Differentiable Manifolds (MAE622): Διαφορά μεταξύ των αναθεωρήσεων

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(Νέα σελίδα με '=== General === {| class="wikitable" |- ! School | School of Science |- ! Academic Unit | Department of Mathematics |- ! Level of Studies | Undergraduate |- ! Course Code | MAE622 |- ! Semester | 6 |- ! 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 |...')
 
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[[Undergraduate Courses Outlines]] - [https://math.uoi.gr  Department of Mathematics]
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Αναθεώρηση της 00:20, 2 Ιουλίου 2022

Undergraduate Courses Outlines - Department of Mathematics

General

School

School of Science

Academic Unit

Department of Mathematics

Level of Studies

Undergraduate

Course Code

MAE622

Semester

6

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) -

Learning Outcomes

Learning outcomes

In this lecture, the fundamental concept of a differentiable manifold will be developed. In particular, this lecture is a basic prerequisite for the upcoming class of Riemannian geometry. After a quick review of basic facts from general topology we will introduce the notions of a smooth manifold, tangent bundle, vector field, submanifold, connection, geodesic curve, parallel transport and Riemannian metric. On the completion of this course we expect that the students fully understand these important concepts and the main theorems that will be presented in the lectures.

General Competences
  • Working independently
  • Decision-making
  • Production of free, creative and inductive thinking
  • Criticism and self-criticism

Syllabus

Review of basic facts from general topology, smooth manifolds, tangent bundle, vector fields, immersions and embeddings, Lie bracket, Frobenius' theorem, Whitney's embedding 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
Activity Semester Workload
Lectures (13X3) 39
Working independently 78
Exercises-Homeworks 33
Course total 150
Student Performance Evaluation

Weekly exercises and homeworks, presentations, final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems.

Attached Bibliography

  • 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.