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Information
| Code | MT418 |
| Name | Module Theory |
| Term | 2024-2025 Academic Year |
| Semester | 8. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. ZEYNEP ÖZKURT |
| Course Instructor |
1 2 |
Course Goal / Objective
The aims of this course are understand the definitions and basic theorems of modules, learn the properties of finitely generated and free modules,
Course Content
In this course are tauched module definition and basic features, Sub-modules, homomorphisms and Quotient modules, Some special modules, Decomposition theorems, Applications to Finitely generated Abelyen Groups
Course Precondition
none
Resources
Rings, Modules and Linear algebra, B. Hartley and T.O. Hawkes
Notes
Hungerford, Algebra
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows the definition of modules and their properties. |
| LO02 | Knows the definitions and properties of submodules, quotient modules and homomorphisms. |
| LO03 | understands direct sum and direct product of modules |
| LO04 | Understands the structure of finitely generated and free modules |
| LO05 | Understands the decomposition theorems. |
| LO06 | Makes applications on finite abelian groups. |
| LO07 | Obtaines the Jordan canonical form |
| LO08 | Understands the structure of Torsion modules |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 3 |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 3 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrates the ability to express the basic theories of mathematics accurately both in writing and orally. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Comprehends at least one of the computer programming languages. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 3 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | 1 |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | 3 |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | |
| PLO19 | Bilgi - Kuramsal, Olgusal | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | 3 |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 3 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Definition of modules and proporties | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 2 | sub modules | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 3 | Homomorphisms and quotient modules | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 4 | Direct sums | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 5 | Finite generated modules | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 6 | Torsion modules | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 7 | Free modules | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 8 | Exercises | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Soru-Cevap |
| 9 | Mid Term Exam | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 10 | Quotient rings and maximal ideals | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 11 | Hilbert bases theorem | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 12 | Submodules of free modules | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 13 | Decomposition theorems | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 14 | Finitely generated abelian groups | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 15 | Solving problem 1 | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Soru-Cevap |
| 16 | Exercises1 | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Soru-Cevap |
| 17 | Term Exams | examination | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||