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• Information on Degree Programmes COURSE INFORMATON
Course Title Code Semester L+P Hour Credits ECTS
Geometries MTS   221 3 2 2 3

 Prerequisites and co-requisites Analytic Geometry Recommended Optional Programme Components None

Language of Instruction Turkish Course Level First Cycle Programmes (Bachelor's Degree)
Course Type
Course Coordinator Prof.Dr. Doğan DÖNMEZ
Instructors
 Prof.Dr. DOĞAN DÖNMEZ 1. Öğretim Grup:A Prof.Dr. DOĞAN DÖNMEZ 2. Öğretim Grup:A

Assistants
Goals
To understand the significance of Euclid s fifth postulate and awareness of the existence of a geometry not satisfying this postulate. Also to have some knowledge of the spherical and projective geometries.
Content
Definitions, Axioms an d Postulates in Euclid's first book. Equivalent forms of Eclid's fifth postulate. Attempts to prove the fifith postulate. Existence of non-Euclidean Geometries. SOme formulas in non Euclidean geometry. Projective geometry. Klein' s definition of geometry.

Learning Outcomes
1) Understands the significance of Euclid s fifth postulate
2) Konws some propositons equivalent to the fifth postulate
3) Understands the futility of efforts to prove the fifth postulate
4) Knows some properties of the Hyperbolic Geometry
5) Knows some properties of the Spherical Geometry
6) Knows some properties of the Projective Geometry
7) Grasps F. Klein s definition of Geometry
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Course's Contribution To Program
NoProgram Learning OutcomesContribution
12345
1
Is able to prove Mathematical facts encountered in secondary school.
X
2
Recognizes the importance of basic notions in Algebra, Analysis and Topology
X
3
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
X
4
Is able to express basic theories of mathematics properly and correctly both written and verbally
X
5
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
X
6
Expresses clearly the relationship between objects while constructing a model
X
7
Draws mathematical models such as formulas, graphs and tables and explains them
X
8
Is able to mathematically reorganize, analyze and model problems encountered.
X
9
Knows at least one computer programming language
10
Uses effective scientific methods and appropriate technologies to solve problems
11
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
12
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields
13
Knows programming techniques and is able to write a computer program
14
Is able to do mathematics both individually and in a group.

Course Content
WeekTopicsStudy Materials _ocw_rs_drs_yontem
1 Contents of Euclid s first book of Elements Read the relevant sections of the course notes Lecture
2 Critics of Euclid s first book. Ptolemy and Proclus Read the relevant sections of the course notes Lecture
3 Propositions equivalent to the fifth postulate Read the relevant sections of the course notes Lecture
4 Brief introduction to spherical and projective geometries (Pappus, Pascal and Desargues Theorems) Read the relevant sections of the course notes Lecture
5 Attempts to prove the fifth postulate (Al Hazen, O. Hayyam, Saccheri and Lambert) Read the relevant sections of the course notes Lecture
6 Gauss, Bolyai and Lobachevski: Non-Euclidean Geometry Read the relevant sections of the course notes Lecture
7 Models of the Non-Euclidean geometry (Beltrami, Klein, Poincare) Read the relevant sections of the course notes Lecture
8 MIDTERM EXAM Review Testing
9 A comparison of trigonometric formulas in three geometries Read the relevant sections of the course notes Lecture
10 Classification of Geometries. Introduction to Projective Geometry Read the relevant sections of the course notes Lecture
11 Algebraic construction of the Projective Geometry Read the relevant sections of the course notes Lecture
12 Algebraic construction of the Projective Geometry (Contd.) Read the relevant sections of the course notes Lecture
13 Some theorems in Projective Geometry Read the relevant sections of the course notes Lecture
14 Some theorems in Projective Geometry (Contd.) Read the relevant sections of the course notes Lecture
15 Klein s definition of Geometry and the Erlangen Program Read the relevant sections of the course notes Lecture
16-17 FINAL EXAM Review

Recommended or Required Reading
Textbook  