A French-language MOOC in linear algebra accessible to all, taught in a rigorous way and requiring no pre-requisites. (automatic translation)
Would you like to learn linear algebra, a valuable tool to complement the knowledge you've acquired during your studies in economics, engineering, physics or statistics? Or simply for the beauty of it? Then this course is for you! In addition to its role as a tool in the various branches mentioned above (enabling concrete problems to be solved), linear algebra, which captures the essence of mathematics - namely, algebra and geometry - will introduce you to the more abstract world of mathematics. Offered as a complementary course for first-year engineers at the Ecole Polytechnique Fédérale de Lausanne, this MOOC (consisting of three parts) is nonetheless a course in its own right and can be considered a solid foundation in linear algebra for any student interested in learning the subject. Although the videos form the core of the course, MCQ (Multiple Choice Question) exercises and series in PDF format will be available each week, along with appropriate answer keys. More specifically, the series of exercises will be accompanied by a PDF answer key, and some problems will benefit from a detailed video correction, in which one of the teachers will present the solution, step by step. Finally, each course video will be followed by a quiz, designed to test the degree of assimilation of the knowledge acquired. The course is organized into ten chapters, each of which offers a detailed approach to theoretical concepts, as well as numerous illustrative examples:
Systems of linear equations.
Matrix algebra.
Vector spaces.
Bases and dimensions.
Linear applications.
Matrices and linear applications.
Determinants.
Eigenvectors, eigenvalues, diagonalization.
Scalar products and Euclidean spaces.
Orthogonal and symmetrical matrices.
This second part of the course will be devoted to the study of chapters 5 to 8 mentioned above. A good knowledge of the material taught in MOOC Linear Algebra (Part 1) is required. It is therefore advisable to work regularly and assiduously, so as not to fall behind when learning the material. (automatic translation)
