Differentiable Manifolds (MAE728)
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Undergraduate Courses Outlines - Department of Mathematics
General
| School |
School of Science |
|---|---|
| Academic Unit |
Department of Mathematics |
| Level of Studies |
Undergraduate |
| Course Code |
MAE728 |
| Semester |
7 |
| Course Title |
Differentiable Manifolds |
| Independent Teaching Activities |
Lectures, laboratory exercises (Weekly Teaching Hours: 3, Credits: 6) |
| Course Type |
Special Background |
| Prerequisite Courses | - |
| Language of Instruction and Examinations |
Greek, English |
| Is the Course Offered to Erasmus Students |
Yes |
| Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
In this lecture we introduce basic notions of modern Differential Geometry. More precisely, we introduce among others the notions of manifold, tangent bundle, connection, parallel transport and Riemannian metric. |
|---|---|
| General Competences |
|
Syllabus
- Smooth manifolds.
- Smooth maps.
- Tangent vectors.
- Vector fields.
- Regular values and Sard's Theorem.
- Homotopy and Isotopy.
- Lie bracket.
- Frobenius' Theorem.
- Connections and parallel transport.
- Riemannian metrics.
Teaching and Learning Methods - Evaluation
| Delivery |
Classroom (face-to-face) | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | - | ||||||||
| Teaching Methods |
| ||||||||
| Student Performance Evaluation |
Weakly homeworks and written final examination. |
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Additionally:
- M. do Carmo, Riemannian Geometry, Birkhaüser Boston, Inc., Boston, MA, 1992.
- V. Guillemin & A. Pollack, Differentiable Topology, Prentice-Hall, Inc, Englewood Cliffs, 1974.
- J. Lee, Introduction to Smooth Manifolds, Graduate Texts in Mathematics, 218, 2013.
- J. Milnor, Topology From the Differentiable Viewpoint, Princeton University Press, NJ, 1997.
- L. Tu, An Introduction to Manifolds, Universitext. Springer, New York, 2011.
- Δ. Κουτρουφιώτης, Διαφορική Γεωμετρία, Πανεπιστήμιο Ιωαννίνων, 1994.