| Course Name | Code | Semester | T+U Hours | Credit | ECTS |
|---|---|---|---|---|---|
| Lineer Functional Analysis I | MAT 501 | 0 | 3 + 0 | 3 | 6 |
| Precondition Courses | Funcional Analysis I-II |
| Recommended Optional Courses | |
| Course Language | Turkish |
| Course Level | yuksek_lisans |
| Course Type | Optional |
| Course Coordinator | Doç.Dr. SELMA ALTUNDAĞ |
| Course Lecturers | Doç.Dr. SELMA ALTUNDAĞ, |
| Course Assistants | |
| Course Category | |
| Course Objective | Metric and Topological Spaces, Linear spaces and Linear metric spaces, The understanding of normed linear spaces, Convergence and completeness in these spaces, linear operators and functionals, Banach Steinhauss Theorem, Open mapping and Closed graph theorems, Hahn-Banach extension theorem,weak convergence |
| Course Content | Metric and Topological Spaces (Metric and semi metric spaces, complete metric spaces, some concepts of metric and topological, continuous functions on metric and Topological Spaces,compact sets, category and uniform boundedness), Linear and linear metric spaces (Linear spaces, subspaces, dimensionality, factorspaces, convex spaces, linear metric spaces, paranorms ,seminorms and norms, basis, distributions), normed linear spaces (convergence and completeness, linear operators and functionals, Banach Steinhauss Theorem, Open mapping and Closed graph theorems, weak convergence) |
| # | Course Learning Outcomes | Teaching Methods | Assessment Methods |
|---|---|---|---|
| 1 | He/she distinguishes the difference between Metric and Topological Spaces. | Lecture, Question-Answer, Discussion, Simulation, Self Study, | Testing, Homework, |
| 2 | He/she describes Linear spaces and Linear metric spaces. | Lecture, Question-Answer, Discussion, Simulation, Self Study, | Testing, Homework, |
| 3 | He/she illustrates normed linear spaces. | Lecture, Question-Answer, Discussion, Simulation, Self Study, | Testing, Homework, |
| 4 | He/she explains the interpretation of linear operators and functionals. | Lecture, Question-Answer, Discussion, Simulation, Self Study, | Testing, Homework, |
| 5 | He/she expresses Banach Steinhauss Theorem, Open mapping and Closed graph theorem, Hahn-Banach extension theorems. | Lecture, Question-Answer, Discussion, Simulation, Self Study, | Testing, Homework, |
| 6 | He/she compares the concept of weak convergence and strong convergence. | Lecture, Question-Answer, Discussion, Simulation, Self Study, | Testing, Homework, |
| Week | Course Topics | Preliminary Preparation |
|---|---|---|
| 1 | Basic concepts in metric and topological spaces | |
| 2 | Metric and semi Metric spaces, complete metric spaces, some concepts of metric and topological | |
| 3 | Continuous functions on Topological Spaces, compact sets | |
| 4 | Category and uniform boundedness | |
| 5 | Linear spaces, subspaces, dimensionality | |
| 6 | Factor spaces, convex sets | |
| 7 | Linear metric spaces | |
| 8 | Paranorms ,seminorms and norms, basis, distributions | |
| 9 | Mid-term | |
| 10 | Normed linear spaces | |
| 11 | Convergence and completeness | |
| 12 | Banach Steinhauss Theorem, Open mapping and Closed graph theorems | |
| 13 | Hahn-Banach extension theorem | |
| 14 | Weak convergence |
| 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 | |||
| 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. | ||||||
| 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 | |||||
| Evaluation System | |
|---|---|
| Semester Studies | Contribution Rate |
| 1. Ara Sınav | 70 |
| 1. Ödev | 30 |
| 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 | ||