MATZ307 Algebra

2 ECTS - 2-0 Duration (T+A)- 5. Semester- 2 National Credit

Information

Code MATZ307
Name Algebra
Term 2022-2023 Academic Year
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 Instructor Doç. Dr. ZEYNEP ÖZKURT (A Group) (Ins. in Charge)


Course Goal / Objective

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

Update Time: 18.11.2022 03:00