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Course Information
Course Unit Title : Maps and Geometries I
Course Unit Code : MAT405
Type of Course Unit : Compulsory
Level of Course Unit : First Cycle
Year of Study : 4
Semester : 7.Semester
Number of ECTS Credits Allocated : 5,00
Name of Lecturer(s) : ---
Course Assistants :
Learning Outcomes of The Course Unit : Affine spaces, Motions, Afine geometry, Isometries
Mode of Delivery : Face-To-Face
Prerequisities and Co-requisities Courses : Unavailable
Recommended Optional Programme Components : Unavailable
Course Contents : What is Geometry?:. Definition and history of geometry, geometrical maps, classifying new geometry types by means of maps. Affine spaces:. Affine frame, affine coordinate system, change of affine coordinate system, affine map and group, parallelism in affine subspaces, parametric expression in affine subspaces and convex set. General introduction to maps: Definition of geometrical maps, inverse of a map, group of maps, invariant of geometry. Motions on Euclidean plane: Some properties of motion, motions and congruence, translation, rotation, group of rigid motion, reflection and the other opposite motions. Similarity maps: General properties of similarity maps, radial maps, equations of similarity group, metric geometry. Affine Maps: A fundamental affine map, analysis of general affine map, affine geometry, affine equivalence and distance in affine geometry. Isometries: Isometries of Euclidean spaces, equivalence isometries, equivalence of plane isometries. Projections: Parallel projection of a straight line, paralel projection of plane, central projection.
Languages of Instruction : Turkish-English
Course Goals : To developed a way of thinking of geometry via maps and to obtain new geometry types and systems by applying maps.
Course Aims : To developed a way of thinking of geometry via maps and to obtain new geometry types and systems by applying maps.
WorkPlacement   Not Available
Recommended or Required Reading
Textbook :
Additional Resources : i-) Hacısalihoğlu, H. H., ?2 ve 3-Boyutlu Uzaylarda Dönüşümler ve Geometriler?, Ankara Üniversitesi Fen Fakültesi Matematik Bölümü, Ocak 1998.
İi-) Hacısalihoğlu, H. H., ?Yüksek Boyutlu Uzaylarda Dönüşümler ve Geometriler?, İnönü Üniversitesi Temel Bilimler Yayınları, Mat No.1, 1980.
İii-) Kaya, R. ?Projektif Geometri?, Fırat Üniversitesi Fen Fakültesi Yayınları, 1978.
Iv) Levi, H., ?Foundations of Geometry and Trigonometry? , Engleweed-Clifts, N. J., Prentice-Hall, 1960.
v) Robinson, G. De B., ?The Foundations of Geometry?, Toronto University of Toronto Press, 1940.
vi) Dodson, C.T.J., Poston, T., ?Tensor Geometry?, Pitman, London, 1979.
Material Sharing
Documents :
Assignments :
Exams :
Additional Material :
Planned Learning Activities and Teaching Methods
Lectures, Practical Courses, Presentation, Seminar, Project, Laboratory Applications (if necessary)
ECTS / Table Of Workload (Number of ECTS credits allocated)
Student workload surveys utilized to determine ECTS credits.
Activity :
Number Duration Total  
Course Duration (Excluding Exam Week) :
15 3 45  
Time Of Studying Out Of Class :
15 4 60  
Homeworks :
1 15 15  
Presentation :
0 0 0  
Project :
0 0 0  
Lab Study :
0 0 0  
Field Study :
0 0 0  
Visas :
1 15 15  
Finals :
1 15 15  
Workload Hour (30) :
30  
Total Work Charge / Hour :
150  
Course's ECTS Credit :
5      
Assessment Methods and Criteria
Studies During Halfterm :
Number Co-Effient
Visa :
0 0
Quiz :
0 0
Homework :
0 0
Attendance :
0 0
Application :
0 0
Lab :
0 0
Project :
0 0
Workshop :
0 0
Seminary :
0 0
Field study :
0 0
   
TOTAL :
0
The ratio of the term to success :
0
The ratio of final to success :
0
TOTAL :
0
Weekly Detailed Course Content
Week Topics  
1 Why is geometry? Short history of Geometry.
 
2 The definition of geometric mapping
 
3 The definition of of affine space, affine mapping, affine coordinate system and affine Groups
 
4 The definition of Geometric mappings
 
5 Some motion on Euclidean Spaces and some properties of motion, motions
 
6 Motions and congruence, translation, rotation, group of rigid motion, reflection and the other opposite motions.
 
7 Motions and congruence, translation, rotation, group of rigid motion, reflection and the other opposite motions and exercises
 
8 Similarity maps and General properties of similarity maps
 
9 Radial maps, equations of similarity group, metric geometry.
 
10 Affine Maps and A fundamental affine map, analysis of general affine map, affine geometry
 
11 Affine equivalence and distance in affine geometry
 
12 Isometries and Isometries of Euclidean spaces, equivalence isometries, equivalence of plane isometries
 
13 Projections and Parallel projection of a straight line, parallel projection of plane, central projection.
 
14 Projections: and Parallel projection of a straight line, parallel projection of plane, central projection and exercises