University of Bordeaux

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).
 

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.

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.

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.

This course familiarizes students with the fundamental semantic notion of cohesion. Indeed, it is cohesion that makes it possible to form a discursive whole, whether written or oral. The main cohesive links defined by Halliday and Hasan's COHESION IN ENGLISH (1976) are reviewed, defined and discussed: reference, substitution, ellipsis, the main types of reiteration and comparison. Conjunction and collocation are omitted. Each lesson is devoted to recognizing, locating, and activating these various links.

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.
 

This course uses economic theories such as trade specialization and investment strategy to create a foundation for international economic analysis. Primarily, the course focuses on the impacts of globalization, its roots, the current state of global trade and the concept of “de-globalization.” As well as this, it discusses the link between free-trade and growth, and why we do not see this connection in certain developing countries.

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.

The course deals with the long nineteenth century in Britain and the twentieth century in the United States. It defines and explores the concept of "radicalism" in these two contexts, and illustrates this with reference to the main radical groups and political parties, their principal actions, and their political legacy.

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.