GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
THEORY OF MANIFOLDS II/5461305
Course Title: THEORY OF MANIFOLDS II
Credits 3 ECTS 7.5
Course Semester 1 Type of The Course Elective
COURSE INFORMATION
 -- (CATALOG CONTENT)
 -- (TEXTBOOK)
 -- (SUPPLEMENTARY TEXTBOOK)
 -- (PREREQUISITES AND CO-REQUISITES)
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- COURSE OBJECTIVES
 -- COURSE LEARNING OUTCOMES
They learn the properties of vector field on a manifold
They can give the response of the derivative in analysis for the manifold
They learn a differential equation definition on a manifold
They learn Frobenius Theorem
They learn Lie group structure
They learn Lie algebra
 -- MODE OF DELIVERY
  The mode of delivery of this course is Face to face
 --WEEKLY SCHEDULE
1. Week  Definitions and characteristic properties of vector fields, The tangent bundle.
2. Week  Independent vector fields,orientable manifolds
3. Week  Differentiable equations of first order definitions and examples, Maximal integral curves.
4. Week  Differentiable equations on a quotient manifold, eigenvalues of a vector field
5. Week  Lineer connections definitions and charecteristic properties, the curvature and torsion of a linear connection.
6. Week  The horizontal distribution, Riemannian connection.
7. Week  Differential equations of second order definitions and basic properties, Sprays
8. Week  The Riemannian Spray, The metric structure on a Riemannian Manifold
9. Week  Distributions definitions and examples, Frobenius Theorem
10. Week  Integral manifolds of a distribution, an application to linear connections
11. Week  Lie groups definitions and examples, some topological properties of Lie groups, Lie subgroups,the Lie algebra of a Lie Group
12. Week  The exponential mapping for a Lie Group, A special chart of a Lie Group
13. Week  Lie Transformation Groups definition and examples,A Lie algebra of vector fields
14. Week  Orbits under a Lie transformatin group, An exponential mapping
15. Week  
16. Week  
 -- TEACHING and LEARNING METHODS
 -- ASSESSMENT CRITERIA
 
Quantity
Total Weighting (%)
 Midterm Exams
1
20
 Assignment
4
15
 Application
0
0
 Projects
0
0
 Practice
0
0
 Quiz
2
15
 Percent of In-term Studies  
50
 Percentage of Final Exam to Total Score  
50
 -- WORKLOAD
 Activity  Total Number of Weeks  Duration (weekly hour)  Total Period Work Load
 Weekly Theoretical Course Hours
14
3
42
 Weekly Tutorial Hours
0
 Reading Tasks
0
 Searching in Internet and Library
6
15
90
 Material Design and Implementation
0
 Report Preparing
0
 Preparing a Presentation
0
 Presentation
0
 Midterm Exam and Preperation for Midterm Exam
1
20
20
 Final Exam and Preperation for Final Exam
1
30
30
 Other (should be emphasized)
0
 TOTAL WORKLOAD: 
182
 TOTAL WORKLOAD / 25: 
7.28
 Course Credit (ECTS): 
7.5
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1To be able to develop their knowledge of theory and applications at master degree depending on the competencies acquired in undergraduate level.X
2To be able to recognize different problems encountered in mathematics and to be able to make studies for their solutions.X
3To be able to formulate new solutions with scientific methods mostly based on analysis and synthesis.X
4To be able to carry out his/her works either independently or in groups within a project considering his/her knowledge on the field he/she works in a critical approach.X
5To be able to continue his/her works considering social, scientific and ethical values.X
6To be able to follow scientific and social developments related to his/her field.X
7To be able to carry out his/her works within the framework of quality management, workplace safety and environmental awareness and to be able to present systematically his/her works using various methods like written, oral or visual.
8To be able to use methods of accessing knowledge effectively in accordance with ethical values.X
9To be able to use knowledge in other disciplines by combining it with mathematical information.X
10To be able to make activities in the awareness of need for lifelong learning.
11To be able to make connections between mathematical and social concepts and produce solutions with scientific methods.
12To be able to use his/her mathematical knowledge in technology.X
 -- NAME OF LECTURER(S)
   (Assoc.Prof. Mustafa ÖZKAN)
 -- WEB SITE(S) OF LECTURER(S)
   (http://websitem.gazi.edu.tr/site/ozkanm)
 -- EMAIL(S) OF LECTURER(S)
   (ozkanm@gazi.edu.tr)