Algebra is much more than solving real-number equations for x. Rather, it is the study of structure: the way the rules of a system influence its behavior, e.g. the fact that addition, multiplication, and exponentiation of real numbers can all be inverted allows us to solve aforementioned equations. Linear algebra, the study of the structure of vector spaces, generalizes these ideas for the first time. You will see the first but by no means last appearance of structure-preserving maps between mathematical objects. These will be understood by means of matrices looked at from both the concrete point of view—systems of equations, row reduction, determinants—and the abstract point of view—linear independence, linear transformations, bases, eigenvectors and eigenvalues.
You will be assessed by way of weekly homework (40%), a midterm exam (30%), and a final (30%). Extra credit will be available. Note well that a C (70-79) is awarded to students who have met expectations; a B (80-89), to students who have met expectations well; and an A (90-100), to students who met expectations and knocked my socks off doing so.
- Systems of linear equations (5/25 & 5/26)
- Matrix algebra (5/31 – 6/2)
- Determinants (6/6 & 6/7)
- Introduction to vector spaces (6/13 – 6/16)
- Linear transformations (6/16 – 6/20)
- The big idea: coordinatization (6/21)
- The eigenvalue problem (6/22)