Differential Topology (ΓΕ4): Διαφορά μεταξύ των αναθεωρήσεων
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| Γραμμή 60: | Γραμμή 60: | ||
=== Syllabus === | === Syllabus === | ||
* | * Manifolds. | ||
* | * Immersions, embeddings and submersions. | ||
* | * Milnor’s proof of the fundamental theorem of algebra. | ||
* | * Sard’s theorem and Morse functions. | ||
* | * Partition of unity and Whitney’s embedding theorem. | ||
* | * Homotopy and isotopy. | ||
* | * Brouwer’s degree. | ||
* | * Whitney’s approximation theorem. | ||
* | * Differential forms and integration. | ||
* | * Hopf's invariant. | ||
* Hopf's degree theorem. | |||
=== Teaching and Learning Methods - Evaluation === | === Teaching and Learning Methods - Evaluation === | ||
Αναθεώρηση της 17:19, 21 Νοεμβρίου 2022
Graduate Courses Outlines - Department of Mathematics
General
| School | School of Science |
|---|---|
| Academic Unit | Department of Mathematics |
| Level of Studies | Graduate |
| Course Code | ΓΕ4 |
| Semester | 2 |
| Course Title | Differential Topology |
| Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
| Course Type | Special Background |
| Prerequisite Courses | - |
| Language of Instruction and Examinations |
Greek |
| Is the Course Offered to Erasmus Students | Yes (in Greek) |
| Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
In this lecture we present applications of Algebraic and Differential Topology in the study of topological invariants of smooth manifolds. |
|---|---|
| General Competences |
|
Syllabus
- Manifolds.
- Immersions, embeddings and submersions.
- Milnor’s proof of the fundamental theorem of algebra.
- Sard’s theorem and Morse functions.
- Partition of unity and Whitney’s embedding theorem.
- Homotopy and isotopy.
- Brouwer’s degree.
- Whitney’s approximation theorem.
- Differential forms and integration.
- Hopf's invariant.
- Hopf's degree theorem.
Teaching and Learning Methods - Evaluation
| Delivery |
Face-to-face | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Use of Information and Communications Technology | - | ||||||||||
| Teaching Methods |
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| Student Performance Evaluation |
Weakly HomeWorks, presentations in the blackboard of HomeWorks, written final examination. |
Attached Bibliography
- T. Bröcker, K. Jänich, Introduction to differential topology, Cambridge Univ. Press, 1982.
- V. Guillemin and A. Pollack, Differential Topology, Prentice Hall, 1974.
- J. Milnor, Morse Theory, Annals of Mathematical Studies, 51. Princeton University Press, Princeton, N.J. 1963.
- J. Milnor, Topology from a differentiable viewpoint, The University Press of Virginia, Charlottesville, Va. 1965.