What's on the final exam?
=========================

1. Emphasized stuff:

- Inner product spaces.  A significant portion of the exam will involve 
  material from this section of the course.  You are responsible for _all_ 
  of this material.  Statements, proofs, examples.  Everything.

- Diagonalizability, eigenvalues, eigenvectors.  You should know all the 
  statements of the various theorems concerning eigenvalues, 
  diagonalizability, etc., from all different parts of the course.

- Tensor products & exterior powers of vector spaces.  You should know 
  how to formally manipulate these objects, and how to use the "universal
  properties" to construct linear transformations involving these spaces.

- Matrix algebra.  You are responsible for the material we convered in the
  first few weeks of the course (special matrices, matrix limits, etc.).  
  However, you do not need to know how to prove that fussy theorem about the 
  eigenvalues of regular stochastic matrices.  (You know, the one with all 
  those nasty inequalities....)

- Applications of Jordan canonical form.  We proved several things 
  using the existence/uniquess of Jordan canonical.  You are responsible 
  for knowing these proofs.


2. De-emphasized stuff:

- General theory of canonical forms, primary subspaces/generalized 
  eigenspaces, etc.  The material on Assignments 3 & 4 (which formed a
  significant part of the midterm) is not part of the final exam,
  except as it relates to the material indicated above.  You can safely
  expect not to be asked for any proofs from this part of the course,
  but it may still be helpful to know some of the statements.

- Algorithm for computing a Jordan canonical basis.  You do not need
  to know this algorithm.

- Theory of bilinear & quadratic forms.  I'm tentatively planning to talk
  about this on the last couple of days of class.  However, even if we 
  actually get there, you will not be responsible for this material on 
  the final exam.

- Formal construction of tensor products & exterior powers of vector spaces,
  and proofs of the universal properties.  As indicated above the emphasis
  will be on using the universal properties, not proving them.  You can
  safely expect not to be asked to produce proofs that I skipped or merely
  sketched in class.  (However, if I wrote "Proof: Exercise" on the board,
  it's fair game!)


3. If it's not on either list:

- You should know it!  The exam is not finalized, and could easily end up
  including any topic that I haven't explicitly put on list #2.