# Open Math

# Welcome to Open Math

This courseware is freely available for everyone with an interest in mathematics.

Whether you want a complete set of course materials, to look up the definition of linear independence, or to test your skills against a large suite of exercises with instant feedback, this site is for you.

Enjoy.

Steven Furino.

Associate Dean, Undergraduate Studies, Faculty of Mathematics, University of Waterloo

P.S. This is university-level material. If you’re interested in high school mathematics courseware, visit the CEMC Courseware site.

We invite you to share your thoughts and make suggestions for other resources that you would find helpful on our forum page.

## Open Classes

Linear Algebra 1 is a study of n-dimensional Euclidean spaces, systems of linear equations, matrix algebra, elementary matrices, vector spaces and subspaces, basis and dimension, linear transformations and matrix representations, determinants, eigenvalues and eigenvectors, and diagonalization.

Topics include orthogonal and unitary matrices and transformations; orthogonal projections; the Gram-Schmidt procedure; and best approximations and the method of least squares. Inner products; angles and orthogonality; orthogonal diagonalization; singular value decomposition; and other applications will also be explored.

This course explores systems of linear equations, matrix algebra, determinants, and introduces vector spaces and their applications.

Topics include a continued discussion on vector spaces. Linear transformations and matrices are examined more fully. Inner products, eigenvalues and eigenvectors, and diagonalization are introduced and disucssed. Applications to linear algebra are also examined.