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| MATH0013-1 | Algebra
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| Duration : | 30h Th, 20h Pr |
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| Number of credits : |
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| Lecturer : | Eric Delhez |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the first semester, review in January |
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Course contents :
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| 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 :
- Matrix algebra : determinant, inverse matrix, normal, hermitian, unitary matrices...
- Linear algebra : linear application, rank, basis, linear independence, linear systems, eigenvalues, eigenvectors, quadratic forms,...
- Discrete mathematics : mathematical induction, congruence, difference equations, counting, graph theory...
Each of these topics is introduced through applications showing how the corresponding tools can be used to tackle practical problems, while keeping a rigorous theoretical presentation of the concepts. |
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Learning outcomes of the course :
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| 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 discrete mathematics 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. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| Algebra of real and complex numbers |
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Planned learning activities and teaching methods :
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| The course includes both ex-cathedra lectures (30 h) and exercise sessions (20 h).
- 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.
These two activities are complementary and form a coherent approach of the subject. Mastering the techniques used to solve the exercise requires a good knowledge of the underlying theory. Conversely, the illustrations developed during the exercise sessions help to understand the abstract concepts.
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.
- Question and answer sessions are planned at various key moments of the academic year. These provide good opportunities to meet the professor and assistants and ask them all possible questions about both theoretical and practical aspects.
- 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.
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Mode of delivery (face-to-face ; distance-learning) :
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| Face-to-face |
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Recommended or required readings :
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| Algèbre, E.J.M. DELHEZ (2 volumes in french). Lecture notes distributed by the AEES and including all the theory and exercices. |
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Assessment methods and criteria :
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| Evaluation happens through a single written exam in January. The test is based on all the theory presented and the corresponding exercises.
At the exam, candidates are never asked to reproduce full demonstrations. The theoretical results and hypothesis of the main theorems must however be known. All the theoretical concepts must also 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 and to elaborate short abstract reasonings similar to those developed during the lectures.
Students can use the official notes of Discrete Mathematics (volume 2) during the tests.
Retake
First year students who are unhappy with their mark 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. |
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Work placement(s) :
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Organizational remarks :
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| 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 the full group of students. In order to promote a better interaction, the group is then split into smaller groups for the exercise sessions.
The detailed schedule and organization details are available at http://www.mmm.ulg.ac.be/. |
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Contacts :
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| Eric J.M. DELHEZ
Institut de Mathématique, B37
Tél. 04/366.94.19
E.Delhez@ulg.ac.be
List of assistants and their contact details available at http://www.mmm.ulg.ac.be. |
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| Items online : |
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| Syllabus |
| Lecture notes (in French). |
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