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

Τελευταία αναθεώρηση της 12:32, 15 Ιουνίου 2023

Ελληνική Έκδοση
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Department of Mathematics
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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)	See eCourse, the Learning Management System maintained by the University of Ioannina.

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. Books and other resources, not provided by Eudoxus:

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.

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 === Attached Bibliography ===
-* Π. Πάμφιλου, Γεωμετρία, Εκδόσεις Τροχαλία, 1989.
-* M.J. Greenberg, Euclidean and non-Euclidean Geometry-Development and History, W.H. Freedmann and Company, 1973.
+<!-- In order to edit the bibliography, visit the webpage -->
-* R. Hartshorne, Geometry: Euclid and beyond, Springer, 2000.
+<!-- https://wiki.math.uoi.gr/index.php/%CE%A0%CF%81%CF%8C%CF%84%CF%85%CF%80%CE%BF:MAE727-Biblio -->
-* H. Meschkowski, Noneuclidean Geometry, Academic Press, 1964.
+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. Books and other resources, not provided by Eudoxus:
+{{MAE727-Biblio}}