TÜRKÇE
ENGLISH
Information
| Code | MT523 |
| Name | Commutative Algebra |
| 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 | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator |
Course Goal / Objective
Study of commutative rings, and of the ideals of commutative rings
Course Content
Study of commutative rings, and of the ideals of commutative rings
Course Precondition
Algebra
Resources
Introduction to Commutative Algebra, M.F. Atiyah, I. G. MacDonald
Notes
Lecture Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Learns the concept of a ring and an ideal. |
| LO02 | Learns the concept of a module. |
| LO03 | Learns the concept of localization. |
| LO04 | Learns Expanding and Contracting Ideals in Fraction Rings. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Knows the results of previous research in a special field of mathematics | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. | 3 |
| 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. | 4 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Sets up original problems in her field and offers different solution techniques | 5 |
| PLO08 | Bilgi - Kuramsal, Olgusal | It carries out original and qualified scientific studies on the subject related to its field. | |
| 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. | 2 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | To have foreign language knowledge at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. | 4 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | It presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders. | 5 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Rings, Ideals, Prime and Maximal Ideals and Examples | 1 Reading Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 2 | Operations on Ideals, Extensions. | 2 Reading notes from the book | Öğretim Yöntemleri: Anlatım |
| 3 | Modules and Operations on Modules. | 3 Studying Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 4 | Finitely generated Modules and Complete Sequences | 4 Reading Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 5 | Tensor Product of Modules and Completeness of Tensor Product | 5 Reading Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 6 | Fraction Rings and Localization | 6 Reading Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 7 | Expanding and Contracting Ideals in Fraction Rings | 7 Reading Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | 8 Reading Lecture Notes | Öğretim Yöntemleri: Soru-Cevap |
| 9 | Prime Decompositions | 9 Reading Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 10 | 1st and 2nd Uniqueness Theorems | 10 Reading Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 11 | Chain Conditions | 11 Reading Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 12 | Noether Rings | 12 Reading Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 13 | Prime Decomposition in Noether Rings | 13 Reading Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 14 | Artin Rings | 14 Reading Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 15 | Repetition of lecture notes | 15 Reading Lecture Notes | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | 16 Reading Lecture Notes | Öğretim Yöntemleri: Soru-Cevap |
| 17 | Term Exams | 17 Reading Lecture Notes | Öğretim Yöntemleri: Soru-Cevap |
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 | ||