TÜRKÇE
ENGLISH
Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT313 |
| Name | Group Theory |
| Term | 2021-2022 Academic Year |
| Semester | 5. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Label | E Elective |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. HAYRULLAH AYIK |
| Course Instructor |
Prof. Dr. HAYRULLAH AYIK
(Güz)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course is to make students comprehend basic definitions and theorems of group theory, some special groups and groups construction, normal subgroups and quotient groups, permutation groups and counting its elements, isomorphism theorems and problem solving using isomorphism theorems, Sylow Theorems and problem solving using Sylow Theorems.
Course Content
In this course fundamental definitions and theorem of group theory, some special groups and group construction, permutation groups and counting its elements, groups symmetry, normal subgroups and its properties, quotient groups, counting with groups, isomorphism theorems, examples of using isomorphism theorems, group actions, basic groups, Sylow Theorems and its applications, clasification of small order groups under isomorphism are described.
Course Precondition
Resources
C. F. Gardiner ´´ A first course in group theory´´ Springer - Verlag, New York Inc. 1980<br> J.J. Rotman, ´A first course in abstract algebra´ Second Edition, Prentice Hall, 2000.
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Realises basic definitions and theorems of group theory. |
| LO02 | Recognises some special groups and group constructions. |
| LO03 | Recognises normal subgroups and its properties. |
| LO04 | Recognises quotient subgroups. |
| LO05 | Calculates the elements of permutation groups by recognizing permutation groups. |
| LO06 | Realises isomorphism theorems and problem solving using isomorphism theorems. |
| LO07 | Realises Sylow Theorems and problem solving using Sylow Theorems. |
| LO08 | Realises the clasification of small order groups under isomorphism. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | - | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 4 |
| PLO02 | - | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 5 |
| PLO03 | - | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 5 |
| PLO04 | - | Demonstrate the ability to express the basic theories of mathematics both correctly. | 5 |
| PLO05 | - | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 4 |
| PLO06 | - | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 3 |
| PLO07 | - | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 3 |
| PLO08 | - | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 3 |
| PLO09 | - | Comprehends at least one of the computer programming languages. | 0 |
| PLO10 | - | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 3 |
| PLO11 | - | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | 0 |
| PLO12 | - | 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. | 2 |
| PLO13 | - | Understands the programming techniques and shows the ability to do programming. | 0 |
| PLO14 | - | Demonstrates the ability to study mathematics both independently and as a group. | 2 |
| PLO15 | - | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 2 |
| PLO16 | - | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | 4 |
| PLO17 | - | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | 3 |
| PLO18 | - | Gains the ability to use information technologies effectively for contemporary mathematical applications. | 3 |
| PLO19 | - | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | 3 |
| PLO20 | - | Gains the consciousness of prefesional ethics and responsibility. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Fundamental definitions and theorem of group theory | Review of the relevant pages from sources | |
| 2 | Some special groups and group construction | Review of the relevant pages from sources | |
| 3 | Permutation groups and counting its elements | Review of the relevant pages from sources | |
| 4 | Symmetry groups | Review of the relevant pages from sources | |
| 5 | Normal subgroups and their properties | Review of the relevant pages from sources | |
| 6 | Quotient groups | Review of the relevant pages from sources | |
| 7 | Counting with groups | Review of the relevant pages from sources | |
| 8 | Mid-Term Exam | Review and Problem Solving | |
| 9 | Isomorphism theorems | Review of the relevant pages from sources | |
| 10 | Examples of using isomorphism theorems | Review of the relevant pages from sources | |
| 11 | Group actions | Review of the relevant pages from sources | |
| 12 | Simple groups | Review of the relevant pages from sources | |
| 13 | Sylow Theorems and their applications | Review of the relevant pages from sources | |
| 14 | Classification groups of small order up to isomorphism | Review of the relevant pages from sources | |
| 15 | Classification groups of small order up to isomorphism | Review of the relevant pages from sources | |
| 16 | Term Exams | Review and Problem Solving | |
| 17 | Term Exams | Review and Problem Solving |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |
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 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||