MT514 Algebra II

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

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

Update Time: 17.06.2024 02:35