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Information
| Code | MT003 |
| Name | Module Theory |
| Term | 2024-2025 Academic Year |
| Term | Fall |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. ZEYNEP ÖZKURT |
| Course Instructor |
Prof. Dr. YILMAZ DURĞUN
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
Understand the basic definitions and theorems about modules and associate them with different algebraic structures.
Course Content
Modules, Homomorphisms,submodules and quotient modules. Short exact Sequences. Direct products, tensor product. Free, Projective, injective and flat modules. Modules over Principal Ideal Domains. Jordan and Normal Canonical forms.
Course Precondition
no
Resources
David Dummit, Richard Foote Abstract Algebra
Notes
Hungerford, Algebra
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows definition of modules and its properties |
| LO02 | Knows submodules, quotient modules and homomorphisms has an idea about the structure of free modules |
| LO03 | Knows the structure of tensor product and properties |
| LO04 | Create an exact sequence |
| LO05 | Defines projective, injective and flat modules |
| LO06 | Has an idea about the structure of modules on principal ideal domain |
| LO07 | Knows the Rational and Jordan canonical forms |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in his area of expertise and other areas of mathematics. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Has basic knowledge in all areas of mathematics. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | 2 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have knowledge of a foreign language at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | 3 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. | 4 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Main Definitions | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 2 | Quotient modules and Homomorphisms | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 3 | Direct sums | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 4 | Free modules | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 5 | Free modules1 | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 6 | Tensor product of modules | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 7 | Tensor product of modules1 | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Read the relevant sections in the textbook and solving problems | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Exact Sequences | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 10 | Projective modules | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 11 | İnjective modules | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 12 | Flat Modules | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 13 | Modules on principal ideal domain | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 14 | Rational Canonical Forms | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 15 | Jordan Canonical forms | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 16 | Exercises | Read the relevant sections in the textbook and solving problems | Öğretim Yöntemleri: Anlatım |
| 17 | Term Exams | Read the relevant sections in the textbook and solving problems | 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 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||