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Information
| Code | MT212 |
| Name | Algebra II |
| Term | 2024-2025 Academic Year |
| Semester | 4. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 7 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. HAYRULLAH AYIK |
| Course Instructor |
1 2 |
Course Goal / Objective
The aim of this course is to make students comprehend the fundamentals of groups, cyclic groups, abelian groups, normal subgroups, group homomorphisms and abstract thinking by recognizing such abstract mathematical concepts.
Course Content
In this course binary operations, groups, finite groups and group tables, subgroups, cyclic groups, permutation groups, alternating group, isomorphism and Cayleys theorem, direct product, finitely generated abelian groups, normal subgroups and factor groups, isomorphism theorems are described.
Course Precondition
NONE
Resources
Soyut Cebir, H.Hilmi Hacısalihoğlu A first Course in Group Theory , J.B. Fraleigh,
Notes
Cebir Dersleri , Halil İbrahim Karakaş
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Proves properties of groups using basic concepts. |
| LO02 | Computes orders of elements of cyclic groups by recognizing between different group structures. |
| LO03 | Proves whether a given subset is or is not a subgroup. |
| LO04 | Makes applications of Lagrange theorem in solving problems. |
| LO05 | Proves basic facts about group homomorphisms. |
| LO06 | Determines whether two given groups are isomorphic. |
| LO07 | Relates geometric structures with groups. |
| LO08 | Determines the isomorphism classes of finite abelian groups. |
| LO09 | Solves various problems using isomorphism theorems. |
| LO10 | Uses the abstract and concrete information about the groups to solve the problems. |
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. | |
| 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. | 3 |
| 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. | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 4 |
| 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. | |
| 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. | |
| 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. | |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | |
| 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. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Groups | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Finite groups and group tables, subgroups | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 3 | Example of groups (The group Zn and dihedral group) | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap, Alıştırma ve Uygulama |
| 4 | Permutation groups | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Cyclic groups | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Cyclic groups and cosets | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 7 | Lagranges Theorem | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Normal subgroups and factor groups | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Isomorphisms and automorphisms | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Direct products | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Fundamental theorem of finite abelian groups | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Alıştırma ve Uygulama |
| 13 | Homomorphisms of groups | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Isomorphisms theorems | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Solving problems | Review of the relevant pages from sources | Öğretim Yöntemleri: Problem Çözme |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources again | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 4 | 56 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 6 | 84 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 8 | 8 |
| Final Exam | 1 | 16 | 16 |
| Total Workload (Hour) | 164 | ||
| Total Workload / 25 (h) | 6,56 | ||
| ECTS | 7 ECTS | ||