TÜRKÇE
ENGLISH
Information
| Code | MATZ307 |
| Name | Algebra |
| Semester | 5. Semester |
| Duration (T+A) | 2-0 (T-A) (17 Week) |
| ECTS | 2 ECTS |
| National Credit | 2 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. PERİHAN ARTUT |
Course Goal
To analyze the theoretical structure of Algebra which forms the basis of mathematics.
Course Content
Binary operations, group definition and basic features, subgroups, permutation groups, cyclic groups, regular n-gen symmetry group, cyclic permutations, single and even permutations, homomorphisms, Kosets and Lagrange theorem, isomorphism theorems, the effect of a group on a set, rings, sub-ring and ideals, prime and maximal ideals, ring homomorphisms, arithmetic in rings, polynomial rings, bodies; Burnside theorem and its applications, p-groups and related theorems.
Course Precondition
None
Resources
1) Ahmet Sinan Çevik, Cebire Giriş,
Notes
https://library.cu.edu.tr/cu/e-kaynaklar/veritabanlari
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows the basics of sets, relations, functions and binary operations. |
| LO02 | Explain groupe and subgroupe terms, give examples an suitable to this concepts. |
| LO03 | Express and proof the Lagrange Theorem and be able to explain the ralations with cyclic group and be able to solve problems. |
| LO04 | Explain the concept of normal subgroup and the features of this concept |
| LO05 | Explain the concepts of homeomorphism and isomorphism founctions and be aware of their importance for groups |
| LO06 | Get difference groups using rotation and spin functions and explain the importance these groups in daily mathematics |
| LO07 | Be aware of commutative feature of groups and make interactions around the special formed groups |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Has enough knowledge about mathematics. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Has pedagogical knowledge about teaching profession and field. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Implements classroom management approaches to be used in educational environments effectively. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Prepares the learning environments in which appropriate teaching methods are used for effective mathematics education in accordance with development and age levels. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Knows the relationship between Mathematics-Society-Environment-History and uses it in professional and daily life. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Uses Turkish properly and effectively according to the rules. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Selects and designs appropriate materials, in mathematics teaching. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Monitors students' progress using different assessment and evaluation methods and techniques. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Takes responsibility as an individual and as a team member to solve problems related to the field. | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Has life-long learning awareness. | |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Shares his/her knowledge and skills, problems and solutions that he/she identified by means of oral and written communication with the expert and non-expert people. | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Uses information and communication technologies and other related materials for an effective mathematics teaching. | |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Has enough foreign language knowledge to follow foreign resources related to the field. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Has the knowledge of the purpose, structure and functioning of the Turkish education system. | |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Becomes a teacher who adheres to Atatürk's principles and revolutions. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | The features of sets, relations and functions | Related resource review | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | Modular arithmetic, divisibility on the integers | Related resource review | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 3 | The theory of groups | Related resource review | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Bireysel Çalışma |
| 4 | Subgroups | Related resource review | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 5 | The cosets, right and left cosets | Related resource review | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 6 | Problem Solving | Related resource review | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Lagrange Theorem | Related resource review | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Mid-Term Exam | prepare to exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Normal subgroups | Related resource review | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 10 | Factor Groups | Related resource review | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | Homomorphisms | Related resource review | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 12 | Isomorphism | Related resource review | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 13 | Permutation groups, Ring, sub ring and ideals | Related resource review | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 14 | Burnside's theorem and its applications | Related resource review | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Bireysel Çalışma |
| 15 | General evaluation and application | Related resource review | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Grup Çalışması, Bireysel Çalışma |
| 16 | Term Exams | prepare to exam | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | prepare to exam | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 2 | 28 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 1 | 14 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 4 | 4 |
| Final Exam | 1 | 8 | 8 |
| Total Workload (Hour) | 54 | ||
| Total Workload / 25 (h) | 2,16 | ||
| ECTS | 2 ECTS | ||