CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

Course Title | Code | Semester | Laboratory+Practice (Hour) | Pool | Type | ECTS |

ALGEBRA I | MAT303 | FALL | 4+0 | C | 6 |

Learning Outcomes | 1-To explain the concepts of group, subgroup, factor group and cyclic group. 2-To explain the group homomorphisms, isomorphisms and automorphisms. 3-To classify the isomorphism class of a given finitely generated abelian group. 4-To make direct product of groups. |

Activity | Percentage (100) | Number | Time (Hours) | Total Workload (hours) |

Course Duration (Weeks x Course Hours) | 14 | 4 | 56 | |

Classroom study (Pre-study, practice) | 14 | 5 | 70 | |

Assignments | 10 | 2 | 6 | 12 |

Short-Term Exams (exam + preparation) | 10 | 2 | 6 | 12 |

Midterm exams (exam + preparation) | 30 | 1 | 14 | 14 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 14 | 14 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 178 | |||

Total Workload (hours) / 30 (s) | 5,93 ---- (6) | |||

ECTS Credit | 6 |

Week | Topics | Study Metarials |

1 | Mappings and binary relations | |

2 | Groups and tables of groups | |

3 | Subgroups | |

4 | Cosets and Lagrange Theorem | |

5 | Normal subgroups | |

6 | Quotient groups | |

7 | Symmetric groups | |

8 | Mid-term exam | |

9 | Group homomorphisms | |

10 | Automorphisms and isomorphism theorems | |

11 | Cyclic groups | |

12 | Cyclic groups | |

13 | Direct products | |

14 | Direct products |

Prerequisites | - |

Language of Instruction | Turkish |

Course Coordinator | Assist. Prof. Dr. Nihal BİRCAN |

Instructors |
1-)Doktor Öğretim Üyesi Nihal Bircan Kaya |

Assistants | - |

Resources | Soyut Cebir, Dursun TAŞÇI, Alp Yayınevi, Ankara, 2007. |

Supplementary Book | [1] Abstract Algebra, I. N. Herstein, John Wiley&Sons Inc., NY., 1996. [2] Abstract Algebra, David S. Dummit, Richard M. Foote, Wiley, 2003. |

Document | Lecture Notes. |

Goals | The aim of the course is to work the fundamentals concepts and properties in group theory. |

Content | Groups, subgroups. Cyclic groups. Cosets, Lagrange theorem. Normal subgroups, factor groups. Isomorphisms and automorphisms. Direct products. |

Program Learning Outcomes | Level of Contribution | |

1 | To have a grasp of theoretical and applied knowledge in main fields of mathematics | 5 |

2 | To have the ability of abstract thinking | 4 |

3 | To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps | 5 |

4 | To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life | 2 |

5 | To have the qualification of studying independently in a problem or a project requiring mathematical knowledge | 3 |

6 | To be able to work compatibly and effectively in national and international groups and take responsibility | - |

7 | To be able to consider the knowledge gained from different fields of mathematics with a critical approach and have the ability to improve the knowledge | 4 |

8 | To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge | 4 |

9 | To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time | 2 |

10 | To be able to transfer thoughts on issues related to mathematics, proposals for solutions to the problems to the expert and non-expert shareholders written and verbally | 4 |

11 | To be able to produce projects and arrange activities with awareness of social responsibility | - |

12 | To be able to follow publications in mathematics and exchange information with colleagues by mastering a foreign language at least European Language Portfolio B1 General Level | - |

13 | To be able to make use of the necessary computer softwares (at least European Computer Driving Licence Advanced Level), information and communication technologies for mathematical problem solving, transfer of thoughts and results | - |

14 | To have the awareness of acting compatible with social, scientific, cultural and ethical values | - |

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