MAA206 - Euclidean and Hermitian Spaces (2023-2024)

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.