ECTS - Operator Theory
Operator Theory (MATH658) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Operator Theory | MATH658 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Ph.D. |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Discussion, Question and Answer. |
| Course Lecturer(s) |
|
| Course Objectives | This is an introductory course in Operator Theory and its applications. We will start with a short review of Banach and Hilbert Spaces and their linear bounded operators, then we turn to the Spectral Theory of linear bounded operators. Classes of Hilbert Space operators that appear frequently in applications, e.g. self adjoint, positive operators, are considered in detail. The course is aimed at Mathematics students who want to pursue a career in Analysis and its applications, but Math students from other domains and also graduate engineering students who want to understand mathematical foundations of many of the subjects considered in Engineering Mathematics are welcome as well. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | This is an introductory course in Operator Theory and its applications. We will start with a short review of Banach and Hilbert Spaces and their linear bounded operators, then we turn to the Spectral Theory of linear bounded operators. Classes of Hilbert Space operators that appear frequently in applications, e.g. self adjoint, positive operators, are considered in detail. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | A Review of Normed and Banach Spaces | [1], 2.2, 2.6, 2.7 [2], 3.1 |
| 2 | Bounded operators on Normed Spaces | [1], 2.7 [2], 4.3 |
| 3 | A Review of Inner Product and Hilbert Spaces | [1], 3.1,3.3,3.4 [2], 2.2—2.5 |
| 4 | Hilbert Adjoint Operator | [1], 3.8,3.9 |
| 5 | Spectral Theory in Normed Spaces: Introduction | [1], 7.2 |
| 6 | Spectral Theory of Bounded Linear Operators | [1], 7.3 |
| 7 | Spectral Mapping Theorem | [1], 7.4 |
| 8 | Review and Midterm | |
| 9 | Spectral Theory of Bounded Self Adjoint Linear Operators | [1], 9.1 |
| 10 | Spectral Theory of Bounded Self Adjoint Linear Operators | [1], 9.2 |
| 11 | Positive Operators | [1], 9.3 |
| 12 | Square Roots of a Positive Operator | [1], 9.4 |
| 13 | Projection Operators | [1], 9.5 |
| 14 | Further Properties of Projections | [1], 9.6 |
| 15 | Further properties of Projections | [1], 9.6 |
| 16 | Review |
Sources
| Course Book | 1. E. Kreyszig, Introductory Functional Analysis with Applications, Wiley Clas. Lib. Ed, 1989. |
|---|---|
| 2. G. Chacón, H. Rafeiro, J. Vallejo, Functional Analysis, De Gruyter, 2017. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 3 | 30 |
| Presentation | 1 | 20 |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 1 | 20 |
| Final Exam/Final Jury | 1 | 30 |
| Toplam | 6 | 100 |
| Percentage of Semester Work | 70 |
|---|---|
| Percentage of Final Work | 30 |
| Total | 100 |
Course Category
| Core Courses | X |
|---|---|
| Major Area Courses | |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Is independently able to build a problem in the area of study, solve the problem by developing solution techniques and assess the solutions. | X | ||||
| 2 | Is capable of creating a groundwork in the fundamental branches of mathematics as well as in his/her research area | X | ||||
| 3 | follows the latest national and international literature in Mathematics and in his/her area of research; and uses them in his/her related studies | X | ||||
| 4 | observes and adopts the scientific ethical values in his/her professional and social life | X | ||||
| 5 | presents in Turkish and English in academic/scientific events the results of his/her research or the latest studies and findings on a special topic and participates in discussions | X | ||||
| 6 | Develops skills to work independently or as a member of a team | X | ||||
| 7 | Develops competences in the areas of creative and critical thinking, problem solving and producing original studies. Follows recent scientific studies, is capable of making an analysis, synthesis and assessment of the knowledge acquired | X | ||||
| 8 | Is open to lifelong improvement of his/her acquired knowledge, skills and competences. | X | ||||
| 9 | Is able to apply the acquired knowledge and problem-solving skills to interdisciplinary studies, proposes different solution methods to problems in terms of mathematical models and from a mathematical point of view | X | ||||
| 10 | Uses the mathematical based softwares, informatics and communication technologies for scientific purposes | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | 16 | 3 | 48 |
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 14 | 2 | 28 |
| Presentation/Seminar Prepration | 1 | 10 | 10 |
| Project | |||
| Report | |||
| Homework Assignments | 3 | 5 | 15 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 1 | 12 | 12 |
| Prepration of Final Exams/Final Jury | 1 | 12 | 12 |
| Total Workload | 125 | ||