COURSE INFORMATION PACKAGE · MAT262
Linear Algebra II
Compulsory · French Open to Erasmus+ exchange students
On this page
Content Weekly Contents Assessment System Relation of Proficiency ECTS
Course Instructor(s)
Oğuzhan KAYA
oguzabel@gmail.com
oguzabel@gmail.com
Content
Objective
Get to grips with basis Linear Algebra.
Course 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.
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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.
Weekly Contents
| 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 |
| 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 |
Assessment System
| Activities | Number | Contribution |
|---|---|---|
| Contribution of in-term studies to overall grade | 2 | 50 |
| Contribution of final exam to overall grade | 1 | 50 |
| Total | 3 | 100 |
| Activities | 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 |
| Total | 2 | 50 |
Relation of Proficiency
| 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 | ||||
ECTS
| 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 | ||