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| MATH0215-3 | Algebra
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| Duration : | 35h Th, 15h Pr |
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| Credits/ECTS : |
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| Holder(s) : | Michel Rigo |
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| Language : | French language |
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| Course contents : | This course pursues the study of vector spaces initiated during the first year. The main part of it 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 and the corresponding ideals. 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 : | Linear algebra is a fundamental tool useful in almost every part of mathematics but also in many applications in physics. The aim of this course is to present basic notions and some more advanced results about finite dimensional linear algebra. |
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| Prerequisites : | Perfect knowledge from previous courses in mathematics is expected, especially about the theory of matrices (e.g., manipulating determinants, complex numbers,...). |
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| Workshops : | 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. |
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| Organization : | The theoretical lectures are given three hours a week. The schedule will be communicated on the first day of the academic year. Lectures are common with first year students in mathematics. |
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| Written notes : | Lecture notes are available (in french) and can be downloaded from http://www.discmath.ulg.ac.be/ |
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| Assessment : | 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 : | 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 : | Some useful informations are given on http://www.discmath.ulg.ac.be/ |
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