| Course Type | Elective Course |
|---|
| Course Level | Bachelor's Degree |
|---|
| Year of Study | - |
|---|
| Semester | - |
|---|
| ECTS | 4 |
|---|
| Name of Lecturer(s) |
- |
| Learning Outcomes |
At the end of this course, the students;
- Know and explain the axiomatic structures and their
fundamental elements.
- Know the axiomatic structures of planar (Euclidean), elliptic (spherical) and hyperbolic geometries and compare them.
- Know and prove some well-known results from Euclidean,
elliptic and hyperbolic plane geometries.
|
| Mode of Delivery | Face to face |
|---|
| Prerequisites | No |
|---|
| Recommended Optional Programme Components | No |
|---|
| Course Description | In this course, topics include Euclidean geometry, Euclid's axioms, Hilbert's axiomatic system, non-Euclidean geometries, the emergence of non-Euclidean geometries, Riemann geometry (spherical geometry), Lobachevsky geometry (hyperbolic geometry), the place of Riemann and Lobachevsky geometries in the history of mathematics and science, and finite geometries (Fano geometry). |
|---|
| Course Contents |
| WEEK |
TOPICS |
|
1st Week |
What is an axiomatic system? |
|
2nd Week |
Examples of axiomatic systems |
|
3rd Week |
Finite geometries (Fano plane) |
|
4th Week |
Axioms of Euclidean plane geometry |
|
5th Week |
Hilbert's axiom system for Euclidean space |
|
6th Week |
Historical birth of non-Euclidean geometries (Gauss, Bolyai and Lobachevsky) |
|
7th Week |
Neutral geometry |
|
8th Week |
Midterm |
|
9th Week |
Plane models for elliptical (spherical) geometry (map projections) |
|
10th Week |
Examination of some results valid for Euclidean plane geometry in elliptic plane models |
|
11th Week |
Examination of some results valid for Euclidean plane geometry in elliptic plane models |
|
12th Week |
Plane models for hyperbolic geometry |
|
13th Week |
Examination of some results valid for Euclidean plane geometry in hyperbolic plane models |
|
14th Week |
Examination of some results valid for Euclidean plane geometry in hyperbolic plane models |
|
15th Week |
General review |
|
| Recommended or Required Reading | Gerard A. Venema, Foundations of Geometry, Pearson; 2nd edition (2011)
GeoGebra, NonEuclid ve Spherical Easel programları |
|---|
| Planned Learning Activities and Teaching Methods |
- Lecture
- Questions/Answers
- Project
|
|---|
| Assessment Methods and Criteria |
|
Quantity |
Percentage (%) |
| Mid-term |
1 |
40 |
| Project |
1 |
20 |
| Total(%) |
|
60 |
| Contribution of In-term Studies to Overall Grade(%) |
|
60 |
| Contribution of Final Examination to Overall Grade(%) |
|
40 |
| Total(%) |
|
100 |
|
| ECTS Allocated Based on Student Workload |
| Activities |
Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Midterm exam |
1 |
2 |
2 |
| Preparation for Quiz |
|
|
|
| Individual or group work |
13 |
3 |
39 |
| Preparation for Final exam |
|
|
|
| Course hours |
13 |
3 |
39 |
| Preparation for Midterm exam |
1 |
15 |
15 |
| Laboratory (including preparation) |
|
|
|
| Final exam |
|
|
|
| Homework |
|
|
|
| Project |
1 |
25 |
25 |
| Total Work Load | 120 |
| Total Work Load / 30 (h) | 4 |
| ECTS Credit of the Course | 4 |
|
| Language of Instruction | Turkish |
|---|
| Work Placement(s) | No |
|---|
