Course Name Code Semester T+U Hours Credit ECTS
Sequence Spaces and Matrix Transformations I MAT 601 0 3 + 0 3 6
Precondition Courses Linear Functional Analysis I-II
Recommended Optional Courses
Course Language Turkish
Course Level Doctorate Degree
Course Type Optional
Course Coordinator Prof.Dr. METİN BAŞARIR
Course Lecturers
Course Assistants
Course Category
Course Objective The understanding of Matrix transformations in sequence spaces, The learning of general summability theory, The understanding of classical summability methods
Course Content 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)
# Course Learning Outcomes Teaching Methods Assessment Methods
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,
Week Course Topics Preliminary Preparation
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
Resources
Course Notes [1] Musayev, Binali; Fonksiyonel Analiz, Balcı Yayınları, 2000, İstanbul
Course Resources [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.
Order Program Outcomes Level of Contribution
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.
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 60
1. Ödev 10
2. Ödev 10
1. Kısa Sınav 20
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
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
Total Workload 161
Total Workload / 25 (Hours) 6.44
dersAKTSKredisi 6