Cet ouvrage, à destination des candidats à l’agrégation interne de mathématiques, propose une série de 30 développements possibles pour les épreuves orales de leçons et d’exercices. Le développement, effectué sans notes le jour du concours, consiste à détailler une situation mathématique importante afférente au sujet choisi. Il peut s’agir de la démonstration d’un théorème (pour l’oral 1) ou de la résolution d’un exercice (pour l’oral 2). Il est donc important de montrer une aisance dans l’exposé des énoncés ainsi que dans la maîtrise des concepts mis en jeu. Pour chaque développement, les candidats trouveront une série de commentaires ayant pour but de faire un point sur les pré-requis nécessaires. Quelques ouvertures sont également proposées afin de placer le sujet dans un cadre plus large. Dans cet ouvrage, plusieurs démonstrations peuvent être exposées pour un même développement et ce, dans un but de croiser les concepts et les différentes branches des mathématiques. Sommaire Représentation décimale propre d’un rationnel Théorème de Lagrange et sous-groupe distingué Arithmétique et périodicité Théorème de Riesz Théorème de Weierstrass Théorème de d’Alembert-Gauss Equivalence des normes Théorème de Carathéodory Théorème de Kakutani Une application des théorèmes de Kakutani et de Carathéodory Théorème spectral Matrices de Moore Théorème d’inversion locale Norme d’une forme linéaire continue Disques de Gerschgorin Injectivité de l’exponentielle sur l’ensemble des matrices réelles diagonalisables Bicontinuité de l’exponentielle sur l’ensemble des matrices symétriques réelles Théorème de Cayley-Hamilton Surjectivité de l’exponentielle sur l’ensemble des matrices carrées à coefficients complexes Rayon spectral et série (dans l’ensemble des matrices carrées à coefficients complexes) Calcul de l’intégrale de Dirichlet Théorème de Cauchy-Lipschitz linéaire Fonction continue dont la série de Fourier diverge Théorème de Fejér Images des entiers pairs par la fonction zeta Phénomène de Gibbs Equation de Bessel Nombres de Bell Approximation d’intégrales Méthode de Newton pour la décomposition polaire

Black Skin, White Masks is a classic, devastating account of the dehumanising effects of colonisation experienced by black subjects living in a white world. First published in English in 1967, this book provides an unsurpassed study of the psychology of racism using scientific analysis and poetic grace.Franz Fanon identifies a devastating pathology at the heart of Western culture, a denial of difference, that persists to this day. A major influence on civil rights, anti-colonial, and black consciousness movements around the world, his writings speak to all who continue the struggle for political and cultural liberation.With an introduction by Paul Gilroy, author of There Ain't No Black in the Union Jack.

In the late 1950s, like tens of thousands of young men of his generation, Pierre Bourdieu, having recently passed the agrégation in philosophy, found himself immersed in the Algerian war. Motivated by an impulse that, as he himself says, ‘was civic rather than political’, nothing seemed more important to him than to understand the Algerian situation and provide the elements that would enable others to come to an informed judgement about it. In extremely tough conditions and along with a small group of students, Bourdieu undertook a series of studies across an Algeria that was tightly patrolled by the army, leading him to discover the shocking reality of the resettlement camps and to analyse the mechanisms of destruction of Algerian society of which they were emblematic. To achieve the objectives he had set himself, Bourdieu had to carry out a genuine intellectual conversion, acquiring an ethnographic understanding of Algerian society, learning sociological analysis at a breakneck pace and inventing new instruments - both theoretical and empirical - that would enable him to understand the relations of domination specific to colonialism. These new tools also enabled him to analyse the nature of the crisis that the war had both produced and manifested. This unique volume brings together the first texts written by Bourdieu in the midst of the Algerian conflict, as well as later writings and interviews in which he returns to the topic of Algeria and the decisive role it played in the development of his work.

"This volume covers the period from the end of the Neolithic era to the beginning of the seventh century of our era. This lengthy period includes the civilization of Ancient Egypt, the history of Nubia, Ethiopia, North Africa and the Sahara, as well as of the other regions of the continent and its islands."--Publisher's description

Much orthodox economic theory is based on assumptions which are treated as self-evident: supply and demand are regarded as independent entities, the individual is assumed to be a rational agent who knows his interests and how to make decisions corresponding to them, and so on. But one has only to examine an economic transaction closely, as Pierre Bourdieu does here for the buying and selling of houses, to see that these abstract assumptions cannot explain what happens in reality. As Bourdieu shows, the market is constructed by the state, which can decide, for example, whether to promote private housing or collective provision. And the individuals involved in the transaction are immersed in symbolic constructions which constitute, in a strong sense, the value of houses, neighbourhoods and towns. The abstract and illusory nature of the assumptions of orthodox economic theory has been criticised by some economists, but Bourdieu argues that we must go further. Supply, demand, the market and even the buyer and seller are products of a process of social construction, and so-called ‘economic' processes can be adequately described only by calling on sociological methods. Instead of seeing the two disciplines in antagonistic terms, it is time to recognize that sociology and economics are in fact part of a single discipline, the object of which is the analysis of social facts, of which economic transactions are in the end merely one aspect. This brilliant study by the most original sociologist of post-war France will be essential reading for students and scholars of sociology, economics, anthropology and related disciplines.

The hardcover edition of volume 8 was published in 1994. This paperback edition is the eighth and final volume to be published in the UNESCO General History of Africa. Volume 8 examines the period from 1935 to the present, and details the role of African states in the Second World War and the rise of postwar Africa. This is one of the most important books in the entire series, and as such, it is an unabridged paperback.