Differenrial Manifolds
| Title | ΘΕΩΡΙΑ ΔΙΑΦΟΡΙΣΙΜΩΝ ΠΟΛΛΑΠΛΟΤΗΤΩΝ / Differenrial Manifolds |
| Code | 0658 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter |
| Coordinator | Panagiotis Batakidis |
| Common | Yes |
| Status | Active |
| Course ID | 40000046 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Core Courses A3 | 1 | 1 | 10 |
| Academic Year | 2017 – 2018 |
| Class Period | Winter |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Class ID | 600112020
|
Course Type 2016-2020
- Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600112020
Language of Instruction
- Greek (Instruction, Examination)
- English (Instruction, Examination)
- French (Instruction, Examination)
Prerequisites
General Prerequisites
Calculus.
Linear Algebra.
Differentiable Manifolds I and II
General Competences
- Apply knowledge in practice
- Work autonomously
- Work in teams
Course Content (Syllabus)
Differentiable Manifolds (basic concepts). Riemannian Metrics. Linear connections. Geodesics. Curvature. Riemannian submanifolds. Complete manifolds. Manifolds of constant curvature.
Educational Material Types
- Notes
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Communication with Students
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | 1.3 | ✓ | ||
| Seminars | 9 | 0.3 | |||
| Total | 48 | 1.6 |
Student Assessment
Description
Presentation. Written Examination.
Student Assessment methods
- Written Assignment (Formative, Summative)
- Oral Exams (Formative)
- Performance / Staging (Formative)
Bibliography
Additional bibliography for study
1) M. P. do Carmo, Riemannian Geometry, Birkhäuser 1992.
2) John M. Lee, Riemannian manifolds. An introduction to curvature, GTM 176, Springer-Verlag 1997.
3) W. Boothby, An introduction to differentiable manifolds and Riemannian geometry, Academic Press 1975.
4) Loring W. Tu, An introduction to Manifolds, Universitext, Springer 2011.
5) John M. Lee, Introduction to Smooth Manifolds, GTM 218, Springer 2003.
Last Update
09-07-2013
