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Course Information
Course Unit Title : Maps and Geometries II
Course Unit Code : MAT406
Type of Course Unit : Compulsory
Level of Course Unit : First Cycle
Year of Study : 4
Semester : 8.Semester
Number of ECTS Credits Allocated : 5,00
Name of Lecturer(s) : ---
Course Assistants :
Learning Outcomes of The Course Unit : Projective maps,Mobius Space, Geometry of n-dimensional complex Space
Mode of Delivery : Face-To-Face
Prerequisities and Co-requisities Courses : Unavailable
Recommended Optional Programme Components : Unavailable
Course Contents : Projective Maps:. Definition of a projective map, equations of a projective map, projective group, conics, projective geometry of Euclidean plane. Topologic Maps: Topologic maps of plane, topologic properties of curves, models of plane, projective plane, analytic projective geometry, projective definitions of conics. Mobius Spaces: Spheres in the cartesian spaces, Stereographic projection, spherical affinite, inversion, productions of spherical affinites. Complex Spaces: Geometry of n-dimensional complex space, metric concept in the complex space, inner product in the complex space, geomerty of projective complex space, isotropic directions.
Languages of Instruction : Turkish-English
Course Goals : Öğrencinin geometride dönüşümler ile düşünmeyi kazanması, dönüşümleri uygulayarak hangi yeni geometri tiplerinin veya sistemlerinin nasıl elde edilebileceğini görmesi ve öğrenmesi.
Course Aims : To developed an understanding of thinking of geometry via maps, seeing and learning how 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) Kobayashi, S., Nomizu, K., ?Foundations of Differential Geometry II?, John Wiley New York,1967.
vii) Chern, S. S., Chen, W. H., Lam, K. S., ?Lectures on Differential Geometry? World Scientific Co. Pte. Ltd., Singapore, 1999.
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 Definition of a projective map
 
2 Definition of a projective map, equations of a projective map
 
3 Projective groups
 
4 Projective geometry of Euclidean Plane and its Applications.
 
5 Topologic maps of plane
 
6 Topologic maps of plane, topologic properties of curves, models of plane
 
7 Projective plane
 
8 Analytic projective geometry, projective definitions of conics
 
9 Mobius Spaces and exercises
 
10 Mobius Spaces: Spheres in the cartesian spaces, Stereographic projection and its applications
 
11 Complex Spaces: Geometry of n-dimensional complex space
 
12 Metric concept in the complex space, inner product in the complex space
 
13 Geomerty of projective complex space
 
14 İsotropic directions