THEORY OF DIFFERENTIAL MANIFOLDS
| Title | ΘΕΩΡΙΑ ΔΙΑΦΟΡΙΣΙΜΩΝ ΠΟΛΛΑΠΛΟΤΗΤΩΝ / THEORY OF DIFFERENTIAL MANIFOLDS |
| Code | Θ029 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 2nd / Postgraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Fani Petalidou |
| Common | Yes |
| Status | Active |
| Course ID | 600025918 |
Programme of Study: PMS Tmīmatos Mathīmatikṓn (2025-2030)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| THEŌRĪTIKA MATHĪMATIKA | Elective Courses belonging to the selected specialization | Winter | - | 10 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 3 |
| Total Hours | 39 |
| Class ID | 600268390
|
Type Of Offer
- Disciplinary Course
Course Type 2021
Specialization / Direction
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600268390
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
General Prerequisites
General background on Linear Algebra, Differential Calculus and Groups theory,
Learning Outcomes
Upon successful completion of the course, students will know:
1. the basic theory of the Theory of Differential Manifolds.
2. some historical elements of the development of the notion of Differential Manifold.
3. calculus on the manifolds.
4. connection with other branches of Mathematics.
General Competences
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Make decisions
- Work autonomously
- Work in teams
- Work in an international context
- Work in an interdisciplinary team
- Generate new research ideas
- Advance free, creative and causative thinking
Course Content (Syllabus)
Differentiable manifolds and smooth maps. Tangent and cotangent spaces. Tangent and cotangent bundle. Immersions and embeddings. Submanifolds. Theory of distributions and Frobenius's Theorem. Lie Groups and Lie algebras. Cartan calculus. Integration on manifolds and Stokes's theorem
Keywords
Manifolds, Tangent and cotangent bundle, Immersions, Embeddings, Submanifolds, Lie Groups and Lie Algebras, Distribution, Integration
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
Description
Online communication with students.
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | ||||
| Reading Assigment | 143 | ||||
| Tutorial | 13 | ||||
| Project | 70 | ||||
| Written assigments | 35 | ||||
| Total | 300 |
Student Assessment
Description
Homeworks - Exercises - Presentations.
A mini thesis for the final evaluation of the students. Analysis, reduction and presentation of a advanced subject of the course.
Student Assessment methods
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Assignment (Formative, Summative)
- Oral Exams (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Additional bibliography for study
1. Loring W. Tu, An introduction to Manifolds, Universitext, Springer 2011. (Εισαγωγικό)
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
13-05-2025
