| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Hıperbolıc Geometry | MAT 580 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | Students are assumed to be familiar with the course Differential Geometry I and Differential Geometry II. |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | YUKSEK_LISANS |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Prof.Dr. SOLEY ERSOY |
| Dersi Verenler | |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Alanına Uygun Öğretim |
| Dersin Amacı | The hyperbolic geometry course aims to give the fundamental knowledge for the studies of graduate students who study at geometry branch. |
| Dersin İçeriği | Euclids parallel postulate, independence of the parallel postulate, Euclid n-space, spherical n- space, elliptic n-space, spherical arc length, spherical volume, spherical trigonometry, Lorentzian n- space, hyperbolic n- space, hyperbolic arc length, hyperbolic volume, hyperbolic trigonometry, reflections, stereographic projection, Mobius transformation, conformal disc model of hyperbolic space, Poincaré half-plain model, isometries of hyperbolic space |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | He/She knows the fundamental consepts of hyperbolic geometry | Lecture, Question-Answer, Discussion, Group Study, Problem Solving, | Testing, Homework, |
| 2 | He/She defines the fundamental calculations on Euclidean n-space, spherical n-space and eliptical n-space. | Lecture, Question-Answer, Discussion, Group Study, Problem Solving, | Testing, Homework, |
| 3 | He/She calculate hyperbolic arc length and hyperbolic volume | Lecture, Question-Answer, Discussion, Group Study, Problem Solving, | Testing, Homework, |
| 4 | He/She defines Mobious transformations, Poincare half plain model and isometries of the hyperbolic spaces. | Lecture, Question-Answer, Discussion, Group Study, Problem Solving, | Testing, Homework, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Euclids parallel postulate, independence of the parallel postulate, Euclid n-space | |
| 2 | Spherical n- space, elliptic n-space, spherical arc length, spherical volume | |
| 3 | Spherical trigonometry | |
| 4 | Lorentzian n- space, hyperbolic n- space | |
| 5 | Hyperbolic arc length | |
| 6 | Hyperbolic volume | |
| 7 | Hyperbolic trigonometry | |
| 8 | Reflections | |
| 9 | Mid term exam | |
| 10 | Stereographic projection | |
| 11 | Mobius transformation | |
| 12 | Conformal disc model of hyperbolic space | |
| 13 | Poincaré half-plain model | |
| 14 | Isometries of hyperbolic space |
| Kaynaklar | |
|---|---|
| Ders Notu | 1.Ratcliffe, J. G., (1994), Foundations of Hyperbolic Manifolds, Springer-Verlag. |
| Ders Kaynakları | 1. Fenchel, W., Walter de Gruyter, (1989), Elementary Geometry in Hyperbolic Space |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 0 | Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise | ||||||
| 2 | Student follows the current journals in his/her field and puts forward problems. | X | |||||
| 3 | Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics | X | |||||
| 4 | Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. | X | |||||
| 5 | Student uses different proof methods to come to a solution by analyzing the problems encountered. | X | |||||
| 6 | Student determines the problems to be solved within his/her field and if necessary takes the lead. | X | |||||
| 7 | Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. | X | |||||
| 8 | Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters | X | |||||
| 9 | Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. | X | |||||
| 10 | Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. | X | |||||
| 11 | Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. | X | |||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 70 |
| 1. Ödev | 30 |
| Toplam | 100 |
| 1. Yıl İçinin Başarıya | 50 |
| 1. Final | 50 |
| Toplam | 100 |
| AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
|---|---|---|---|
| Course Duration (Including the exam week: 16x Total course hours) | 16 | 3 | 48 |
| Hours for off-the-classroom study (Pre-study, practice) | 16 | 3 | 48 |
| Mid-terms | 1 | 20 | 20 |
| Assignment | 1 | 10 | 10 |
| Final examination | 1 | 25 | 25 |
| Toplam İş Yükü | 151 | ||
| Toplam İş Yükü / 25 (Saat) | 6,04 | ||
| Dersin AKTS Kredisi | 6 | ||