A first course in vectors, matrices, vector spaces, and linear transformations. The ideas in this course serve not only as an introduction to more abstract mathematics courses at the junior-senior level, but also have many useful applications outside mathematics. The course is not intended to replace a more advanced linear algebra course at the junior-senior level. It must cover the following topics: vectors; operations on matrices; matrices; inverse of a matrix; solution of systems of linear equations; rank of a matrix; vector spaces and subspaces; linear dependence and independence; basis and dimension; linear transformations; sums, composites, inverses of linear transformations; range and kernel of a linear transformation; student-written proofs. Further topics could include: determinants; eigenvalues and eigenvectors; orthogonality and inner product spaces; and quadratic forms. Prerequisite: MTH 902 or M1900-2, Calculus II.
Minor wording revision for course content and prerequisite clarification - 11/12/2018