CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

ABSTRACT MATHEMATICS I | MAT103 | FALL | 3+0 | Fac./ Uni. | C | 5 |

Learning Outcomes | 1-To be able to express an idea in the language of mathematics 2-To be able to apply methods of proof 3-To be able to use basic properties of sets, relations and functions |

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 | Basic notions about propositions and introduction to algebra of propositions (conjunction and disjunction) | |

2 | Implication (conditional) and equivalence (biconditional) | |

3 | Quantifiers | |

4 | The notions of axiom, theorem and proof, introduction to methods of proof (proof by truth table and direct proof) | |

5 | Indirect proof methods, proof by contrapositive and proof by contradiction, falsification methods (giving counterexample, finding conflict) | |

6 | Mathematical induction | |

7 | More examples about methods of proof | |

8 | Basic notions of sets, Boolean operations on sets | |

9 | Finite-infinite intersections and unions, products of sets and basic notions about product sets | |

10 | Relations and their basic properties | |

11 | Equivalance relation | |

12 | Order relations | |

13 | Functions and their basic notions | |

14 | Equivalance Sets |

Prerequisites | - |

Language of Instruction | Turkish |

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

Instructors | - |

Assistants | - |

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

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

Document | - |

Goals | To gain the student the ability of expressing an idea in the language of mathematics and proof skills, to teach the notions of set, relation and function |

Content | Basic notions on propositions. If and if and only if connectives. Quantifiers. Notions of axiom, theorem, and proof, introduction to proof techniques. Indirect proof techniques. Proof by induction. Eamples to proof techniques. Basic notions on sets. Finite-infinite intersections and unions, basic notions on product sets. Relation and basic properties. Equivalence relation. Ordering relations. Functions and basic notions on them. Equivalent sets. |

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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