Euclidean and Non Euclidean Geometries (MAE727): Διαφορά μεταξύ των αναθεωρήσεων

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=== Attached Bibliography ===
=== Attached Bibliography ===


See [https://service.eudoxus.gr/public/departments#20 Eudoxus]. Additionally:
See the official [https://service.eudoxus.gr/public/departments#20 Eudoxus site] or the [https://cloud.math.uoi.gr/index.php/s/62t8WPCwEXJK7oL local repository] of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Additionally:
* Π. Πάμφιλου, Γεωμετρία, Εκδόσεις Τροχαλία, 1989.
* Π. Πάμφιλου, Γεωμετρία, Εκδόσεις Τροχαλία, 1989.
* M.J. Greenberg, Euclidean and non-Euclidean Geometry-Development and History, W.H. Freedmann and Company, 1973.
* M.J. Greenberg, Euclidean and non-Euclidean Geometry-Development and History, W.H. Freedmann and Company, 1973.
* R. Hartshorne, Geometry: Euclid and beyond, Springer, 2000.
* R. Hartshorne, Geometry: Euclid and beyond, Springer, 2000.
* H. Meschkowski, Noneuclidean Geometry, Academic Press, 1964.
* H. Meschkowski, Noneuclidean Geometry, Academic Press, 1964.

Αναθεώρηση της 12:54, 26 Ιουλίου 2022

Undergraduate Courses Outlines - Department of Mathematics

General

School

School of Science

Academic Unit

Department of Mathematics

Level of Studies

Undergraduate

Course Code

MAE727

Semester

7

Course Title

Euclidean and Non Euclidean Geometries

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

This is an introductory course on non Euclidean geometries. The aim is to study how the attempt to prove Euclid's fifth postulate led the way to non Euclidean geometries. On completion of the course the student should be familiar with the foundations of Euclidean and non Euclidean geometries.

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

Syllabus

Euclid's geometry, Hilbert's system of axioms, the fifth postulate, compatibility of axioms, neutral geometry, independence of the fifth postulate, hyperbolic geometry, Poincarẻ model, spherical geometry, Platonic solids.

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

Final written exam in Greek (in case of Erasmus students in English) which includes resolving application problems.

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:

  • Π. Πάμφιλου, Γεωμετρία, Εκδόσεις Τροχαλία, 1989.
  • M.J. Greenberg, Euclidean and non-Euclidean Geometry-Development and History, W.H. Freedmann and Company, 1973.
  • R. Hartshorne, Geometry: Euclid and beyond, Springer, 2000.
  • H. Meschkowski, Noneuclidean Geometry, Academic Press, 1964.