Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
---|---|---|---|---|---|
Sequence Spaces and Matrıx Transformatıons I | MAT 601 | 0 | 3 + 0 | 3 | 6 |
Ön Koşul Dersleri | Linear Functional Analysis I-II |
Önerilen Seçmeli Dersler | |
Dersin Dili | Türkçe |
Dersin Seviyesi | Doktora |
Dersin Türü | Seçmeli |
Dersin Koordinatörü | Prof.Dr. METİN BAŞARIR |
Dersi Verenler | |
Dersin Yardımcıları | |
Dersin Kategorisi | Diğer |
Dersin Amacı | The understanding of Matrix transformations in sequence spaces, The learning of general summability theory, The understanding of classical summability methods |
Dersin İçeriği | Matrix Transformations in sequence spaces (Matrix and Linear Transformations, Matrix Algebras, Summability, Tauberian Theorems), General Summability Theory (Main Definitions and Concepts, Silverman-Toeplitz Theorem, Invertibility, Inclusion, Translativity), Classical Summability Methods (The Nörlund Mean, Hölder and Cesaro Mean, Euler, Taylor and Borel Transformations, Hausdorff Mean) |
# | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
---|---|---|---|
1 | He/she recognizes sequence spaces. | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, |
2 | He/she expresses matrix transformations between sequence spaces. | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, |
3 | He/she summarizes general summability theory. | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, |
4 | He/she explains and interprets classical summability methods. | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, |
5 | He/she expresses and proves Silverman-Toeplitz theorem. | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, |
6 | He/she interprets Tauberian theorems. | Lecture, Question-Answer, Discussion, Self Study, | Testing, Homework, |
Hafta | Ders Konuları | Ön Hazırlık |
---|---|---|
1 | Sequence Spaces | |
2 | Matrix and Linear Transformations | |
3 | Matrix Algebras, Summability | |
4 | Tauberian Theorems | |
5 | General Summability Theory | |
6 | Silverman-Toeplitz Theorem, Invertibility | |
7 | Inclusion, Translativity | |
8 | Adjoint Operator, Simetric Operator | |
9 | Mid-Term | |
10 | The Nörlund Mean | |
11 | Cayley Mean | |
12 | Hölder and Cesaro Mean | |
13 | Euler, Taylor and Borel Transformations | |
14 | Hausdorff Mean |
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 | |||
1 | At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. | X | |||||
1 | At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. | ||||||
2 | Student completes the missing or limited knowledge by using the scientific methods. | ||||||
2 | Student completes the missing or limited knowledge by using the scientific methods. | X | |||||
3 | Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. | X | |||||
3 | Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. | ||||||
4 | Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. | ||||||
4 | Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. | X | |||||
5 | Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. | X | |||||
5 | Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. | ||||||
6 | At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. | ||||||
6 | At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. | X | |||||
7 | Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. | X | |||||
7 | Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. | ||||||
8 | Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. | ||||||
8 | Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. | X | |||||
9 | Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. | X | |||||
9 | Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. | ||||||
10 | Student follows the necessary technological developments in his/her field, and s/he uses them. | ||||||
10 | Student follows the necessary technological developments in his/her field, and s/he uses them. | X | |||||
11 | Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. |
Değerlendirme Sistemi | |
---|---|
Yarıyıl Çalışmaları | Katkı Oranı |
1. Ara Sınav | 60 |
1. Ödev | 10 |
2. Ödev | 10 |
1. Kısa Sınav | 20 |
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 |