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| MATH0201-1 | Algebra I
- part a) Introduction to Algebra
- part b) Algebra
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| Duration : | part a) Introduction to Algebra : 10h Th
part b) Algebra : 50h Th, 50h Pr
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| Credits/ECTS : |
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| Holder(s) : | part a) Introduction to Algebra : Michel Rigo
part b) Algebra : Michel Rigo
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| Language : | French language |
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| Course contents : |
 | | part a) Introduction to Algebra |
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| As an introduction to the course, we present the complex numbers and their main properties. We take this opportunity to recall the leading concepts of mathematical reasoning and mathematical proofs. |
| | part b) Algebra |
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| The main part of the course is dedicated to the study of finite dimensional linear algebra as well as polynomials. For the latter, we present the fundamental theorem of algebra, the ring of polynomials over an arbitrary field and the corresponding ideals. About linear algebra, we start with matrix computations and the theory of determinants. Next we study systems of linear equations. We carefully present and discuss the structure of the solutions of such systems. A chapter of the course introduces the algebraic structures of group, ring and field. More specifically, we present the ring of integers modulo p. Finally, an important part of the course presents vector spaces. In that context, we introduce linear operators, eigenvectors, eigenvalues, the problem of diagonalization, including the Jordan normal form decomposition but also normal, hermitian and unitary transformations. |
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| Course objective : |
| | part b) Algebra |
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| Linear algebra is a fundamental tool useful in almost every part of mathematics but also in many applications. The aim of this course is to present basic results on matrices and finite dimensional linear algebra. |
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| Prerequisites : |
| | part b) Algebra |
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| Perfect knowledge from secondary school is expected. Being trained to abstraction and mathematical reasoning is an advantage. The beginning of this course is dedicated to train these capabilities. |
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| Workshops : |
| | part b) Algebra |
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| The practical sessions are mainly dedicated to solve exercises corresponding to the theory considered during the lecture sessions. These sessions are also useful to obtain extra informations or enlightenments on the concepts presented during the lecture sessions.
During those sessions, the class is divided into smaller groups. The schedule will be communicated on the first day of the academic year.
Moreover, the preparation of lists of exercices for the next practical session will be systematically asked (this will be taken into account as personal work). |
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| Organization : |
| | part b) Algebra |
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| The theoretical lectures are given three hours a week. The schedule will be communicated on the first day of the academic year. For the practical sessions, a detailed schedule will be given later. |
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| Written notes : |
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| Assessment : |
| | part b) Algebra |
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| Students are tested all along the year. These tests are aimed to encourage regular work and study and to help students to auto-evaluate themselves. High marks to those tests will be taken into account for the final examination. Bad results to those tests are not taken into account but constitute a serious reminder.
A recapitulative interrogation (written examination) is organized during January. A student succeeding in this test will be exempted of the corresponding subjects for the final examination (in June). The expected knowledge needed for this interrogation will be officially announced during the year (usually in December).
The final examination consists of two parts: a written one and an oral one. The written part is devoted to the resolution of problems and exercises. The oral part is devoted to the theory (mainly proofs of theorems) but also includes direct applications of the theory. Once again, the expected knowledge needed for this examination will be officially announced during the year (usually in April). |
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| Contacts : |
| | part b) Algebra |
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| M. Rigo
Institut de Mathématique (B37) -
Grande Traverse 12 -
Sart Tilman, 4000 Liège
Tél. : (04) 366.94.87 -
E-mail : M.Rigo@ulg.ac.be |
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| Remarks : |
| | part b) Algebra |
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| Some useful informations are given on http://www.discmath.ulg.ac.be/ |
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