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Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MTS221 |
| Name | Geometries |
| Term | 2017-2018 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 2-0 (T-A) (17 Week) |
| ECTS | 3 ECTS |
| National Credit | 2 National Credit |
| Teaching Language | Türkçe |
| Level | Üniversite Dersi |
| Type | Normal |
| Label | E Elective |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. DOĞAN DÖNMEZ |
| Course Instructor |
Prof. Dr. DOĞAN DÖNMEZ
(Güz)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
To understand the significance of Euclid s fifth postulate and awareness of the existence of a geometry not satisfying this postulate. Also to have some knowledge of the spherical and projective geometries.
Course Content
Definitions, Axioms an d Postulates in Euclid's first book. Equivalent forms of Eclid's fifth postulate. Attempts to prove the fifith postulate. Existence of non-Euclidean Geometries. SOme formulas in non Euclidean geometry. Projective geometry. Klein' s definition of geometry.
Course Precondition
Analytic Geometry
Resources
Notes
http://math.cu.edu.tr/Dersler/MTS221/MTS221.htm
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Understands the significance of Euclid s fifth postulate |
| LO02 | Konws some propositons equivalent to the fifth postulate |
| LO03 | Understands the futility of efforts to prove the fifth postulate |
| LO04 | Knows some properties of the Hyperbolic Geometry |
| LO05 | Knows some properties of the Spherical Geometry |
| LO06 | Knows some properties of the Projective Geometry |
| LO07 | Grasps F. Klein s definition of Geometry |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | - | Is able to prove Mathematical facts encountered in secondary school. | |
| PLO02 | - | Recognizes the importance of basic notions in Algebra, Analysis and Topology | |
| PLO03 | - | Develops maturity of mathematical reasoning and writes and develops mathematical proofs. | |
| PLO04 | - | Is able to express basic theories of mathematics properly and correctly both written and verbally | |
| PLO05 | - | Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. | |
| PLO06 | - | Expresses clearly the relationship between objects while constructing a model | |
| PLO07 | - | Draws mathematical models such as formulas, graphs and tables and explains them | |
| PLO08 | - | Is able to mathematically reorganize, analyze and model problems encountered. | |
| PLO09 | - | Knows at least one computer programming language | |
| PLO10 | - | Uses effective scientific methods and appropriate technologies to solve problems | |
| PLO11 | - | Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | - | In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields | |
| PLO13 | - | Knows programming techniques and is able to write a computer program | |
| PLO14 | - | Is able to do mathematics both individually and in a group. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Contents of Euclid s first book of Elements | Read the relevant sections of the course notes | |
| 2 | Critics of Euclid s first book. Ptolemy and Proclus | Read the relevant sections of the course notes | |
| 3 | Propositions equivalent to the fifth postulate | Read the relevant sections of the course notes | |
| 4 | Brief introduction to spherical and projective geometries (Pappus, Pascal and Desargues Theorems) | Read the relevant sections of the course notes | |
| 5 | Attempts to prove the fifth postulate (Al Hazen, O. Hayyam, Saccheri and Lambert) | Read the relevant sections of the course notes | |
| 6 | Gauss, Bolyai and Lobachevski: Non-Euclidean Geometry | Read the relevant sections of the course notes | |
| 7 | Models of the Non-Euclidean geometry (Beltrami, Klein, Poincare) | Read the relevant sections of the course notes | |
| 8 | MIDTERM EXAM | Review | |
| 9 | A comparison of trigonometric formulas in three geometries | Read the relevant sections of the course notes | |
| 10 | Classification of Geometries. Introduction to Projective Geometry | Read the relevant sections of the course notes | |
| 11 | Algebraic construction of the Projective Geometry | Read the relevant sections of the course notes | |
| 12 | Algebraic construction of the Projective Geometry (Contd.) | Read the relevant sections of the course notes | |
| 13 | Some theorems in Projective Geometry | Read the relevant sections of the course notes | |
| 14 | Some theorems in Projective Geometry (Contd.) | Read the relevant sections of the course notes | |
| 15 | Klein s definition of Geometry and the Erlangen Program | Read the relevant sections of the course notes | |
| 16 | FINAL EXAM | Review | |
| 17 | FINAL EXAM | Review |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 40 |
| General Assessment | ||
| Midterm / Year Total | 100 | 40 |
| 1. Final Exam | - | 60 |
| Grand Total | - | 100 |