This is a first course on linear algebra. It emphasizes a theoretical approach to the material. Topics include vector spaces, subspaces, dimension, linear transformations and matrices, determinants, eigenvalues and eigenvectors, and diagonalization of linear operators. If time permits, additional topics such as inner product spaces, Hermitian and unitary transformations, and elementary spectral theory will be discussed.
MATH 221 and MATH 223 cover very similar material--they are both linear algebra courses--but they are intended for students with different experience in 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 takes a more concrete approach to the material, and it is suitable for students who have not yet engaged with proof-based mathematics. 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.