| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Topologıcal Vector Spaces-II | MAT 508 | 0 | 3 + 0 | 3 | 6 |
| Ön Koşul Dersleri | Topological Vector Spaces-I |
| 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 | Alanına Uygun Temel Öğretim |
| Dersin Amacı | To apprehend the properties of linear transformations,to learn the concept of dual, general open mapping and closed graph theorems, tensor products and nuclear spaces,absolute summability, weak compactness,to understand the Eberlein and Krein theorems. |
| Dersin İçeriği | Linear transformations(continuous linear transformations and topological homomorphism,Banach Homomorphism Theorem,Linear transformation spaces,equcontinuity,the principle of uniform boundedness and Banach-Steinhaus theorem,Bilinear transformations,topological tensor products,nuclear transformations and spaces,examples,approximation,compact transformations).The concept of dual(dual systems and weak topologies, the fundamental properties of adjoint transformations,the compatible local convex topologies with a given dual,Mackey-Arens theorem,Projective duals and reduction topologies,The strong dual of local convex spaces,bidual,reflexive spaces,the dual characterization of completeness,metrizable spaces,the adjoint of the closed linear transformations,general open mapping and closed graph theorems,tensor products and nuclear spaces,absolute summability,weak compactness,Eberlein and Krein theorems |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 1 | He/she recognizes the continuous linear transformations and topological homomorphism, Banach Homomorphism Theorem, Space of linear transformations and the concept of equcontinuity. | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, |
| 2 | He/she expresses and proves the principle of uniform boundedness and Banach-Steinhaus theorem, | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, |
| 3 | He/she explains Bilinear transformations,topological tensor products, nuclear transformations and spaces,examples,approximation problem and compact transformations. | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, |
| 4 | He/she expresses the Dual systems and weak topologies, main properties of adjoint transformations | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, |
| 5 | He/she expresses the General open mapping and closed graph theorems. | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, |
| 6 | He/she interprets the Tensor products and nuclear spaces. | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, |
| 7 | He/she interprets the absolute summability,weak compactness,Eberlein and Krein theorems. | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 1 | continuous linear transformations and topological homomorphism | |
| 2 | Banach Homomorphism Theorem,Linear transformation spaces | |
| 3 | equcontinuity,the principle of uniform boundedness and Banach-Steinhaus theorem, | |
| 4 | Bilinear transformations | |
| 5 | topological tensor products,nuclear transformations and spaces | |
| 6 | approximation,compact transformations | |
| 7 | dual systems and weak topologies | |
| 8 | the fundamental properties of adjoint transformations,the compatible local convex topologies with a given dual | |
| 9 | intermediate examination | |
| 10 | Mackey-Arens theorem,Projective duals , reduction topologies | |
| 11 | The strong dual of local convex spaces,bidual,reflexive spaces,the dual characterization of completeness, | |
| 12 | general open mapping and closed graph theorems | |
| 13 | tensor products and nuclear spaces, | |
| 14 | weak compactness,Eberlein and Krein theorems |
| Kaynaklar | |
|---|---|
| Ders Notu | [1] Musayev, Binali; Fonksiyonel Analiz, Balcı Yayınları, 2000, İstanbul |
| Ders Kaynakları | [2] Maddox,I.J.; Elements of Functional Analysis, Cambridge Un.Press,1970,London. [3] Şuhubi, Erdoğan; Fonksiyonel Analiz, İTÜ Vakfı, 2001, İstanbul [4] Naylor, Arch; Linear Operator Theory in Engineering and Science, Springer-Verlag, 1982. |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 2 | Student follows the current journals in his/her field and puts forward problems. | 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 | |||||
| 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 | |||||
| 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 | |||||
| 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 | |||||
| 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 | |||||
| 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 | |||||
| 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 | |||||
| 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 | |||||
| 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 | 80 |
| 1. Ödev | 10 |
| 2. Ödev | 10 |
| 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 | 2 | 10 | 20 |
| Final examination | 1 | 25 | 25 |
| Toplam İş Yükü | 161 | ||
| Toplam İş Yükü / 25 (Saat) | 6,44 | ||
| Dersin AKTS Kredisi | 6 | ||