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: 7
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Core Courses A3 | 1 | 1 | 10 |
| Academic Year | 2022 – 2023 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Class ID | 600223656
|
Course Type 2021
Specific Foundation
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/1/600223656
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
General Prerequisites
Calculus.
Linear Algebra. Group Theory. Differential Geometry
Differentiable Manifolds I and II
Learning Outcomes
Upon successfully completing the course, students will have acquired basic knowledge of the theory of differentiable manifolds. They will furthermore submerge into advanced subjects of differential geometry and solidify a deeper understanding of the relations between Geometry, Algebra and Analysis.
General Competences
- Apply knowledge in practice
- Work autonomously
- Work in teams
- Work in an interdisciplinary team
Course Content (Syllabus)
Differentiable Manifolds (basic concepts). Fibre bundles. Covectors and 1-forms. Flow of a vector field and integral curves. Distributions. Frobenius theorem. Integral submanifolds. Basic concepts of foliations. Lie groups and Lie algebras (geometric aspects). Invariant vector fields. Integrations of Lie algebras and the exponential map. Examples.
Educational Material Types
- Notes
- Book
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 | 160 | 5.3 | ✓ | ||
| Seminars | 20 | 0.7 | |||
| Reading Assigment | 115 | 3.8 | |||
| Exams | 5 | 0.2 | |||
| Total | 300 | 10 |
Student Assessment
Description
Seminars. Written Examination.
Student Assessment methods
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Assignment (Formative, Summative)
- Oral Exams (Formative)
- Performance / Staging (Formative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Additional bibliography for study
1) Loring W. Tu, An introduction to Manifolds, Universitext, Springer 2011.
2) John M. Lee, Introduction to Smooth Manifolds, GTM 218, Springer 2003.
3) D. Barden and Ch. Thomas, An Introduction to Differential Manifolds, Imperial College Press, 2003.
4) Lawrence Conlon, Differentiable Manifolds, Second Edition, Modern Birkhäuser Classics, Birkhäuser Boston, Inc., Boston, MA, 2008.
5) Frank W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Graduate Texts in Mathematics, 94, Springer-Verlag, New York-Berlin, 1983.
Last Update
24-05-2023
