Beyond the mathematical tools it presents (algebraic structures, vector spaces, linear applications and matrices), this course trains students in the abstract manipulation, precision and rigorous reasoning that Computer Science requires. In particular, the emphasis is on the principles and mechanisms of proving results (theorems) deducible from the introduced tools, on understanding and on the mechanisms of reasoning.
This course introduces the basic concepts of algebra, such as algebraic structures, vector spaces, linear applications and matrices. It thus lays the foundations for the Algebra course (Part 2), which is more oriented towards algorithms and numerical methods (solving systems of linear equations and calculating the eigenvalues of a matrix, among others).
This course introduces in a first part the mathematical concepts of algebraic structure, vector space and linear application, to concretize them in a second part through matrices as a calculation tool.
Chapter 1: Algebraic Structures
Chapter 2: Vector spaces
Chapter 3: Linear applications
Chapter 4: Matrices
Exercise sessions are given for 1h30 per week.
Formula: Two exams per session: an oral exam (theory) and a written exam (exercises), offered in June and August. Both parts of the examination are closed-book. The oral exam consists of a demonstration question (from a list provided during the year), a definition and five targeted questions on the understanding of concepts seen in the course. Students have time to prepare for the demonstration and definition questions.
Method: The teaching unit (TU) consists of two learning activity assessments (LAAs) per session: one on the theory covered in the course, the other on exercises. The TU will be considered as passed if the average of the two marks obtained for each A.A. reaches at least 10/20 AND no A.A. evaluation 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.