|
2 |
Recognizes the importance of basic notions in Algebra, Analysis and Topology |
5 |
|
3 |
Develops maturity of mathematical reasoning and writes and develops mathematical proofs. |
5 |
|
4 |
Is able to express basic theories of mathematics properly and correctly both written and verbally |
2 |
|
5 |
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. |
2 |
|
6 |
Expresses clearly the relationship between objects while constructing a model |
3 |
|
7 |
Draws mathematical models such as formulas, graphs and tables and explains them |
5 |
|
8 |
Is able to mathematically reorganize, analyze and model problems encountered. |
5 |
|
9 |
Knows at least one computer programming language |
4 |
|
10 |
Uses effective scientific methods and appropriate technologies to solve problems |
0 |
|
11 |
Knows programming techniques and is able to write a computer program |
0 |
|
12 |
Is able to do mathematics both individually and in a group. |
0 |
|
13 |
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians |
0 |
|
14 |
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields |
0 |
| * Contribution levels are between 0 (not) and 5 (maximum). |
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| Student Workload - ECTS |
| Works | Number | Time (Hour) | Total Workload (Hour) |
| Course Related Works |
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Class Time (Exam weeks are excluded) |
14 |
3 |
42 |
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Out of Class Study (Preliminary Work, Practice) |
14 |
3 |
42 |
| Assesment Related Works |
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Homeworks, Projects, Others |
0 |
0 |
0 |
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Mid-term Exams (Written, Oral, etc.) |
1 |
15 |
15 |
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Final Exam |
1 |
20 |
20 |
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Total Workload: | 119 |
| Total Workload / 25 (h): | 4.76 |
| ECTS Credit: | 5 |
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