This is course about vector spaces and linear transformations. It is not a course about vectors, in the sense of lists of numbers, and matrices (for this see Math 220), although we will of course make use of these concepts as needed. This course has a theoretical bent: we want to understand vector spaces and linear transformations, rather than use them to solve specific problems. For a more applied, engineering-oriented approach, try Math 441. This is a mathematics class, and you will be expected to read and do proofs. Students come to this class with a range of backgrounds. This is a second course in linear algebra, and emphasizes proofs and an abstract point of view (understanding vector spaces and linear transformations, not manipulating lists and matrices of numbers). We build up to and use structure theorems for linear operators.