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Information
| Code | MT483 |
| Name | Geometries |
| Term | 2024-2025 Academic Year |
| Semester | 7. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. GONCA AYIK |
| Course Instructor |
1 2 |
Course Goal / Objective
The aim of this course is to teach the properties of different geometries.
Course Content
Euclidean and non-Euclidean geometries are explained.
Course Precondition
NONE
Resources
Geometry, Richard S. Millman, George D. Parker, Springer.
Notes
Geometry, Richard S. Millman, George D. Parker, Springer.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows the history of geometry and the Playfair axiom. |
| LO02 | Recognizes projective geometry. |
| LO03 | Recognizes incident geometry. |
| LO04 | Recognizes metric geometry. |
| LO05 | Recognizes special rulers. |
| LO06 | Uses the relation of being in between. |
| LO07 | Uses plane separation axioms. |
| LO08 | Recognizes Pasch geometry. |
| LO09 | Uses angle measurement. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Understands importance of basic consepts of Algebra, Analaysis and Topology. | |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrates the ability to express the basic theories of mathematics accurately both in writing and orally. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 4 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 4 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Comprehends at least one of the computer programming languages. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 3 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | 3 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | 4 |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 3 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | 4 |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | |
| PLO19 | Bilgi - Kuramsal, Olgusal | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | 3 |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | The history of geometry and the Playfair axiom. | Review of related concepts from lecture notes and sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | Projektive geometry | Review of related concepts from lecture notes and sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | Incident geometry. | Review of related concepts from lecture notes and sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | Metric Geometry | Review of related concepts from lecture notes and sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 5 | Special Rulers | Review of related concepts from lecture notes and sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 6 | The relation of being in between. | Review of related concepts from lecture notes and sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 7 | Plane separation axioms | Review of related concepts from lecture notes and sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Mid-Term Exam | Review of topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Plane separation axioms 1 | Review of related concepts from lecture notes and sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 10 | Pasch geometries | Review of related concepts from lecture notes and sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | Perpendicularity and angle equivalence | Review of related concepts from lecture notes and sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 12 | Angle measurement | Review of related concepts from lecture notes and sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Moulton plane | Review of related concepts from lecture notes and sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | Euclidean and Poincare Angel Measure | Review of related concepts from lecture notes and sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 15 | Neutral Geometry | Review of related concepts from lecture notes and sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 16 | Term Exams | Review of topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review of topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||