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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 506HIGHER DIFFERENTIAL GEOMETRY-II3 + 01st Semester7,5

COURSE DESCRIPTION
Course Level Doctorate Degree
Course Type Elective
Course Objective The goal of the course is to express geometrical concepts with the tensor.
Course Content Lie Groups and Differentials, Lie Subalgebras, Matrix Lie Groups and Frame Bunches, Reduced Riemann Metrics, Vector Valued Forms, Orthonormal Frame Bunches on Width, Left-invariant Forms on Matrix Lie Groups, Structure Bunches of Matrix Lie Groups, Fundamental relations for Frame Bunches on Width one Submanifold, Generalizations. (High Order Curveture of a Curve).
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Knows Lie groups and differential, reognizes Lie sub-algebra, matrix Lie groups and bundles.
2Learns Riemannian metric of the reduced, vector forms, orthonormal roof on E'n.
3Recognizes left-invariant forms on Lie groups, structure bundle of matrix Lie groups.
4Knows the basic equations for roof bundles on E'n submanifolds, recognizes generalizations.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08
LO 0014 54   5
LO 0025 44   4
LO 0034 45   5
LO 0045 54   4
Sub Total18 1817   18
Contribution50540005

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 2022-2023 Fall1CANSEL AYCAN
Details 2019-2020 Spring1CANSEL AYCAN
Details 2016-2017 Spring1CANSEL AYCAN
Details 2015-2016 Spring1CANSEL AYCAN
Details 2014-2015 Spring1ŞEVKET CİVELEK
Details 2013-2014 Spring1ŞEVKET CİVELEK


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 506 HIGHER DIFFERENTIAL GEOMETRY-II 3 + 0 1 Turkish 2022-2023 Fall
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. CANSEL AYCAN c_aycan@pau.edu.tr FEN A0313 FEN A0316 %70
Goals The goal of the course is to express geometrical concepts with the tensor.
Content Lie Groups and Differentials, Lie Subalgebras, Matrix Lie Groups and Frame Bunches, Reduced Riemann Metrics, Vector Valued Forms, Orthonormal Frame Bunches on Width, Left-invariant Forms on Matrix Lie Groups, Structure Bunches of Matrix Lie Groups, Fundamental relations for Frame Bunches on Width one Submanifold, Generalizations. (High Order Curveture of a Curve).
Topics
WeeksTopics
1 structure of manifold
2 structure of submanifold
3 tensors
4 algebra of tensörs
5 symetric product and external product
6 lie Groups
7 algebra of lie Groups
8 roof beams
9 midterm exam
10 Maximal integral curves
11 flow of a vector field
12 manifold varieties
13 trend lines, curvatures
14 fınal exam
Materials
Materials are not specified.
Resources
ResourcesResources Language
yüksek diferensiyel geometriye giriş, H.H HacısalihoğluTürkçe
Course Assessment
Assesment MethodsPercentage (%)Assesment Methods Title
Final Exam50Final Exam
Midterm Exam50Midterm Exam
L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes