University of Bordeaux

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.

This course discovers various representations of India through the cross-study of literary and cinematographic works of the twentieth century. Students read works including A BARBARIAN IN ASIA by Henri Michaux and A CERTAIN IDEA OF ​​INDIA by Alberto Moravia; and view works including ABOARD THE DARJEELING LIMITED by Wes Anderson and the documentary by Louis Malle, GHOST INDIA.

This course demonstrates how computers can be used as a tool and a medium in the domain of the arts. The first half of this course focuses on the basics of Adobe Photoshop including photo manipulation, keyboard shortcuts, and an introduction to gif making. The second half focuses on Adobe Illustrator and an introduction to paper layout and typography. The objective of the second half of class is to understand Illustrator well enough to create and design a new logo and a new music album cover.