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Information
| Code | MT514 |
| Name | Algebra II |
| Term | 2024-2025 Academic Year |
| Semester | . Semester |
| 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 Goal / Objective
The aim is to introduce the basic concepts of the Ring Theory at Graduate level.
Course Content
In this lesson Ring structure, sub-rings and ideals, prime and maximal ideals, decomposition in commutative rings, principal ideal domains (PID), Unique Factorization domains (UFD), Euclidean Domains, decomposition in polynomial rings , polinoamial ring with several variables are described.
Course Precondition
none
Resources
David Dummit, Richard Foote Abstract Algebra,
Notes
Hungerford, Algebra
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Learns the concepts such as definition of the ring, subring and ring homomorphism . |
| LO02 | Learns the concepts in detail an ideal in a ring, prime and maximal ideals. |
| LO03 | Knows irreducible elements in a commutative rings. |
| LO04 | Recognizes the Unique Factorization Domains (UFD). |
| LO05 | Knows the properties of Euclidean Rings. |
| LO06 | Knows the ring homomorphism. |
| LO07 | Knows prime elements in a commutative rings. |
| LO08 | Knows the isomorphism theorems. |
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. | 4 |
| 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. | |
| 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. | 4 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Analyzes existing mathematical theories and develops new theories. | 3 |
| 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. | 3 |
| 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. | 2 |
| 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. | 3 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Rings and Ring homomorphisms | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | Ideals | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 3 | Prime and maximal ideals | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | solving problems (problems in the first source pages 120, 133, 134) Sol | Solving problems in advance | Öğretim Yöntemleri: Alıştırma ve Uygulama, Anlatım, Soru-Cevap |
| 5 | Inner direct product and Chinese Remainder Theorem | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 6 | Decomposition in commutative rings | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 7 | Solving problems (problems in the first source page 140) | Solving problems in advance | Öğretim Yöntemleri: Alıştırma ve Uygulama, Soru-Cevap |
| 8 | Mid-Term Exam | Review of topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Euclidean Rings | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 10 | Quotient Rings and Localizations | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım |
| 11 | Quotient Rings and Localizations2 | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım |
| 12 | Solving problems (problems in page 148) | Solving problems in advance | Öğretim Yöntemleri: Alıştırma ve Uygulama, Anlatım, Soru-Cevap |
| 13 | Rings and formal power series | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım |
| 14 | Factorization in polynomial rings | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 15 | Theorems in polynomial rings | Reviewing the relevant chapters in the Sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 16 | Polynomials | Review of the topics discussed in the lecture notes and sources | Öğretim Yöntemleri: Anlatım |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources | 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 | ||