

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 
: 
FaceToFace

Prerequisities and Corequisities 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 
: 
TurkishEnglish

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 3Boyutlu 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? , EngleweedClifts, N. J., PrenticeHall, 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

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Assignments

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Exams

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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

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Course Duration (Excluding Exam Week)

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Time Of Studying Out Of Class

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Homeworks

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Presentation

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Project

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Lab Study

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Field Study

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Visas

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Finals

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Workload Hour (30)

:


Total Work Charge / Hour

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Course's ECTS Credit

:



Assessment Methods and Criteria
Studies During Halfterm

: 

Visa

: 

Quiz

: 

Homework

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Attendance

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Application

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Lab

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Project

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Workshop

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Seminary

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Field study

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TOTAL

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The ratio of the term to success

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The ratio of final to success

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TOTAL

: 


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



























































































