GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
GEOMETRIES AND TOPOLOGIES/MAT- 425
Course Title: GEOMETRIES AND TOPOLOGIES
Credits 3 ECTS 5
Semester 7 Compulsory/Elective Elective
COURSE INFO
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- NAME OF LECTURER(S)
  Prof. AYSEL VANLI
 -- WEB SITE(S) OF LECTURER(S)
  www.gazi.edu.tr/~avanli
 -- EMAIL(S) OF LECTURER(S)
  avanli@gazi.edu.tr
 -- LEARNING OUTCOMES OF THE COURSE UNIT
To understand Moebius Spaces and complex projective spaces,ability to solve problems releated to topological transformations.
Have information about homeomorphisms of the circle, lines and planes
To learn non-affine topological transformations.






 -- 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  Moebius Spaces
2. Week  Spherical affinities
3. Week  Inversion
4. Week  Complex projective space P
5. Week  Lines and hyperplanes in P
6. Week  Affine concept, hyperplanes, metric concepts in C
7. Week  Topological transformations
8. Week  Midterm Exam
9. Week  Non-affine topological transformations
10. Week  Topological properties of the curve
11. Week  Homeomorphisms of lines and circles
12. Week  Homeomorphisms of hypersurfaces
13. Week  Plane models, non-homeomorfhic plane surfaces
14. Week  Plane models, non-homeomorfhic plane surfaces
15. Week  A model of delimited Euclidean space
16. Week  Final Exam
 -- RECOMMENDED OR REQUIRED READING
  Hacısalihoğlu, H.Hilmi. Yüksek boyutlu uzaylarda Dönüşümler ve Geometriler, Ankara Üniversitesi Fen Fakültesi, Matematik Bölümü.,2000 "Transformation Geometri (George E.Martin) Transformation Geometri (J.N.Kapur) Donusumler ve Geometriler (H.Hilmi Hacisalihoglu)"
 -- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
  Lecture, Question & Answer, Demonstration, Drill - Practise
 -- WORK PLACEMENT(S)
  none
 -- ASSESSMENT METHODS AND CRITERIA
 
Quantity
Percentage
 Mid-terms
1
30
 Assignment
1
10
 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
3
42
 Practising Hours of Course Per Week
0
 Reading
9
3
27
 Searching in Internet and Library
9
3
27
 Designing and Applying Materials
0
 Preparing Reports
0
 Preparing Presentation
0
 Presentation
0
 Mid-Term and Studying for Mid-Term
1
15
15
 Final and Studying for Final
1
19
19
 Other
0
 TOTAL WORKLOAD: 
130
 TOTAL WORKLOAD / 25: 
5.2
 ECTS: 
5
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1To train individuals who are contemporary, entrepreneur and have unique and aesthetic values, self-confidence and capable of independent decision-making.X
2To give good education in the program fields as algebra, geometry, applied mathematics, topology and analysis in order to be equipped with enough mathematics.X
3To teach mathematical thinking methods in order to improve the ability to express mathematics both orally and in writing.X
4To train individuals who are knowledgeable about the history of mathematics and the production of scientific knowledge and can follow developments in these disciplines.X
5To provide necessary equipments to take positions such areas as banking, finance, econometrics, and actuarial.X
6To acquire ability to solve problems encountered in real life by means of mathematical modeling using mathematical methods.X
7To provide ability to do necessary resource researches in the areas of mathematics and to use accessed information.X
8To give appropriate training in such areas as in computer programming and creating algorithms in order to take parts in developing IT sector.X
9To gain substructure to be able to study at graduate level.X
10To enable the student to gain the ability of relating mathematics with the other sciences.X