Linear Algebra II(MAT262)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| MAT262 | Linear Algebra II | 4 | 4 | 0 | 0 | 4 | 7 |
| Prerequisites | |
| Admission Requirements |
| Language of Instruction | French |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | Ayşegül ULUS aulus@gsu.edu.tr (Email) |
| Assistant | |
| Objective | Get to grips with basis Linear Algebra. |
| Content | Reminder: Determinant, Dual basis, Dual space, Annulators. Reduction of linear operators (Eigenvalues, Eigenvectors, Diagonalization, Endomorphism Polynomials, Triangulation, Jordan Forms) |
| Course Learning Outcomes |
To understand the structure of linear operators. To be able to recognize diagonalizable and triangulated linear operators or matrices. To be able to decompose a finite-dimensional vector space using linear operators. Different definitions of Determinant and Trace. ? |
| Teaching and Learning Methods | Lecture and exercises. |
| References |
Linear Algebra Right Done, S. Axler Algebre Linéaire, Joseph Grifone, Algèbre linéaire et bilinéaire, F. Cottet Emard, de Boeck, 2007. |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Introduction of course. Recall: Determinant. Motivation Exercices |
| 2 | Dual Spaces |
| 3 | Annulators |
| 4 | Eigenvalues, Eigenvecteurs, Diagonalisation |
| 5 | Complex Operators |
| 6 | Generalized Eigenvectors |
| 7 | Revision |
| 8 | Midterm Exam |
| 9 | Polynomial of endomorphisms |
| 10 | Polynomial of endomorphisms |
| 11 | Trigonalisation |
| 12 | Trigonalisation |
| 13 | Jordan decomposition |
| 14 | Determinant and Trace: New Definitions |
Practice Topics
| Week | Weekly Contents |
|---|---|
| 1 | Exercices |
| 2 | Exercices |
| 3 | Exercices |
| 4 | Exercices |
| 5 | Exercices |
| 6 | Exercices |
| 7 | Exercices |
| 8 | Exam |
| 9 | Exercices |
| 10 | Exercices |
| 11 | Exercices |
| 12 | Exercices |
| 13 | Exercices |
| 14 | Exercices |
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 2 | 50 |
| Contribution of final exam to overall grade | 1 | 50 |
| Toplam | 3 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 1 | 25 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 25 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 0 | 0 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Make-up | 0 | 0 |
| Toplam | 2 | 50 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways; | X | ||||
| 2 | can properly state and use concepts and results of major mathematical interest; | X | ||||
| 3 | masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools; | X | ||||
| 4 | is able to express one’s mathematical ideas in an organised way both in written and oral forms; | X | ||||
| 5 | understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...); | X | ||||
| 6 | has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems; | X | ||||
| 7 | has a theoretical and practical knowledge in computer science well adapted for learning a programming language; | X | ||||
| 8 | has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions; | X | ||||
| 9 | has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement; | X | ||||
| 10 | masters French language as well as other foreign languages, to a level sufficient to study or work abroad. | X | ||||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 4 | 56 |
| Working Hours out of Class | 14 | 4 | 56 |
| Assignments | 2 | 4 | 8 |
| Presentation | 2 | 1 | 2 |
| Midterm Examinations (including preparation) | 2 | 6 | 12 |
| Project | 1 | 20 | 20 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 0 | 0 | 0 |
| Final Examinations (including preparation) | 1 | 7 | 7 |
| Quiz | 0 | 0 | 0 |
| Term Paper/ Project | 0 | 0 | 0 |
| Portfolio Study | 0 | 0 | 0 |
| Reports | 0 | 0 | 0 |
| Learning Diary | 0 | 0 | 0 |
| Thesis/ Project | 0 | 0 | 0 |
| Seminar | 0 | 0 | 0 |
| Other | 0 | 0 | 0 |
| Total Workload | 161 | ||
| Total Workload / 25 | 6,44 | ||
| Credits ECTS | 6 | ||