Learning outcomes

The course proposes to learn fundamental concepts of linear algebra and their representations or applications in analytical geometry. The concepts covered in this course are central to many disciplines in mathematics and physics, including functional analysis, classical and quantum mechanics, differential geometry, relativity, dynamical systems, field theory (electromagnetism, etc.) and numerical computation.

Goals

The main objective is to establish several essential elementary notions of linear algebra, and its applications in geometry, as well as several central theorems and results for the rest of the curriculum.

Content

The course successively addresses the following fundamental notions of linear algebra: vector spaces, duality, multilinearity, determinant, Hermitian forms, unitarity. Each chapter begins with the algebraic structure before giving a representation or an application in geometry (affine spaces, lines and planes, parallelism, contravariant and covariant coordinates, tensors, vector product, volume, orthogonality, length, etc.). A last chapter on vector analysis in 3- dimensional Euclidean space closes the course by mixing several concepts seen previously.

Teaching methods

Ex-cathedra theory course. Examples of applications of concepts and tools in mathematics and physics will be given throughout the course, as a motivation for the course and as an opening to the rest of the curriculum. Geometry can serve as a thread for understanding mathematics and physics, and as a bridge and unification of the two disciplines. For the mathematician as well as for the physicist, no one enters here who is not a geometer

Assessment method

The evaluation is twofold: one part is about theory and the other focusing on computational skills.

In June, the oral exam is on theory, without notes, including notably definitions and demonstrations of important results.

In August, the exam on theory is written.

In both June and August, there will have one written exam based on computation skills developed during the exercise sessions.

Sources, references and any support material

Two syllabi are available at the reproduction service, one for the theoretical course, the other for the exercises.

Language of instruction

French
Training Study programme Block Credits Mandatory
Bachelor in Physics Standard 0 4
Bachelor in Physics Standard 1 4