CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

ABSTRACT MATHEMATICS II | MAT104 | SPRING | 2+2 | C | 6 |

Learning Outcomes | 1-To explain how to construct natural numbers, integers, rational numbers. 2-To explain the concept of countable sets. 3-To determine countability of a set. 4-To comment "operation" and its properties. 5-To describe basic algebraic structures and the transformations conserving structures (homomorphisms). |

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

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

Classroom study (Pre-study, practice) | 15 | 5 | 75 | |

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) | 183 | |||

Total Workload (hours) / 30 (s) | 6,1 ---- (6) | |||

ECTS Credit | 6 |

Week | Topics | Study Metarials |

1 | Operations, definition and examples | |

2 | Properties of an operation (commutative property,associative property, inverse element, identity element) | |

3 | Construction of natural numbers,definition of addition and multiplication | |

4 | Properties of addition and multiplication in natural numbers | |

5 | Countable sets | |

6 | Construction of integers and definition of addition and multiplication | |

7 | Additional properties of addition and multiplication in the set of integers | |

8 | Construction of rational numbers and definition of addition and multiplication | |

9 | Additional properties of rational numbers | |

10 | Group | |

11 | Examples of Groups (Z, Z_m,Q) | |

12 | Ring; definition and examples(Z, Zm,Q) | |

13 | Field; definition and examples (Q, Z_p p asal) | |

14 | Group, ring homomorfizms |

Prerequisites | ABSTRACT MATHEMATICS I |

Language of Instruction | Turkish |

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

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

Assistants | - |

Resources | Matematiğin Temelleri, Halil İbrahim Karakaş, ODTÜ Geliştirme Vakfı Yayınları, 2011. |

Supplementary Book | [1] Soyut Matematik, Hüseyin Irmak, Pegem Akademi, 2008. [2] Soyut Matematiğe Giriş, Genişletilmiş İkinci Basım, Karaçay, T., 2009. |

Document | Lecture Notes |

Goals | To explain the construction of natural numbers, integers, rational numbers, to teach algebraic structures and homomorphisms. |

Content | - |

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 | 3 |

5 | To have the qualification of studying independently in a problem or a project requiring mathematical knowledge | 2 |

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 | 2 |

8 | To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge | 2 |

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

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 | 3 |

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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