| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Fixed Point Theory I İn Metric Spaces | MAT 527 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | YUKSEK_LISANS |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Doç.Dr. AYNUR ŞAHİN |
| Dersi Verenler | Doç.Dr. AYNUR ŞAHİN, |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Alanına Uygun Öğretim |
| Dersin Amacı | The understanding of fixed point theory in metric spaces, the knowing of hyperbolic metric spaces and non-positive metric spaces, the learning of normal structures in metric spaces and ultrametric spaces |
| Dersin İçeriği | Metric space, completeness, separability and connectedness, metric convexity and convexity structures, the basic fixed point theorems in metric space, metric spaces of non-positive curvature and their examples, some fixed point theorems in metric spaces of non-positive curvature, hyperbolic metric spaces and their properties, structure of the fixed point set in hyperbolic metric spaces, normal structures in metric space, stability and smoothness, ultrametric spaces and some fixed point results |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | He/She knows the concept of fixed point in metric spaces. | Drilland Practice, Self Study, Problem Solving, | Testing, Homework, Performance Task, |
| 2 | He/She recognizes metric spaces of non-positive curvature. | Problem Solving, Self Study, Drilland Practice, Question-Answer, Lecture, | Testing, Homework, Performance Task, |
| 3 | He/She learns hyperbolic metric spaces and their properties. | Problem Solving, Self Study, Drilland Practice, Question-Answer, Lecture, | Performance Task, Homework, Testing, |
| 4 | He/She knows the normal structures in metric spaces. | Problem Solving, Self Study, Drilland Practice, Question-Answer, Lecture, | Performance Task, Homework, Testing, |
| 5 | He/She learns the concept of ultra metric space. | Problem Solving, Self Study, Drilland Practice, Question-Answer, Lecture, | Performance Task, Homework, Testing, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Metric space and its examples | |
| 2 | Completeness, separability and connectedness | |
| 3 | Metric convexity and convexity structures | |
| 4 | The basic fixed point theorems in metric space | |
| 5 | Metric spaces of non-positive curvature and their examples | |
| 6 | Some fixed point theorems in metric spaces of non-positive curvature | |
| 7 | Hyperbolic metric spaces and their properties | |
| 8 | Midterm exam | |
| 9 | Structure of the fixed point set in hyperbolic metric spaces | |
| 10 | Normal structures in metric space | |
| 11 | Some fixed point theorems in normal structures | |
| 12 | Stability and smoothness | |
| 13 | Ultrametric spaces and their properties | |
| 14 | Some fixed point theorems in ultrametric spaces |
| Kaynaklar | |
|---|---|
| Ders Notu | |
| Ders Kaynakları | 1) K. Goebel, W.A. Kirk, Topics in Metric Fixed Point Theory, Cambridge University Press, 1990. 2) M.R. Bridson, A. Haefliger, Metric Spaces of Non-Positive Curvature, Springer, 1991. 3) M.A. Khamsi, W.A. Kirk, An Introduction to Metric Spaces and Fixed Point Theory, Pure and Applied Mathematics, A Wiley-Intersicence Series of Texts, Monographs and Tracks, 2001. |
| 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. | ||||||
| 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. | ||||||
| 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. | ||||||
| 11 | Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. | ||||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 50 |
| 1. Kısa Sınav | 20 |
| 1. Ödev | 15 |
| 2. Ödev | 15 |
| Toplam | 100 |
| 1. Final | 50 |
| 1. Yıl İçinin Başarıya | 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 |
| Mid-terms | 1 | 24 | 24 |
| Assignment | 2 | 8 | 16 |
| Final examination | 1 | 48 | 48 |
| Hours for off-the-classroom study (Pre-study, practice) | 14 | 1 | 14 |
| Toplam İş Yükü | 150 | ||
| Toplam İş Yükü / 25 (Saat) | 6 | ||
| Dersin AKTS Kredisi | 6 | ||