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This course covers number theory. Topics include integers on a ring: completely closed rings, quadratic bodies, norm, trace, discriminant in the case of extensions of bodies. Example of cyclotomic bodies of degree p-1; Dedekind rings: Noetherian property; application to integer elements, fractional ideals, fraction rings, localization, group of fractional ideals, norm of an ideal, multiplicativity; decomposition of ideals in an extension: prime ideal, discriminant and ramification, quadratic and cyclotomic bodies of degree p-1, quadratic reciprocity law; class group and unit theorem: networks, canonical folding, statement and proof of the finiteness of the class group, statement of the unit theorem, illustration in the case of quadratic bodies, Fermat cases (or other Diophantine equations); analytical opening (Riemann zeta function, Dirichlet L-functions, Dedekind zeta functions, link to counting prime numbers and ideals).
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This course focuses on French cities in the modern era. It explores in greater depth how, in concrete terms, French towns revealed the workings of modern France. Themes such as demography, society, economy, and cultural life, are covered.
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The course is composed of 3 parts: phonetics, communication, and comprehension. The phonetics section covers: International Phonetic Alphabet, sounds of French language, notions of systems, combinatory phonetics, standard and regional accents, prosodic phenomena, contrastive and corrective phonetics, phonetic and musical transcription. The communication section covers: oral expression and oral presentation, argumentation. The comprehension section covers: exercises of note taking, technics of summary.
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Economic science was built around the debate over the existence or otherwise of a harmonious, spontaneous order, ensuring the coordination of decentralized individual actions. The notions of order and disorder are understood by economists through the concepts of equilibrium, disequilibrium, optimum, crisis and regulation, as well as rationality and self-control. Equilibrium refers to a situation in which the plans of agents are compatible with each other, and in which the rational decisions of individuals are optimal and coherent. Imbalance, whether in the market or during individual decision-making, refers to the opposite situation. An equilibrium can be optimal, i.e. efficient, or sub-optimal; it can be stable or unstable, i.e. it can reproduce itself or not. This course examines how economic theories have historically tried to answer the question of whether the economy tends spontaneously towards a harmonious or optimal "natural" equilibrium or order, or whether it tends towards imbalance, disorder, crisis or the irrationality of individual decision-making. This questioning implies an inter-disciplinary reading of the discipline of economics, which itself draws on concepts of equilibrium and rationality from the natural and life sciences (such as physics, biology, neuroscience, etc.), as well as from other social and human sciences such as psychology, sociology, philosophy and anthropology.
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This course offers a reflection on science and acquires cross-disciplinary analytical skills. It addresses the notions of problematization, definition, and reasoning, notably through the reading of philosophical texts.
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This is the second part of a two-semester course covering the period from the fifteenth to the seventeenth centuries. It focuses on the arts of the Classicism. Rather than the global and idealizing point of view, often confining to the "family novel" of the great heroic artists, it places greater emphasis on a whole series of problems, artistic and inartistic, considered as sensitive questions: problems of space, place of Antiquity, religious devotion, funerary practices, political images, mannerisms and bodily movements, and mannerism and technique. In other words, a history of forms and styles allows a deeper questioning of the profound inventiveness of the visual productions of the Renaissance and the Baroque age.
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This course is a communicative course aimed at developing students' understanding and production of the language at CEFR level A2/B1. The course consolidates knowledge of French grammar and develops reading and writing skills. Students work on listening and speaking skills and students have the opportunity to practice the language with their peers on a variety of everyday topics such as talking about past experiences and events and expressing opinion, as well as discussing selected movies.
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This course covers French literary works from the seventeenth to twenty-first centuries, focusing on poetry and "factual" genres, a terminology encompassing a wide range of text forms and types of writing (essays, chronicles, historical accounts, reports, diaries, epistolary texts, speeches, etc.). The course is divided into two parts, one devoted to the history of poetic genres and their problematics; the other to a diachronic survey of "factual" texts, exposing their diversity and the difficulties of generic apprehension they give rise to. Each section studies different works and authors in relation with the theme.
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Between the advent of talking pictures in 1927 and the official launch of the New Hollywood in 1967, the classic Hollywood system developed and experienced a golden age, followed by a decline that was to begin in the early 1950s. This is the official story, in line with a certain reality, but one to which the work of numerous historians has added nuance and nuance. This course takes a historical approach, incorporating recent research, to revisit the Hollywood studio system, based on the power of producers and the exploitation of stars. It also studies the structuring of film production into major genres (melodrama, western, musical, biopic, war film, social film, biblical epic, film noir, etc.), which are sometimes called into question by their reception, and whose stability is open to debate. The course also looks at the history of the introduction in the early 1930s of a self-regulatory code, the famous Hays Code, whose interpretation may have changed over time, and whose influence gradually waned between 1952 and 1967. It explores the ideological tensions that divided the Hollywood community, sometimes violently and permanently: the question of American involvement in the Second World War, the inquisitorial system of the "Witch Hunt" in the context of the Cold War. The essential contribution of artists and technicians from European immigrant backgrounds is studied, including producers, directors, actors and actresses, screenwriters, cinematographers and composers. The careers of figures who forged the identity and style of classic Hollywood cinema are also explored, including: Charles Chaplin, Alfred Hitchcock, Ernst Lubitsch, Erich Von Stroheim, Joseph Von Sternberg, Fritz Lang, Billy Wilder, Joseph L. Mankiewicz, Elia Kazan. The course also looks at the homogeneity of the classic Hollywood style described in Janet Staiger, Kristin Thompson, and David Bordwell's (also classic) THE CLASSICAL HOLLYWOOD CINEMA: FILM STYLE & MODE OF PRODUCTION TO 1960. The re-evaluation of the place of female directors (Dorothy Arzner, Ida Lupino), African-American directors (Oscar Micheaux), and marginal genres (horror, animation) in the Hollywood canon provides food for thought on the homogeneity of Hollywood style and the centrality of a hegemonic definition.
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This course provides a better understanding of France, its population, their characteristics, and the country’s political life. The curriculum focuses on current French society and its evolution in relation to the weight of history, its territorial dynamics, and cultural and political ideals.
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