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Abd Alhafid Boussouf Boussouf Mila University Center
Institute of
Mathematics and Computer Science
Date: January 31, 2025
Semester: 2
General Course Information
· Teaching Unit: Fundamental
· Course Title: Algebra 2
· Field/Program/Specialization: Computer Science
· Academic Year: 2024/2025
· Credits: 4
· Coefficient: 2
· Name: Mohamed Kecies
· Email: m.kecies@centre-univ-mila.dz
Learning Objectives: Establish foundational principles of vector spaces.
Recommended Prerequisite Knowledge: Basic notions of algebra.
Chapter 1: Vector Spaces
- Definition of a vector space.
- Subspaces and examples.
- Linearly Independent and Dependent Families, and Spanning Families,
- Properties of finite-dimensional vector spaces.
- Complementary subspaces.
Chapter 2: Linear Mappings
- Definition of a linear mapping.
- Image and kernel of a linear mapping.
- Rank of a linear mapping and the rank theorem.
- Composition of linear mappings.
- Inverse of a bijective linear mapping and the notion of automorphism.
Chapter 3: Matrices
- Matrix associated with a linear mapping.
- Operations on matrices: sum, product, transposition.
- Vector space of matrices with m rows and n columns.
- Ring of square matrices.
- Determinant of a square matrix and its properties.
- Invertible matrices.
- Rank of a matrix and associated mapping.
- Rank invariance under transposition.
Chapter 4: Solving Systems of Linear Equations
- Systems of linear equations and their matrix representation.
- Rank of a system of equations.
- Cramer's method.
Assessment Method:
Weighting of Continuous Assessment and Final
Exam :
|
|
Pondération |
|
Final Exam |
60% |
|
Continuous Assessment |
40% |
|
Attendance and participation |
8=3+3+2 |
|
Quizzes (number): |
12 (1) |
|
Practical Work (number): |
/ |
|
Presentations: |
/ |
|
Reports: |
/ |
|
Internship reports: |
/ |
|
Field trip reports: |
/ |
|
Other 1/ ………………………………………………. |
/ |
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Other 2: ………………………………………………. |
/ |
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Other 3 : ………………………………………………. |
/ |
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Total |
20 |
|
Total |
1 (100% |
Bibliographic References:
Books, Course Notes, Online Resources :
- Algèbre linéaire et bilinéaire, cours et exercices corrigés 510-516
- Introduction a l'algèbre linéaire 510-552
- Toute l’algèbre de la licence, cours et exercices corrigés 510-332
- Algèbre exercices et problèmes 510-420
- Algèbre linéaire, cours et exercices corrigés, mathématiques à l’université 510-24
- Algèbre linéaire -cours et exercices corrigés- 510-1065