Course Language:
English
Course Objectives:
To provide information about the fundamental concepts of geometries defined by invariants of transformations on two dimensional spaces of constant curvature.
Course Content:
Plane Euclidean geometry, Affine transformations in the Euclidean plane, Finite groups of isometries of Euclidean plane, Geometry on sphere, The projective plane, The hyperbolic plane.
Course Methodology:
1: Lecture, 2: Problem Solving
Course Evaluation Methods:
A: Written examination, B: Homework
Vertical Tabs
Course Learning Outcomes
|
Dersin Öğrenme Çıktıları |
Program Öğrenme Çıktıları |
Öğretim Yöntemleri |
Ölçme Yöntemleri |
|
1) Düzlem üzerindeki geometriyi öğrenir. |
1,2,3,4,7 |
1 |
A |
|
2) Küre üzerindeki geometriyi öğrenir |
1,2,3,4,7 |
1 |
A |
|
3) Hiperbolik düzlem üzerindeki geometriyi öğrenir. |
1,2,3,4,7 |
1 |
A |
|
4) Düzlem üzerindeki dönüşümleri öğrenir. |
1,2,3,4,7,9 |
1 |
A |
|
5) Küre üzerindeki dönüşümleri öğrenir. |
1,2,3,4,7,9 |
1 |
A |
|
6) Hiperbolik düzlem üzerindeki dönüşümleri öğrenir. |
1,2,3,4,7,9 |
1 |
A |
Course Flow
| Week | Topics | Study Materials |
| 1 | Plane Euclidean Geometry | From textbook Chapter 1 |
| 2 | Plane Euclidean Geometry | Chapter 1 |
| 3 | Plane Euclidean Geometry | Chapter 1 |
| 4 | Affine transformations in Euclidean Plane | Chapter 2 |
| 5 | Affine transformations in Euclidean Plane | Chapter 2 |
| 6 | Finite Group of Isometries of Euclidean Plane | Chapter 3 |
| 7 | MIDTERM and Discussion of Solutions | |
| 8 | Geometry on Sphere | Chapter 4 |
| 9 | Geometry on Sphere | Chapter 4 |
| 10 | Geometry on Sphere | Chapter 4 |
| 11 | The Projective plane | Chapter 5 |
| 12 | Distance geometry on Projective Plane | Chapter 6 |
| 13 | The Hyperbolic Plane | Chapter 7 |
| 14 | The Hyperbolic Plane | Chapter 7 |
Recommended Sources
| Textbook | P. J. Ryan, Euclidean and Non-Euclidean Geometry An analytic Approach, Cambridge, 1997 |
| Additional Resources |
Material Sharing
| Documents | |
| Assignments | |
| Exams |
Assessment
| IN-TERM STUDIES | NUMBER | PERCENTAGE |
| Mid-terms | 1 | 100 |
| Quizzes | ||
| Assignments | ||
| Total | 100 | |
| CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE | 40 | |
| CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE | 60 | |
| Total | 100 |
| COURSE CATEGORY | Expertise/ Field Courses |
Course’s Contribution to Program
| No | Program Learning Outcomes | Contribution | ||||
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry) | x | ||||
| 2 | Acquiring fundamental knowledge on fundamental research fields in mathematics | x | ||||
| 3 | Ability form and interpret the relations between research topics in mathematics | x | ||||
| 4 | Ability to define, formulate and solve mathematical problems | x | ||||
| 5 | Consciousness of professional ethics and responsibilty | x | ||||
| 6 | Ability to communicate actively | x | ||||
| 7 | Ability of self-development in fields of interest | x | ||||
| 8 | Ability to learn, choose and use necessary information technologies | x | ||||
| 9 | Lifelong education | x | ||||
ECTS
| Activities | Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Course Duration (14x Total course hours) | 14 | 3 | 42 |
| Hours for off-the-classroom study (Pre-study, practice) | 14 | 5 | 70 |
| Mid-terms (Including self study) | 1 | 24 | 24 |
| Final examination (Including self study) | 1 | 36 | 36 |
| Total Work Load | 172 | ||
| Total Work Load / 25 (h) | 6.88 | ||
| ECTS Credit of the Course | 7 |