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| MATH0227-1 | Algebra and Geometry - Introduction to algebra - Linear algebra - Geometry  | |||||
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| Duration : | Introduction to algebra : 15h Th Linear algebra : 30h Th, 15h Pr Geometry : 30h Th, 15h Pr | |||||
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| Holder(s) : | Introduction to algebra : Michel Rigo
Linear algebra : Michel Rigo Geometry : Michel Rigo | |||||
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| Course contents : | In the introductory part, 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) is dedicated to the study of polynomials (with real or complex coefficients) and finite dimensional linear algebra. In particular, we present the fundamental theorem of algebra (D'Alembert-Gauss'theorem). 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 methods of computation of the solutions of such systems. Finally, we present eigenvectors, eigenvalues, the problem of diagonalization of matrices with the special cases of normal, hermitian and unitary matrices. These concepts are enlightened by some examples and applications. Part c) is dedicated to geometry which relies deeply on linear algebra. We first present (finite dimensional) vector spaces (over the field of real numbers). This part is mainly focused on
We insist on the possibility to develop applications of the theory (center of mass, movement of a particle, optical properties, Kepler's laws, ...) and also on the translation of problems into equations. | |||||
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| Course objective : | 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. The aim of part c) is to present the main concepts of geometry insisting on the one hand on the analytical aspects and on the other hand on the abstraction and conceptualization. | |||||
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| Prerequisites : | No specific knowledge is required. Basic knowledge from secondary school is enough. Naturally, being trained to abstraction and mathematical reasoning is an advantage. The part a) is dedicated to train these capabilities. | |||||
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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. During those sessions, the class is divided into smaller groups. The schedule will be communicated on the first day of the academic year. | |||||
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| Organization : | The theoretical lectures are given on a regular basis between two and four 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 : | Lecture notes are available (in french). | |||||
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| Assessment : | Students are tested all along the year. These tests are aimed 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 : | M. Rigo Institute of Mathematics (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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ULg : Students and Studies Administration - Academic Affairs
Contact : Monique Marcourt, direction A.E.E.
Date of data : 27/02/2006
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