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Information
| Code | MT515 |
| Name | Algebra I |
| Term | 2023-2024 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 | Prof. Dr. GONCA AYIK |
Course Goal / Objective
The aim of this course is to make students understand groups and homomorphisms, cyclic groups, permutation groups, normal subgroups and quotient groups, isomorphism theorems and automorphisms, normal series, solvable groups, nilpotent groups, alternating groups, direct products, finitely generated abelian groups, Sylow theorems.
Course Content
In this course groups and homomorphisms, cyclic groups, permutation groups, normal subgroups and quotient groups, isomorphism theorems and automorphisms, normal series, solvable groups, nilpotent groups, alternating groups, direct products, finitely generated abelian groups, Sylow theorems are described.
Course Precondition
none
Resources
P.B. BHATTACHARYA, S.K.JAIN, S.R.NAGPAUL; BASİC ABSTRACT ALGEBRA;CAMBRIDGE UNIVERSITY PRESS, 1994
Notes
P.B. BHATTACHARYA, S.K.JAIN, S.R.NAGPAUL; BASİC ABSTRACT ALGEBRA;CAMBRIDGE UNIVERSITY PRESS, 1994
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Recognize groups and homomorphisms of groups. |
| LO02 | Recognize cyclic groups. |
| LO03 | Recognize permutation groups. |
| LO04 | Recognize normal subgroups and quotient groups. |
| LO05 | Realize isomorphism theorems and automorphisms. |
| LO06 | Realize normal series. |
| LO07 | Recognize solvable groups. |
| LO08 | Recognize nilpotent groups. |
| LO09 | Realize alternating groups |
| LO10 | Realize direct products. |
| LO11 | Realize finitely generated abelian groups. |
| LO12 | Realize Sylow 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. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Establishes new mathematical models with the help of the knowledge gained in the field of specialization. | 1 |
| 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. | 1 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Effectively uses the technical equipment needed to express mathematics. | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | poses original problems related to field and presents different solution techniques. | 5 |
| PLO08 | Bilgi - Kuramsal, Olgusal | carries out original and qualified scientific studies on the subject related to its field. | 1 |
| 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. | 5 |
| 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. | |
| 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. | 4 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Adheres to the ethical rules required by its scientific title | 2 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Semigroups and basic concepts about groups | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | Subgroups, cyclic groups | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | Permutation groups | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | Normal subgroups and quotient groups | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 5 | Isomorphism theorems and automorphisms | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 6 | Normal series | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 7 | Solvable groups | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Mid-Term Exam | Lecture and problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Nilpotent groups | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 10 | Alternating groups | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | Simplicity of alternating groups | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 12 | Direct products | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Finitely generated abelian groups | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | Sylow theorems | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 15 | Groups with a square of a prime number and the product of two prime numbers | Review of relevant pages in sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 16 | Term Exams | Lecture and problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Lecture 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 | 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 | ||