GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
GEOMETRY II/MAT- 416
Course Title: GEOMETRY II
Credits 3 ECTS 5
Semester 8 Compulsory/Elective Elective
COURSE INFO
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- NAME OF LECTURER(S)
  Assoc. Prof. Dr. Mustafa ÖZKAN
 -- WEB SITE(S) OF LECTURER(S)
  http://www.websitem.gazi.edu.tr/site/ozkanm
 -- EMAIL(S) OF LECTURER(S)
  ozkanm@gazi.edu.tr
 -- LEARNING OUTCOMES OF THE COURSE UNIT
They can define the basic definitions about differentiable manifolds
Deal with various examples of differentiable manifolds and smooth maps
They construct a topological structure on differentiable manifolds.
Have familiarity with tangent vectors, tensors and differential forms.
Do work practically with vector fields and differential forms.
Learns derivatived linear functions.
Learns immersions, submanifold and some topological properties.
 -- 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  Some remarks on topological concepts.
2. Week  Maps and atlases on a set.
3. Week  Differentiable maps and atlases
4. Week  Topological and differentiable manifolds. Structure of the reduced manifold topology
5. Week  Real-valued function defined on a manifold at a point of differentiation and derivatives.
6. Week  The partial derivatives of functions defined between two manifolds.
7. Week  Manifold tangent vector of a point
8. Week  Midterm
9. Week  Real-valued function defined on a manifold at a point of directional derivatives.
10. Week  differentiation and derivatives at a point domain of defined functions between two manifolds .
11. Week  Inverse Function Theorem for functions between two manifolds.
12. Week  Leibniz formula
13. Week  Immersions
14. Week  Submanifolds
15. Week  Submanifolds varieties
16. Week  Final Exam
 -- RECOMMENDED OR REQUIRED READING
   F.Brickell and R.S.Clark, Van Nostrand Reinhold Company, London 1970.
 -- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
  Lecture, Question & Answer, Drill - Practise
 -- WORK PLACEMENT(S)
  None
 -- ASSESSMENT METHODS AND CRITERIA
 
Quantity
Percentage
 Mid-terms
1
25
 Assignment
2
15
 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
0
0
 Reading
0
0
0
 Searching in Internet and Library
4
5
20
 Designing and Applying Materials
0
0
0
 Preparing Reports
0
0
0
 Preparing Presentation
0
0
0
 Presentation
0
0
0
 Mid-Term and Studying for Mid-Term
2
10
20
 Final and Studying for Final
3
15
45
 Other
0
0
0
 TOTAL WORKLOAD: 
127
 TOTAL WORKLOAD / 25: 
5.08
 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.
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.
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