GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
NON EUCLIDEAN GEOMETRIES/MAT508A
Course Title: NON EUCLIDEAN GEOMETRIES
Credits 3 ECTS 8
Semester 10 Compulsory/Elective Compulsory
COURSE INFO
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- NAME OF LECTURER(S)
  Prof. Dr. Hasan Hüseyin UĞURLU
 -- WEB SITE(S) OF LECTURER(S)
  w3.gazi.edu.tr/~hugurlu
 -- EMAIL(S) OF LECTURER(S)
  hugurlu@gazi.edu.tr
 -- LEARNING OUTCOMES OF THE COURSE UNIT
Students know the basics of Euclidean geometry. They learn how non-Euclidean geometries that are not verifying the parallel postulate occur.
Students learn spherical geometry, spherical geodesics and triangles.
Students learn hyperbolic geometry, hyperbolic geodesics and triangles. They know the hyperboloid model.
Students know conformal disk model and the upper half-plane model of hyperbolic geometry. They can make applications with them..





 -- MODE OF DELIVERY
  The mode of delivery of this course is Face to face
 -- PREREQUISITES AND CO-REQUISITES
  There is no prerequisite or co-requisite for this course.
 -- RECOMMENDED OPTIONAL PROGRAMME COMPONENTS
  There is no recommended optional programme component for this course.
 --COURSE CONTENT
1. Week  Foundations of Euclidean geometry, Euclid's parallel postulate
2. Week  Construction of non-Euclidean geometries
3. Week  Examples of non-Euclidean geometries
4. Week  Introduction to spherical geometry
5. Week  Geodesics on sphere
6. Week  Spherical triangles and area
7. Week  Midterm
8. Week  Introduction to hyperbolic geometry
9. Week  Hyperboloid model and hyperbolic geodesics
10. Week  Hyperbolic triangles and area
11. Week  Congruence theorems for hyperbolic triangles
12. Week  Conformal disk model
13. Week  The upper half-plane model
14. Week  Applications
15. Week  
16. Week  
 -- RECOMMENDED OR REQUIRED READING
  John G. Ratcliffe, Foundations of Hyperbolic Manifolds, Springer- Verlag New York 1994. Allan Berele; Jerry Goldman, GEOMETRY Theorems and Constru
 -- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
  Lecture, Question & Answer, Demonstration, Drill - Practise
 -- WORK PLACEMENT(S)
  -
 -- ASSESSMENT METHODS AND CRITERIA
 
Quantity
Percentage
 Mid-terms
1
40
 Assignment
0
0
 Exercises
0
0
 Projects
0
0
 Practice
0
0
 Quiz
0
0
 Contribution of In-term Studies to Overall Grade  
40
 Contribution of Final Examination to Overall Grade  
60
 -- WORKLOAD
 Efficiency  Total Week Count  Weekly Duration (in hour)  Total Workload in Semester
 Theoretical Study Hours of Course Per Week
14
2
28
 Practising Hours of Course Per Week
14
2
28
 Reading
0
 Searching in Internet and Library
12
5
60
 Designing and Applying Materials
0
 Preparing Reports
0
 Preparing Presentation
12
3
36
 Presentation
0
 Mid-Term and Studying for Mid-Term
12
2
24
 Final and Studying for Final
12
2
24
 Other
0
 TOTAL WORKLOAD: 
200
 TOTAL WORKLOAD / 25: 
8
 ECTS: 
8
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1Acquisition of scientific thinking skillsX
2Making research and investigation independentlyX
3Acquisition of carefully observing and analytically thinking skillsX
4Acquisition of learning and teaching mathematics problemsX
5Comprehending, applying and explaining the importance of mathematical conceptsX
6Developing the thinking, producing, argumenting and probing abilitiesX
7Having the algorithm and sotftware writing abilities for solving computer supported problemsX
8Developing the ability of reaching information, evaluating and presenting informationX
9Improving yourself parallel to the developing technologyX
10Understands the disciplinary structure of mathematics, its historical development, related philosophical approaches and problems.X