|Course Title||Code||Semester||L+P Hour||Credits||ECTS|
|Prerequisites and co-requisites||Analytic Geometry|
|Recommended Optional Programme Components||None|
|Language of Instruction||Turkish|
|Course Level||First Cycle Programmes (Bachelor's Degree)|
|Course Coordinator||Prof.Dr. Doğan DÖNMEZ|
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.
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.
|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|
|Course's Contribution To Program|
|No||Program Learning Outcomes||Contribution|
Is able to prove Mathematical facts encountered in secondary school.
Recognizes the importance of basic notions in Algebra, Analysis and Topology
Develops maturity of mathematical reasoning and writes and develops mathematical proofs.
Is able to express basic theories of mathematics properly and correctly both written and verbally
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines.
Expresses clearly the relationship between objects while constructing a model
Draws mathematical models such as formulas, graphs and tables and explains them
Is able to mathematically reorganize, analyze and model problems encountered.
Knows at least one computer programming language
Uses effective scientific methods and appropriate technologies to solve problems
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians
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
Knows programming techniques and is able to write a computer program
Is able to do mathematics both individually and in a group.
|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|
|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|
|Recommended or Required Reading|