This course is an introduction to the theory of Riemann surfaces. Riemann surfaces naturally appear is mathematics in many different ways: as a result of analytic continuation, as quotients of complex domains under discontinuous group actions, as algebraic ...
Discrete mathematics is a discipline with applications to almost all areas of study. It provides a set of indispensable tools to computer science in particular. This course reviews (familiar) topics as diverse as mathematical reasoning, combinatorics, disc ...
This course introduces the basics of cryptography. We review several types of cryptographic primitives, when it is safe to use them and how to select the appropriate security parameters. We detail how they work and sketch how they can be implemented. ...
On introduit les bases de l'automatique linéaire discrète qui consiste à appliquer une commande sur des intervalles uniformément espacés. La cadence de l'échantillonnage qui est associée joue un rôle primordial pour assurer la stabilité et la performance d ...
Text, sound, and images are examples of information sources stored in our computers and/or communicated over the Internet. How do we measure, compress, and protect the informatin they contain? ...
Algebraic geometry is the common language for many branches of modern research in mathematics. This course gives an introduction to this field by studying algebraic curves and their intersection theory. ...
The course introduces the paradigm of quantum computating in an axiomatic way. We introduce the notions of quantum bits, gates, and circuits. We introduce themost important quantum algorithms. We also touch upon error-correcting codes. This course is indep ...
In this course we will describe in numerous examples how methods from l-adic cohomology as developed by Grothendieck, Deligne and Katz can interact with methods from analytic number theory (prime numbers, modular forms etc...). ...