Course Name: Algebra 2
General Information:
- Specialization: 1st Year ST ING and ST LMD
- Semester: 2
- Weighting: 2
- Credits: 4
Objectives:
To enable students to understand and apply the fundamental concepts of linear algebra (linear maps, kernel, image, matrices, determinants) in order to solve computational problems and carry out algebraic manipulations.
Targeted Competencies:
- Identify and analyze linear maps between vector spaces.
- Determine the kernel, image, and rank of a linear map.
- Perform matrix operations and solve matrix-related problems.
- Compute determinants and inverses of square matrices.
- Apply linear algebra concepts to solve systems of linear equations and other mathematical problems.
Prerequisites:
- Basic knowledge of vector spaces.
- Operations on vectors (addition and scalar multiplication).
- Basis and dimension of vector spaces.
- Elementary systems of linear equations.
Hourly Volume:
- Lecture: 1 hour 30 minutes
- Tutorial: 1 hour 30 minutes
Approximate Number of Weeks: 15 weeks
Course Outline:
Chapter I: Linear Maps
- Basic Concepts
- Endomorphisms, Isomorphisms, and Automorphisms
- Kernel, Image and Rank of a Linear Map
- Rank–Nullity Theorem
Chapter II: Matrices
- Matrix Operations
- Determinants
- Matrix Inversion
Please watch the introductory video before starting the course.
Video link:
- Enseignant: s.djazia Djazia Saadi