Introduction aux concepts clés du calcul (différenciation et intégration), des probabilités (variables aléatoires discrètes et continues) et de l'algèbre linéaire (espaces vectoriels, matrices et systèmes linéaires).

What are the theoretical limits of computing power? What problems can be solved with computers? Which ones cannot? And how can we reason about the answers to these questions with mathematical certainty? This course explores the answers to these questions and serves as an introduction to discrete mathematics, computability theory, and complexity theory. At the completion of the course, students will feel comfortable writing mathematical proofs, reasoning about discrete structures, reading and writing statements in first-order logic, and working with mathematical models of computing devices. Throughout the course, students will gain exposure to some of the most exciting mathematical and philosophical ideas of the late nineteenth and twentieth centuries.

High-performance computing (HPC) is a field at the forefront of a range of high-tech applications such as computational fluid dynamics, image processing, and financial risk management. With the demands of machine learning outstripping conventional computing, HPC is also at the forefront of artificial intelligence. This course will discuss how HPC clusters are used in large-scale problems in academia and industry alike. Students will learn about HPC clusters from the ground up and gain a solid foundation in parallel computer architectures, cluster operating systems, resource management, and containers. They will build their own systems via the remote installation of physical hardware, configuration and optimization of a high-speed network, and integration of other technologies used throughout the HPC world.