| TYPE OF COURSE UNIT | Elective Course |
| LEVEL OF COURSE UNIT | Bachelor's Degree |
| YEAR OF STUDY | - |
| SEMESTER | - |
| NUMBER OF ECTS CREDITS ALLOCATED | 4 |
| NAME OF LECTURER(S) | -
|
| LEARNING OUTCOMES OF THE COURSE UNIT |
At the end of this course, the students;
1) Know and explain the axiomatic structures and their
fundamental elements.
2) Know the axiomatic structures of planar (Euclidean), elliptic
(spherical) and hyperbolic geometries and compare them.
3) Know and prove some well-known results from Euclidean,
elliptic and hyperbolic plane geometries.
|
| MODE OF DELIVERY | Face to face |
| PRE-REQUISITES OF THE COURSE | No |
| RECOMMENDED OPTIONAL PROGRAMME COMPONENT | No |
| COURSE DEFINITION | Euclidean geometry, Euclidean axioms, Hilbert's Axiom 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, Finite Geometries (Fano Geometry). |
| COURSE CONTENTS | | WEEK | TOPICS |
|---|
| 1st Week | Euclidean geometry, general definitions and theorems | | 2nd Week | Euclidean geometry | | 3rd Week | Euclidean axioms | | 4th Week | Hilbert's Axiom System | | 5th Week | Non-Euclidean geometries | | 6th Week | The emergence and historical development of non-Euclidean geometries | | 7th Week | Riemann Geometry (Spherical geometry) | | 8th Week | Midterm Exam | | 9th Week | Riemann Geometry | | 10th Week | Lobachevsky Geometry (Hyperbolic Geometry) | | 11th Week | The place of Riemann and Lobachevsky geometries in the history of mathematics and science | | 12th Week | Finite Geometries | | 13th Week | Projection Geometry | | 14th Week | General Review |
|
| RECOMENDED OR REQUIRED READING | Gerard A. Venema, Foundations of Geometry, Pearson;
2nd edition (2011)
2) 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 WORKLOAD |
| Activities |
Number |
Hours |
Workload |
| Midterm exam | 1 | 2 | 2 | | Preparation for Quiz | | | | | Individual or group work | 2 | 15 | 30 | | Preparation for Final exam | 1 | 20 | 20 | | Course hours | 13 | 3 | 39 | | Preparation for Midterm exam | 1 | 15 | 15 | | Laboratory (including preparation) | | | | | Final exam | 1 | 2 | 2 | | Homework | | | | | Total Workload | | | 108 |
|---|
| Total Workload / 30 | | | 3,6 |
|---|
| ECTS Credits of the Course | | | 4 |
|---|
|
| LANGUAGE OF INSTRUCTION | Turkish |
| WORK PLACEMENT(S) | No |
| | |
