ECTS - Advanced Linear Algebra
Advanced Linear Algebra (MATH622) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Advanced Linear Algebra | MATH622 | 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, Problem Solving. |
| Course Lecturer(s) |
|
| Course Objectives | This course is designed to introduce the fundamental concepts of advanced linear algebra. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Basic linear algebra, linear transformations, the structure of a linear operator, eigenvalues and eigenvectors, real and complex inner product spaces, structure theory for normal operators, metric vector spaces: the theory of bilinear forms, Hilbert spaces, tensor products, operator factorizations: QR and singular values. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Basic Linear Algebra | pp. 31-49 |
| 2 | Linear Transformations | pp. 55-71 |
| 3 | The Structure of a Linear Operator | pp. 141-151 |
| 4 | Eigenvalues and Eigenvectors | pp. 153-160 |
| 5 | Eigenvalues and Eigenvectors | pp. 161-174 |
| 6 | Real and Complex Inner Product Spaces | pp. 181-195 |
| 7 | Structure Theory for Normal Operators | pp. 201-215 |
| 8 | Structure Theory for Normal Operators | pp. 216-232 |
| 9 | Metric Vector Spaces: The Theory of Bilinear Forms | pp. 239-257 |
| 10 | Hilbert Spaces | pp. 307-318 |
| 11 | Hilbert Spaces | pp. 319-331 |
| 12 | Tensor Products | pp. 337-363 |
| 13 | Tensor Products | pp. 366-374 |
| 14 | Operator Factorizations: QR and Singular Values | pp. 425-434 |
| 15 | Review | |
| 16 | Review and Final Exam |
Sources
| Course Book | 1. Advanced Linear Algebra, Steven Roman, 2nd Edition, Springer, 2005 |
|---|---|
| 2. Matrices: Theory and Applications, Denis Serre, Springer, 2002 | |
| 3. A Guide to Advanced Linear Algebra, Steven H. Weintraub, Dolciani Mathematical Expositions, 2011 |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 4 | 20 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 1 | 40 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 6 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| 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 | Ability to carry out advanced research activities, both individual and as a member of a team | |||||
| 2 | Ability to evaluate research topics and comment with scientific reasoning | |||||
| 3 | Ability to initiate and create new methodologies, implement them on novel research areas and topics | |||||
| 4 | Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions | |||||
| 5 | Ability to apply scientific philosophy on analysis, modelling and design of engineering systems | |||||
| 6 | Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level | |||||
| 7 | Contribute scientific and technological advancements on engineering domain of his/her interest area | |||||
| 8 | Contribute industrial and scientific advancements to improve the society through research activities | |||||
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 | 3 | 42 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 4 | 3 | 12 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 1 | 10 | 10 |
| Prepration of Final Exams/Final Jury | 1 | 13 | 13 |
| Total Workload | 125 | ||