Finite dimensional vector spaces over a field, linear maps, isomorphisms, dual spaces, quotient vector spaces, bilinear and quadratic functions, inner products, canonical forms of linear operators, multilinear algebra, tensors. This course serves as an alternative to MAT 310. It is an intensive course, primarily intended for math majors in Advanced Track program. Students wishing to enroll in MAT 315 should instead enroll in MAT 310. In approximately the 4th week, an assessment will be held and qualified students will be offered the option of moving to MAT 315.