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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT212 |
| Name | Algebra II |
| Term | 2021-2022 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 |
| Label | C Compulsory |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. HAYRULLAH AYIK |
| Course Instructor |
Prof. Dr. HAYRULLAH AYIK
(Bahar)
(A Group)
(Ins. in Charge)
|
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
Resources
Cebir Dersleri , Halil İbrahim Karakaş
Notes
Soyut Cebir, H.Hilmi Hacısalihoğlu<br> A first Course in Group Theory , J.B. Fraleigh,
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 | Understands 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 | - | 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. | 4 |
| 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. | 5 |
| 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. | 3 |
| PLO15 | - | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 4 |
| PLO16 | - | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | 2 |
| 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. | 1 |
| 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. | 2 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Groups | Review of the relevant pages from sources | |
| 2 | Finite groups and group tables, subgroups | Review of the relevant pages from sources | |
| 3 | Example of groups (The group Zn and dihedral group) | Review of the relevant pages from sources | |
| 4 | Permutation groups | Review of the relevant pages from sources | |
| 5 | Cyclic groups | Review of the relevant pages from sources | |
| 6 | Cyclic groups and cosets | Review of the relevant pages from sources | |
| 7 | Lagranges Theorem | Review of the relevant pages from sources | |
| 8 | Mid-Term Exam | Review of the topics discussed in the lecture notes and sources again | |
| 9 | Normal subgroups and factor groups | Review of the relevant pages from sources | |
| 10 | Isomorphisms and automorphisms | Review of the relevant pages from sources | |
| 11 | Direct products | Review of the relevant pages from sources | |
| 12 | Fundamental theorem of finite abelian groups | Review of the relevant pages from sources | |
| 13 | Homomorphisms of groups | Review of the relevant pages from sources | |
| 14 | Isomorphisms theorems | Review of the relevant pages from sources | |
| 15 | Solving problems | Review of the relevant pages from sources | |
| 16 | Term Exams | Review of the topics discussed in the lecture notes and sources again | |
| 17 | Term Exams | Review of the topics discussed in the lecture notes and sources again |
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 | 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 | ||