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Classical Differential Geometry (ΓΕ1): Διαφορά μεταξύ των αναθεωρήσεων

Classical Differential Geometry (ΓΕ1): Διαφορά μεταξύ των αναθεωρήσεων

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(Νέα σελίδα με 'Graduate Courses Outlines - [https://math.uoi.gr Department of Mathematics] === General === {| class="wikitable" |- ! School | School of Science |- ! Academic Unit | Department of Mathematics |- ! Level of Studies | Graduate |- ! Course Code | ΧΧΧ |- ! Semester | 000 |- ! Course Title | ΧΧΧ |- ! Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |- ! Course Type | General Background |- ! Prerequisite Courses | - |- ! L...')
 
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[[Graduate Courses Outlines]] - [https://math.uoi.gr  Department of Mathematics]
* [[Κλασσική Διαφορική Γεωμετρία (ΓΕ1)|Ελληνική Έκδοση]]
{{Course-Graduate-Top-EN}}
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=== General ===
=== General ===
Γραμμή 15: Γραμμή 17:
|-
|-
! Course Code
! Course Code
| ΧΧΧ
| ΓΕ1
|-
|-
! Semester
! Semester
| 000
| 1
|-
|-
! Course Title
! Course Title
| ΧΧΧ
| Classical Differential Geometry
|-
|-
! Independent Teaching Activities
! Independent Teaching Activities
Γραμμή 27: Γραμμή 29:
|-
|-
! Course Type
! Course Type
| General Background
| Special Background
|-
|-
! Prerequisite Courses
! Prerequisite Courses
| -
|
Topology, Calculus of Several Variables, Complex Analysis.
|-
|-
! Language of Instruction and Examinations
! Language of Instruction and Examinations
|
|
ΧΧΧ
Greek
|-
|-
! Is the Course Offered to Erasmus Students
! Is the Course Offered to Erasmus Students
| Yes
|
Yes (in English).
|-
|-
! Course Website (URL)
! Course Website (URL)
Γραμμή 49: Γραμμή 53:
! Learning outcomes
! Learning outcomes
|
|
ΧΧΧ
In this lecture we introduce basic notions of Classical Differential Geometry. More precisely, we introduce among others the notions of a manifold as a subset of the Euclidean space. Then, we present various local and global theorems concerning minimal submanifolds.
|-
|-
! General Competences
! General Competences
|
|
ΧΧΧ
* Work autonomously.
* Work in teams.
* Develop critical thinking skills.
|}
|}


=== Syllabus ===
=== Syllabus ===


ΧΧΧ
* Manifolds of the Euclidean space.
* Tangent and normal bundles.
* 1st and 2nd fundamental forms.
* Weingarten operator and Gauss map.
* Convex hypersurfaces.
* Hadamard’s Theorem.
* 1st and 2nd variation of area.
* Minimal submanifolds.
* Weierstrass representation.
* Bernstein’s Τheorem.


=== Teaching and Learning Methods - Evaluation ===
=== Teaching and Learning Methods - Evaluation ===
Γραμμή 66: Γραμμή 81:
! Delivery
! Delivery
|
|
ΧΧΧ
Face-to-face.
|-
|-
! Use of Information and Communications Technology
! Use of Information and Communications Technology
|
| -
ΧΧΧ
|-
|-
! Teaching Methods
! Teaching Methods
Γραμμή 81: Γραμμή 95:
| 39
| 39
|-
|-
| ΧΧΧ
| Autonomous Study
| 000
| 78
|-
|-
| ΧΧΧ
| Solution of Exercises - Homeworks
| 000
| 70.5
|-
|-
| Course total  
| Course total  
Γραμμή 93: Γραμμή 107:
! Student Performance Evaluation
! Student Performance Evaluation
|
|
ΧΧΧ
Weakly HomeWorks, presentations of the HomeWorks in the blackboard, written final examination.
|}
|}


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Τελευταία αναθεώρηση της 16:28, 15 Ιουνίου 2023

General

School School of Science
Academic Unit Department of Mathematics
Level of Studies Graduate
Course Code ΓΕ1
Semester 1
Course Title Classical Differential Geometry
Independent Teaching Activities Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
Course Type Special Background
Prerequisite Courses

Topology, Calculus of Several Variables, Complex Analysis.

Language of Instruction and Examinations

Greek

Is the Course Offered to Erasmus Students

Yes (in English).

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 Classical Differential Geometry. More precisely, we introduce among others the notions of a manifold as a subset of the Euclidean space. Then, we present various local and global theorems concerning minimal submanifolds.

General Competences
  • Work autonomously.
  • Work in teams.
  • Develop critical thinking skills.

Syllabus

  • Manifolds of the Euclidean space.
  • Tangent and normal bundles.
  • 1st and 2nd fundamental forms.
  • Weingarten operator and Gauss map.
  • Convex hypersurfaces.
  • Hadamard’s Theorem.
  • 1st and 2nd variation of area.
  • Minimal submanifolds.
  • Weierstrass representation.
  • Bernstein’s Τheorem.

Teaching and Learning Methods - Evaluation

Delivery

Face-to-face.

Use of Information and Communications Technology -
Teaching Methods
Activity Semester Workload
Lectures 39
Autonomous Study 78
Solution of Exercises - Homeworks 70.5
Course total 187.5
Student Performance Evaluation

Weakly HomeWorks, presentations of the HomeWorks in the blackboard, written final examination.

Attached Bibliography

  • M. do Carmo, Riemannian Geometry, Birkhaüser Boston, Inc., Boston, MA, 1992.
  • J. Jost, Riemannian Geometry and Geometric Analysis, Universitext, Springer, 2017.
  • J. Lee, Introduction to smooth manifolds, Second edition, Graduate Texts in Mathematics, 218, Springer, 2013.
  • Δ. Κουτρουφιώτης, Διαφορική Γεωμετρία, Πανεπιστήμιο Ιωαννίνων, 1994.
Ανακτήθηκε από «https://wiki.math.uoi.gr/index.php?title=Classical_Differential_Geometry_(ΓΕ1)&oldid=4662»