This is a course on the algebra of matrices and vector spaces. It emphasizes a concrete approach to the material. Topics include solving systems of linear equations, vector algebra, matrix algebra, properties of invertible matrices, determinants, the vector space Rn and its subspaces, dimension, and linear transformations. It concludes with a discussion of eigenvalues, eigenvectors, and matrix diagonalization. If time permits, additional topics such as the dot product, the Gram-Schmidt process, and basic aspects of vector spaces will be discussed.
MATH 221 and MATH 223 cover very similar material, but they are intended for students with different experience in mathematics. MATH 221 takes a more concrete approach to the material, and it is suitable for students who have not yet engaged with proof-based mathematics. MATH 223 takes a more theoretical approach that is appropriate for students who have taken proof-based math courses already or for students with strong mathematics backgrounds who are willing to learn how to read and write proofs in parallel with linear algebra. MATH 221 and MATH 223 fulfill the same requirement for the mathematics major, and students need only select the option that is best suited to their current background in mathematics.