CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

ABSTRACT MATHEMATICS II | MAT104 | SPRING | 3+0 | Fac./ Uni. | C | 5 |

Learning Outcomes | 1- to be able to explain how to construct natural numbers, integers, rational numbers 2-To be able to explain the concept of countable sets 3-To be able to determine countability of a set 4-To be able to comment "operation" and its properties 5-To be able 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 | 3 | 42 | |

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

Assignments | 10 | 2 | 5 | 10 |

Short-Term Exams (exam + preparation) | 10 | 2 | 5 | 10 |

Midterm exams (exam + preparation) | 30 | 1 | 8 | 8 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 12 | 12 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 152 | |||

Total Workload (hours) / 30 (s) | 5,07 ---- (5) | |||

ECTS Credit | 5 |

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 | - |

Language of Instruction | Turkish |

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

Instructors | - |

Assistants | - |

Resources | 1. Matematiğin Temelleri, Halil İbrahim Karakaş, ODTÜ Geliştirme Vakfı Yayınları, 2011 2. Soyut Matematiğe Giriş, Genişletilmiş İkinci Basım, Karaçay, T., 2009 |

Supplementary Book | Soyut Matematik, Hüseyin Irmak, Pegem Akademi, 2008 |

Document | - |

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

Content | Operations, definition and examples.Properties of operations. Construction of natural numbers. Properties of addition and multiplication in the set of natural numbers. Countable sets. Construction of the set of integers. Properties of addition and multiplication in the set of integers. Construction of the set of rational numbers, properties of addition and multiplication. Additional properties of natural numbers. Groups. Group examples. Rings and ring examples |

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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