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 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction. | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and 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 | ||