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 | 1. Semester | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Compulsory Departmental 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 | 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 | 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 | ||