COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 513DIFFERENTIABLE MANIFOLDS -I3 + 02nd Semester6

COURSE DESCRIPTION
Course Level Doctorate Degree
Course Type Elective
Course Objective Manifolds on the development of the basic geometric and topological concepts.
Course Content Differential manifolds and functions, induced topology on a manifold, varieties, Grassmann manifolds, Manifold structure on a topological space, properties of an induced topology, partitions of unity, tengent vectors, derived linear functions, immersions, submanifolds and some topological properties, reguler submanifolds, submersions and fibres, quotient manifolds, transformations groups, tangent bundle, vector fields, orientable manifolds.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to face

COURSE LEARNING OUTCOMES
1Learns differentiable manifolds and functions, knows reduced topology on a manifold, varieties, Grasman manifolds.
2Learns manifold structure on a topological space, properties of the reduced topology, unit breakdown of unit.
3Learns tangent vectors, derivatived linear functions, immersions, submanifold and some topological properties.
4Knows regular submanifolds, submersiyonlar and fibers, section manifolds, transformation groups.
5Knows tangent bundle, vector fields, directional manifolds.

COURSE'S CONTRIBUTION TO PROGRAM
Data not found.

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)14570
Assignments144
Mid-terms11313
Final examination12727
Total Work Load

ECTS Credit of the Course






156

6

COURSE DETAILS
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L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes
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