Duration
26h Th, 26h Pr
Number of credits
| Bachelor of Science (BSc) in Architectural Engineering | 4 crédits | |||
| Bachelor of Science (BSc) in Engineering | 4 crédits |
Lecturer
Language(s) of instruction
French language
Organisation and examination
Teaching in the first semester, review in January
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
The course provides an introduction to the main concepts and tools of linear algebra and discrete mathematics for the engineering science.
The following subjects are covered:
- Complex numbers.
- Matrix algebra, determinant, inverse matrix, normal, hermitian, unitary matrices, block matrices, ...
- Linear algebra : abstract vector space, geomatrical vectors, linear application, rank, basis, linear independence.
- Linear problems : system of linear equations
- Eigenvalues, eigenvectors, change of basis.
- Singular value decomposition
- Quadratic forms.
Learning outcomes of the learning unit
At the end of the course, the student will master the basic theoretical concepts of linear algebra and matrix algebra and will be able to use the corresponding tools in both abstract mathematical contexts and in simple applications taken from the engineering world.
He will be capable of using the mathematical language of linear algebra and matrix algebra to formulate, analyze and solve simple original problems.
The student will also be capable of following and understanding abstract reasonings (demonstrations), reproducing them in a structured way, giving proper rigorous justifications of the different logical steps and producing original abstract reasonings closely resembling those presented to him.
This course contributes to the learning outcomes I.1, II.1, III.1, III.2 of the BSc in engineering.
Prerequisite knowledge and skills
Algebra of real and complex numbers
Planned learning activities and teaching methods
The course includes both ex-cathedra lectures and exercise sessions.
- The new concepts are introduced during the lectures with references to practical or theoretical issues. The main theoretical results are then derived and are used to introduce and justify the tools that are used.
- During the exercise sessions, the focus is on the development of the technical skills of the students, first in a pure mathematical context, then in simple academic problems. In the same time, the theoretical concepts are illustrated and clarified.
In order to benefit from the various learning activities, the students will work regularly in order to keep abreast. The introduction of concepts and derivation of new theoretical results occurs through a gradual approach in which the different elements are presented sequentially and rely on each other. Attending a session requires the understanding of the concepts introduced at the previous sessions.
Volontary learning activites are organized during the semester.
- A forum is open on e-Campus to ease the interaction between the students and the instructors. Questions can be asked at any time about both the theoretical aspects and the applications. Students are strongly encouraged to contribute answers to the questions raised by their classmates.
- Formative assessments are proposed at the end of each of the main chapters. The questions are similar to those of real exams. Through these assessments, the students can better understand the level of understanding that they are expected to reach. Participation is voluntary. The marks are never taken into account in the final evaluation.
Mode of delivery (face to face, distance learning, hybrid learning)
Face-to-face course
Additional information:
Lectures notes and exercices sessions are face to face but podcasts are available at http://www.mmm.uliege.be.
Course materials and recommended or required readings
Algèbre, E.J.M. DELHEZ (in French). Lecture notes distributed by the CdC (Centrale des Cours FSA) including all the theory and exercices.
Exam(s) in session
Any session
- In-person
written exam ( open-ended questions )
Additional information:
Evaluation happens through a single written exam in January. The test is based on all the theory presented and the corresponding exercises.
All the theoretical concepts must be fully understood and mastered. Candidates must be able to solve problems using the exposed mathematical concepts and techniques, to provide theoretical justifications for the methods that they use, to provide clear and comprensive definitions of the concepts. At the exam, candidates are never asked to reproduce long demonstrations. However, the theoretical results and hypothesis of the main theorems must be known and students must be able to elaborate abstract reasonings similar to those developed during the lectures.
Retake
Bloc 1 students who did not pass the January exam can retake the exam in May/June.
Also, students who are not awarded the credits for the course can retake the exam in August/September.
Retakes are organized as written tests and are similar to the January exam.
Students who wants to retake an exam must register though the web interface MyULg in due time. When retaking a exam, the new mark, either better or worse than the initial mark, becomes the official mark taken into account by the jury.
Work placement(s)
Organisational remarks and main changes to the course
The course takes place during the first quadrimester at the rate of one half day per week.
Ex-cathedra lectures are given in front of a large group of students. In order to promote a better interaction, the group is then split into smaller groups for the exercise sessions.
Contacts
Eric J.M. DELHEZ
Institut de Mathématique, B37
Tél. 04/366.94.19
E.Delhez@uliege.be
List of assistants and their contact details available at http://www.mmm.uliege.be.
Association of one or more MOOCs
Items online
Lecture notes
Theory and applications