This course is a continuation of the Algebra course (part 1) of the first bachelor block in Computer Science. It uses the concepts seen in this first part (algebraic structures, vector spaces, linear applications and matrices). This second year course studies determinants, systems of linear equations, the eigenvalue problem, norm vector spaces and quadratic forms.
This second year course studies determinants, systems of linear equations, the eigenvalue problem, normed vector spaces and quadratic forms. While being more oriented towards algorithms and numerical methods, this course aims to train students in the rigorous reasoning and precision required in Computer Science. It also prepares students for the operational mathematics courses in the master programme.
This course introduces determinants and studies the solution of systems of linear equations, the eigenvalue problem, normed vector spaces (including the least squares problem) and quadratic forms.
Chapter 1: Determinants
Chapter 2: Systems of linear equations
Chapter 3: Eigenvalues and eigenvectors
Chapter 4: Normed vector spaces
Chapter 5: Quadratic Forms
Exercise sessions are given for 2h00 per week.
Formula: Two exams per session: an oral exam (theory) and a written exam (exercises), offered in January and August. The oral exam includes a demonstration question (from a list provided during the year), for which the student is given a copy of the syllabus by the teacher, and a knowledge question, prepared in closed-book format.
Modality: The teaching unit (TU) includes two learning activity assessments (LAA) per session: one on the theory covered in the course, the other on exercises. The TU will be considered as passed if the arithmetic average of the two marks obtained for each A.A. reaches at least 10/20 AND no A.A. assessment has a mark lower than 7/20. If the assessment of one of the A.A.'s has a mark lower than 7/20, the maximum mark awarded for the TU will be 9/20. During the same academic year, the student is exempted from repeating the assessment of one of the two A.A. if it is passed (10/20) and provided that he/she presented both parts the first time.
Course syllabus and slides, completed during the class and made available after the class on WebCampus.
| Training | Study programme | Block | Credits | Mandatory |
|---|---|---|---|---|
| Bachelor in Computer Science | Standard | 0 | 6 | |
| Bachelor in Computer Science | Standard | 2 | 6 |