CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

ALGEBRA I | MAT303 | FALL | 4+0 | Fac./ Uni. | C | 8 |

Learning Outcomes | 1-To be able to explain the concepts of group, subgroup, factor group and cyclic group. 2-To be able to explain the group homomorphisms, isomorphisms and automorphisms 3-To be able to classify the isomorphism class of a given finitely generated abelian group 4-To be able to explain the concepts of ring, subring and integral domain |

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

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

Classroom study (Pre-study, practice) | 14 | 8 | 112 | |

Assignments | 10 | 2 | 8 | 16 |

Short-Term Exams (exam + preparation) | 10 | 2 | 8 | 16 |

Midterm exams (exam + preparation) | 30 | 1 | 12 | 12 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 16 | 16 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 228 | |||

Total Workload (hours) / 30 (s) | 7,6 ---- (8) | |||

ECTS Credit | 8 |

Week | Topics | Study Metarials |

1 | Groups | |

2 | Subgroups | |

3 | Group examples | |

4 | Cyclic groups | |

5 | Cosets, Lagrange theorem | |

6 | Normal subgroups, factor groups | |

7 | İsomorphisms and automorphisms | |

8 | Direct products | |

9 | The fundamental theorem of finite Abelian groups | |

10 | Group homomorphisms | |

11 | Rings | |

12 | Integral domains, fields | |

13 | Ideals | |

14 | Factor rings |

Prerequisites | - |

Language of Instruction | Turkish |

Course Coordinator | Assist. Prof. Dr. Faruk KARAASLAN |

Instructors | - |

Assistants | - |

Resources | Cebir Dersleri, H. İbrahim Karakaş, TÜBA yayınları, Ankara, 2008 |

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 | - |

Goals | The aim of the course is to work the fundamentals concepts and properties in group theory, classification of the finitely generated Abelian groups, and to learn the basic concepts of the ring theory. |

Content | Groups, subgroups. Cyclic groups. Cosets, Lagrange theorem. Normal subgroups, factor groups. Isomorphisms and automorphisms. Direct products. The fundamental theorem on finitely generated Abelian groups. Homomorphisms. Rings, integral domains, fields. İdeals, factor rings. |

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 | 5 |

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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