ECTS - Linear Algebra II
Linear Algebra II (MATH232) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Linear Algebra II | MATH232 | 4. Semester | 4 | 0 | 0 | 4 | 7 |
| Pre-requisite Course(s) |
|---|
| MATH231 |
| Course Language | English |
|---|---|
| Course Type | Compulsory Departmental Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | |
| Learning and Teaching Strategies | Lecture, Question and Answer, Drill and Practice. |
| Course Lecturer(s) |
|
| Course Objectives | Being a continuation of Math 231, the aim is to introduce the students to the very heart of the subject including topics such as inner product spaces and linear mappings on them, canonical (diagonal, triangular, Jordan, and rational) matrix forms of linear mappings, bilinear and quadratic forms. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Eigenvalues and eigenvectors, elementary canonical forms, the rational and Jordan forms, inner product spaces, operators on Inner product spaces, bilinear forms. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Division in a Polynomial Ring, Prime Factorization, Factorization of Polynomials over C and R | pp. 1-17 |
| 2 | Ideals, Matrices over Polynomials, Characteristic Polynomial and Minimal Polynomial | pp. 18-40 |
| 3 | Eigenvalues and Eigenvectors, Diagonalization. | pp. 41-52 |
| 4 | Normal Form of Polynomial Matrices, Equivalence of Characteristic Matrices and Similarity | pp. 66-81 |
| 5 | Rational and Jordan Canonical forms | pp. 82-102 |
| 6 | Normal Matrices, Real Symmetric Matrices | pp. 104-118 |
| 7 | Hermitian Matrices, Positive Matrices, Standard Inner Products | pp. 119-132, 137-141 |
| 8 | Unitary and Orthogonal Matrices, Reduction of Quadratic Forms, Orthogonal Similarity | pp. 142-160 |
| 9 | Inner products, Norm and Orthogonality | pp. 162-178 |
| 10 | Matrix Forms of Inner Products, Orthogonal and Orthonormal Basis, Orthogonal Projections | pp. 179-192 |
| 11 | The Gram-Schmidt Orthogonalization process | pp. 193-194 |
| 12 | Linear Operators and Their Adjoints on Inner Product Spaces, Normal Operators, Unitary Operators, Orthogonal Operators. | pp. 203-211 |
| 13 | Linear Functionals on Inner Product Spaces | pp. 212-220 |
| 14 | Bilinear Forms | |
| 15 | General Review | |
| 16 | Final Exam |
Sources
| Course Book | 1. Topics in Linear Algebra, Cemal Koç, Doğuş University, Ankara, 2010 |
|---|---|
| Other Sources | 2. T. S. Blyth and E. F. Robertson, Further Linear Algebra, Springer-Verlag, London, 2002. |
| 3. K. Hoffman and R. Kunze, Linear Algebra, 2nd Edition, Prentice-Hall, New Jersey, 1971. | |
| 4. T.S. Blyth and E.F. Robertson, Basic Linear Algebra, 2nd Edition, Springer-Verlag, London, 2002. | |
| 5. B. Kolman and D. R. Hill, Elementary Linear Algebra, 9th Edition, Prentice-Hall, New Jersey, 2008. |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 5 | 10 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 55 |
| Final Exam/Final Jury | 1 | 35 |
| Toplam | 8 | 100 |
| Percentage of Semester Work | 65 |
|---|---|
| Percentage of Final Work | 35 |
| 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 | Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area | X | ||||
| 2 | Can apply gained knowledge and problem solving abilities in inter-disciplinary research | X | ||||
| 3 | Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary | X | ||||
| 4 | Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study | X | ||||
| 5 | Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework | X | ||||
| 6 | Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility | X | ||||
| 7 | Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation | X | ||||
| 8 | To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) | X | ||||
| 9 | Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge | X | ||||
| 10 | Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. | X | ||||
| 11 | Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | |||
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | |||
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 14 | 28 |
| Prepration of Final Exams/Final Jury | |||
| Total Workload | 28 | ||