Differentiable Manifolds (MAE728)
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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. Books and other resources, not provided by Eudoxus:
- 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.