Fall; Grades 11–12
Prerequisite: Accelerated Calculus or equivalent
Taught by: Indian Springs School
A standard treatment of linear algebra as presented to university-level science and engineering majors. Course topics will include row-reduction, matrix equations, linear transformations, matrix operations, invertibility, subspaces of Euclidean space, dimension, rank, determinants (elementary product definition, expansion by minors, and row-reduction), vector spaces, null and column spaces, linear independence, bases, change of basis, eigen-theory, algebraic and geometric multiplicity, diagonalization, inner product, length, orthogonality, orthogonal sets, projections, the Gram-Schmidt process, QR-factorization, and the method least-squares. Basic programming in Python will be introduced and used to reinforce concepts and speed-up some of the more mundane computations characteristic of linear algebra. Regular problem sets will allow the students to practice and master the techniques introduced in class. Topic mastery will be exhibited through written and oral exams and group projects. Prior programming experience is not expected.