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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 579LORENTZIAN GEOMETRY3 + 02nd Semester7,5

COURSE DESCRIPTION
Course Level Master's Degree
Course Type Elective
Course Objective Teaching connection, curvature and tensor structures on the Riemannian manifold.
Course Content Connections on the Riemann Manifolds; Geodesics of the Model Spaces and Maximal Geodesics; Lengths and Distances on Riemannian Manifolds; Jacobi Fields; Symmetries of the Curvature Tensor, Ricci and Scalar Curvatures; Riemann Isometries; The Gauss–Bonnet Formula and Theorem.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Knows connections on Riemann manifolds, learns geodesic and maximal geodesic.
2Learns the distance and the length on Riemann manifolds, realized Jacobi field. Knows curvature tensor, Ricci and Scalar curvatures.
3Learns Riemann isometries, Gauss Bonnet Theorem and formulas.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08
LO 0014  45 5 
LO 0025  54  4
LO 0034  45 45
Sub Total13  1314 99
Contribution40045033

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14342
Hours for off-the-classroom study (Pre-study, practice)14798
Assignments155
Mid-terms11515
Final examination13535
Total Work Load

ECTS Credit of the Course






195

7,5
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2012-2013 Spring1ŞEVKET CİVELEK


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 579 LORENTZIAN GEOMETRY 3 + 0 1 Turkish 2012-2013 Spring
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
FEN A0305 %60
Goals Teaching connection, curvature and tensor structures on the Riemannian manifold.
Content Connections on the Riemann Manifolds; Geodesics of the Model Spaces and Maximal Geodesics; Lengths and Distances on Riemannian Manifolds; Jacobi Fields; Symmetries of the Curvature Tensor, Ricci and Scalar Curvatures; Riemann Isometries; The Gauss–Bonnet Formula and Theorem.
Topics
WeeksTopics
1 Riemann manifolds
2 Conneksions on Riemann manifols
3 the concept of Geodesic
4 Maximal Geodesics
5 distance on Riemann manifols
6 Jacobi Fields
7 Tensorial structures
8 curveture tensor
9 Ricci tensor
10 Ricci curvatures
11 Riemann isometries
12 midterm exam
13 Gauss Bonnet's Theorem
14 Gauss Bonnet's Formulas
Materials
Materials are not specified.
Resources
Course Assessment
Assesment MethodsPercentage (%)Assesment Methods Title
Final Exam60Final Exam
Midterm Exam40Midterm Exam
L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes