MT515 Algebra I

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

Information

Code MT515
Name Algebra I
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 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 Knows groups and homomorphisms of groups.
LO02 Knows cyclic groups.
LO03 Knows permutation groups.
LO04 Knows normal subgroups and quotient groups.
LO05 Knows isomorphism theorems and automorphisms.
LO06 Knows normal series.
LO07 Knows solvable groups.
LO08 Knows nilpotent groups.
LO09 Knows alternating groups
LO10 Knows direct products.
LO11 Knows finitely generated abelian groups.
LO12 Knows the 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. 2
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. 3
PLO08 Bilgi - Kuramsal, Olgusal carries out original and qualified scientific studies on the subject related to its field.
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. 2
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.
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, Alıştırma ve Uygulama
2 Subgroups, cyclic groups Review of relevant pages in sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Tartışma
3 Permutation groups Review of relevant pages in sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Tartışma
4 Normal subgroups and quotient groups Review of relevant pages in sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
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, Alıştırma ve Uygulama
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, Tartışma
10 Alternating groups Review of relevant pages in sources Öğretim Yöntemleri:
Anlatım, Soru-Cevap, Alıştırma ve Uygulama
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, Alıştırma ve Uygulama
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, Alıştırma ve Uygulama
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

Update Time: 17.06.2024 02:02