TÜRKÇE
ENGLISH
Information
| Code | MT311 |
| Name | Algebra III |
| Term | 2024-2025 Academic Year |
| Semester | 5. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 7 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. GONCA AYIK |
| Course Instructor |
Prof. Dr. GONCA AYIK
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course to make students comprehend basic properties of rings, the structure of field, ideals of rings and their structures, the properties of the ring homomorphism, division rings, integral domains, rings of integers and their properties, polinomial rings and their properties and reduciblaty of polinomial.
Course Content
In this course definitions and elementary properties of rings and fields, ideal and homomorphism, quotion rings, integral domain, construction of the fields of quotients, rings of polynomial, factoring polynomials, irreducibility criteria are described.
Course Precondition
NONE
Resources
A Book of Abstract Algebra, Charles Pinter, Mc Graw Hill. Soyut Cebir Dersleri Cilt II, Hülya Şenkon, İstanbul Üniversitesi Fen Fakültesi Yayınları.
Notes
A Book of Abstract Algebra, Charles Pinter, Mc Graw Hill. Soyut Cebir Dersleri Cilt I, Hülya Şenkon, İstanbul Üniversitesi Fen Fakültesi Yayınları.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Recognizes the structure of ring. |
| LO02 | Recognizes basic properties of rings. |
| LO03 | Recognizes the structure of field. |
| LO04 | Recognizes ideals of rings and ring homomorphisms. |
| LO05 | Recognizes division rings, integral domains. |
| LO06 | Recognizes rings of integers and their properties. |
| LO07 | Recognizes polinomial rings and their properties. |
| LO08 | Recognizes the irreduciblility of a polinomial. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 3 |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrates the ability to express the basic theories of mathematics accurately both in writing and orally. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Comprehends at least one of the computer programming languages. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 3 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | 4 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | 4 |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 4 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | 4 |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | |
| PLO19 | Bilgi - Kuramsal, Olgusal | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Definition of rings and example of rings | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Basic properties of rings | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Definition of fields and example of fields | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Ideals of rings and examples | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Homomorphism of rings | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Division rings | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Integral domain | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 8 | Mid-Term Exam | Review and Problem Solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Charasterictic of integral domains and their properties | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Rings of integers and its properties | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Polynomial rings and its properties | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Polynomial rings and its properties 1 | Review of the relevant pages from sourcesReview of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Reducibility in polynomial rings | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Test about reducibility on polynomial rings | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Introduction to number theory | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 16 | Term Exams | Review and Problem Solving | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review and Problem Solving | 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 | 2 | 5 | 10 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 18 | 18 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 170 | ||
| Total Workload / 25 (h) | 6,80 | ||
| ECTS | 7 ECTS | ||