| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Introductıon To Banach Spaces | MAT 517 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | YUKSEK_LISANS |
| Dersin Türü | Seçmeli |
| Dersin Koordinatörü | Prof.Dr. MAHPEYKER ÖZTÜRK |
| Dersi Verenler | |
| Dersin Yardımcıları | |
| Dersin Kategorisi | Diğer |
| Dersin Amacı | Understanding the relation between normed space and topological space by using the fundamental functionel analysis knowledge.Understanding the Hahn-Banach Extension Theorem and having knowledge about compact transformations. |
| Dersin İçeriği | Preliminares, norms, properties of normed spaces, linear transformations between normed spaces, Baire Category Theorem, Hahn-Banach Extension Theorem, dual spaces, weak topologies, weak compactness,cusp points, linear transformations, conjugate transformations, compact transformations, Schauder basis, fixed points . |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | He/she proves the theorems by using the knowledge of functionel analysis. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
| 2 | He/she remembers the relation between normed spaces and topological spaces. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
| 3 | He/she gains the ability of understanding the relations between mormed spaces and topological spaces. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
| 4 | He/she learns the definition and proof of Hahn-Banach theorem. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
| 5 | He/she proves the theorems by using Hahn-Banach Extension Theorem. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
| 6 | He/she regognizes compact transformations. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | Preliminares | |
| 2 | Norms | |
| 3 | Properties of normed spaces | |
| 4 | Linear transformations between normed spaces | |
| 5 | Baire Category Theorem | |
| 6 | Hahn-Banach Extension Theorem | |
| 7 | Dual spaces | |
| 8 | Weak topologies | |
| 9 | Weak Compactness | |
| 10 | Cusp Points | |
| 11 | Linear transformations | |
| 12 | Conjugate transformations | |
| 13 | Compact transformations | |
| 14 | Schauder basis, fixed points |
| Kaynaklar | |
|---|---|
| Ders Notu | |
| Ders Kaynakları | 1-Robert E. Megginson, An Introduction to Banach space theory, Springer, 1998 |
| 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 | X | |||||
| 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. Ödev | 100 |
| Toplam | 100 |
| 1. Yıl İçinin Başarıya | 40 |
| 1. Final | 60 |
| 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 | 30 | 30 |
| Performance Task (Laboratory) | 1 | 30 | 30 |
| Toplam İş Yükü | 156 | ||
| Toplam İş Yükü / 25 (Saat) | 6,24 | ||
| Dersin AKTS Kredisi | 6 | ||