France

This course surveys the institutional development of the American presidency from the Constitutional Convention through the presidency of Donald Trump. It addresses issues such as how presidential power was constitutionally designed, how the presidency has changed over time, and the place of the presidency in contemporary American politics.

This course covers the theorems usually used for numerical sequences and real functions, and their proofs. It discusses the main idea behind the construction of the integral in Riemann's sense, as well as how to write proofs, use the various notions, and independently study a numerical sequence or a given function. Topics include numerical sequences: theorems of monotonic convergence, adjacent and Cauchy sequences, notions of adherence values, upper/lower bounds and the Bolzano-Weierstrass theorem; local behavior of a function: theorems of extension by continuity and sequential characterization of continuity, applying this characterization to the limit of recurring sequences (a result accepted in advanced math), calculating derivatives, the Taylor-Young theorem, and the limited developments of reference functions, calculating limited developments to find limits and relative positions of curves; global behavior of a function: restoring and using the theorems of intermediate values, Heine, bijection, local extrema, Rolle and finite increments, Taylor with integral remainder and Taylor-Lagrange; Riemann integral: retaining the guiding idea behind the construction of the integral in the Riemann sense, demonstrating general results on the integral of functions, calculating integrals using primitives, integration by parts or change of variables, using the notion of comparison between Riemann integral and sum.