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.