Linear Algebra I (MAT261) | GSÜ - ECTS Information Guide

Content

Objective

Teaching the fundaments of linear algebra

Course Content

Real numbers, Complex numbers, Vector spaces, Finite dimensional vector spaces, Basis, Dimension, Direct sum, Linear transformations, Matrices, Change of basis, Row and column spaces

Course Learning Outcomes

- To have enough knowledge about the linear algebra and to use efficiently this knowledge during the scholar period.
- To adapt and to participate to group workings
- To use abstract thinking.

Teaching and Learning Methods

Examens
Homeworks

References

Axler, Sheldon J, Linear Algebra Done Right.

Weekly Contents

Theory Topics
Week	Weekly Contents
1	Fields
2	Vector spaces-Subspaces
3	Basis-Dimension
4	Direct sum
5	Linear transformations-Image-Kernel
6	Matrix of Linear transformations-Matrices
7	Exam-Change of Basis
8	Inversibles matrices-Elementary matrices
9	System of Linear Equations
10	Subspaces of row and column- Rank-Theorems about ranks
11	Determinant
12	Cofactor and Cramer methods
13	Gauss method
14	Calcul of determinant

Assessment System

Contribution to Overall Grade
Activities	Number	Contribution
Contribution of in-term studies to overall grade	2	55
Contribution of final exam to overall grade	1	45
Total	3	100

In-Term Studies
Activities	Number	Contribution
Assignments	0	0
Presentation	0	0
Midterm Examinations (including preparation)	2	40
Project	0	0
Laboratory	0	0
Other Applications	1	15
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	1	45
Total	4	100

Relation of Proficiency

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	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	5	14	70
Working Hours out of Class	5	14	70
Assignments	3	3	9
Presentation	2	0	0
Midterm Examinations (including preparation)	3	2	6
Other Applications	2	1	2
Quiz	3	2	6
Total Workload			163
Total Workload / 25			6.52
Credits ECTS			7