FMA_2F001_EP - Linear Algebra II (2024-2025)

 

FMA_2F002_EP - Topology and multivariable calculus (2024-2025)

MAA202 is divided into two parts, the first one more theoretical than and setting the foundations of the second one. The theoretical part covers the fundamentals of topology of normed vector spaces and of topology in finite dimension. The second part, more computational, covers differentiation and integration in several (real) variables.

Analysis (MAA 202) builds on the concepts and techniques introduced in MAA102 Introduction to Analysis. In particular, students cover notions in topology.

FMA_2FT01_EP - Linear Algebra II - Tutoring (2024-2025)

FMA_2FT02_EP - Topology and multivariable calculus - Tutorat (2024-2025)

FMA_2S006_EP - Euclidean and Hermitian Spaces (2024-2025)

Euclidean and Hermitian Spaces continues the study of linear maps between vector spaces, started in MAA101. The goal is to obtain simple and efficient models for these applications up to suitable changes of coordinates. The concept of duality is initially introduced in the general context of mere vector spaces. Then, the focus is put on vector spaces enjoying a richer structure, namely prehilbert spaces, which is available in most applications (e.g. in solid mechanics or in quantum mechanics). The geometry of these spaces, as well as their important transformations (e.g. normal or unitary maps) is also discussed.

Algebra (MAA 206) is a continuation of Algebra (MAA 201) and covers objects in bilinear algebra. These objects, mainly quadratic forms, have fundamental applications (e.g. in Number Theory and Mechanics), and also lead to the study of algebraic objects; for instance, some special groups of matrices, whose applications in mathematics and physics are fundamental, from Number Theory and geometry to the classification of particles.

FMA_2S007_EP - Series of Functions, Differential Equations (2024-2025)

Analysis (MAA 207) builds upon the topology notions studied in Analysis (MAA 202) to allow for a more profound study of functions. Examining functions as limits of simpler ones (e.g. for approximation problems) is made possible in a rigorous manner thanks to topological ideas. This provides the possibility of using crucial tools in many scientific fields; the most striking one being Fourier series (first designed to solve the heat equation and now ubiquitous in science and, in a hidden manner, in daily life). The second part of the course deals with a wide array of differential equations, permitting students to better understand complex physical questions.

FMA_2ST06_EP - Algebra - Tutorat (2024-2025)

FMA_2ST07_EP - Analysis - Tutorat (2024-2025)