Algebra I: Linear Systems

This course is an introduction to linear algebra (formalized in S2) based on intuition drawn from plane and solid geometry. It includes an introduction to matrix algebra.

The EU is also introducing the basic language of polynomials.

Geometry of the Plane and Space:

• Points, vectors, translation by a vector, linear combinations, collinearity, independence, bases, reference frames and coordinates, change of reference frame, barycenters
• Lines and planes (without coordinates, then with), relative positions, intersections, equations
• Classical Linear and Affine Transformations: Homotheties, Translations, Symmetries, and Projections in the Plane and in Space
• An Introduction to Euclidean Geometry: scalar product, orthogonality, distance, cross product, orthonormal bases and coordinate systems, orthogonal projections, distance from a point to a line or plane.

Linear Algebra in R², R³, and^Rn:

• Points and vectors in^{R^n}, affine subspaces and vector subspaces of^{R^n}, parametric representation and equations, a subspace generated by a family of vectors, a subspace generated by a point and a vector.
• Linear systems and the pivot method: systems, sets of solutions, the matrix of a system, row-echelon and reduced row-echelon forms, elementary operations, the pivot method
• Matrix Calculus: Operations on Matrices, Matrices of Elementary Row Operations
• Linear Applications of R², R³, and^Rn
• Invertibility of a Matrix and the Gauss-Jordan Method

Polynomials with real coefficients:

• Definitions of a polynomial and a polynomial function, links
• Coefficients, degree, roots, operations
• Factorization and Euclidean Division of Polynomials
• Multiple Roots, Connection to the Derivative, Taylor's Formula for Polynomials

High school mathematics curriculum (including plane and solid geometry and solving equations), at a minimum, the mathematics specialization in 11th grade and the mathematics specialization in 12th grade, or the supplementary mathematics elective.

Recommended prerequisites*:

High school mathematics curriculum (including plane and solid geometry and solving equations), ideally the mathematics track, or even the advanced mathematics track.

Hourly volumes*:

            CM: 24 hours

            TD: 25.5 hours

            TP: 0

            Land: 0