Euclidean and Non Euclidean Geometries (MAE727): Διαφορά μεταξύ των αναθεωρήσεων
| Γραμμή 102: | Γραμμή 102: | ||
=== 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 |
|
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 |
| ||||||||||
| 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.