COURSE INFORMATIONfbe.yeditepe.edu.tr/files/Bologna Paketi Yeni... · Geometry of hypersurfaces,...
Transcript of COURSE INFORMATIONfbe.yeditepe.edu.tr/files/Bologna Paketi Yeni... · Geometry of hypersurfaces,...
COURSE INFORMATION
Course Title Code Semester L+P
Hour Credits ECTS
RIEMANNIAN GEOMETRY MATH 512 1-2 3 + 0 3 10
Prerequisites
Language of
Instruction English
Course Level Graduate
Course Type
Course Coordinator Assoc. Prof. Dr. Ender Abadoğlu
Instructors
Assistants
Goals
To provide basic knowledge about Riemannian manifolds and curvature, to investigate the basic differential geometric structures related to the Riemannian metric.
Content
Riemannian manifolds. Absolute differentiation and connection. Riemann curvature, Bianchi identities. Geometry of hypersurfaces, Riemannian immersions and submersions. Completeness. Isometries and Killing vectors. Properties of curvature tensors.
Learning Outcomes Teaching
Methods
Assessment
Methods
1) Ability to make computations on Riemannian manifolds 1 A, B
2) Ability to analyze a geometric structures related to a
Riemannian manifold 1 A, B
3) Ability to make connections between curvature and
topology of a Riemannian manifold. 1 A, B
4) Ability to read a research article on the topic 1 B
Teaching
Methods: 1: Lecture, 2:Problem solving
Assessment
Methods: A: Written Examination, B: Homework
COURSE CONTENT
Week Topics Study
Materials
1 Review of Tensors, Manifolds and Vector Bundles Ch.2
2 Riemannian metrics and generalizations Ch.3
3 Connections Ch.4
4 Connections Ch.4
5 Riemannian geodesics Ch.5
6 Geodesics and distance Ch.6
7 Curvature Ch.7
8 Curvature Ch.7
9 Riemannian submanifolds Ch.8
10 Riemannian submanifolds Ch.8
11 The Gauss-Bonnet Theorem Ch.9
12 The Gauss-Bonnet Theorem Ch.9
13 Curvature and topology Ch.11
14 Curvature and topology Ch.11
RECOMMENDED SOURCES
Textbook Lee J.M., Riemannian Manifolds: An Introduction to Curvature, Springer,
1997..
Additional Resources Petersen P., Riemannian geometry, Second Edition, Springer, 2006.
MATERIAL SHARING
Documents
Assignments
Exams
ASSESSMENT
IN-TERM STUDIES NUMBER PERCENTAGE
Mid-terms
Quizzes
Assignments 5 100
Total 100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL
GRADE 50
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL
GRADE 50
Total 100
COURSE CATEGORY
COURSE'S CONTRIBUTION TO PROGRAM
No Program Learning Outcomes Contribution
1 2 3 4 5
1 Acquires a rigorous background about the fundamental fields in mathematics and the topics that are going to be specialized.
x
2 Acquires the ability to relate, interpret, analyse and synthesize on
fundamental fields in mathematics and/or mathematics and other sciences. x
3 Follows contemporary scientific developments, analyses, synthesizes and evaluates novel ideas.
x
4 Uses the national and international academic sources, and computer and related IT.
x
5
Participates in workgroups and research groups, scientific meetings, contacts by oral and written communication at national and international levels.
x
6
Acquires the potential of creative and critical thinking, problem solving, research, to produce a novel and original work, self-development in areas of interest.
x
7
Acquires the consciousness of scientific ethics and responsibility. Takes responsibility about the solution of professional problems as a requirement
of the intellectual consciousness. x
ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
Activities Quantity Duration
(Hour)
Total
Workload
(Hour)
Course Duration (14x Total course hours) 14 3 42
Hours for off-the-classroom study (Pre-study, practice) 14 8 112
Mid-terms (Including self study)
Quizzes
Assignments 5 12 60
Final examination (Including self study) 1 36 36
Total Work Load
250
Total Work Load / 25 (h) 10
ECTS Credit of the Course 10