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 |