Course webpage for Math 121
let me know
if any of the links fail to work, or if you spot any errors, or if anything is unclear.
The final exam will be on Thursday 20th May at 2.15pm in Harvard 103. You are responsible for all material
covered in class, except for any material which was specifically described as non-examinable. In addition,
you are responsible for any reading that you needed to do to do any of your homework, plus the following
material from the textbook:
Sections 1.1-1.6 (vector spaces, subspaces, linear combinations, linear independence, bases,
dimension). You do not need to know how to prove that every infinite dimensional vector space has a
Sections 2.1-2.7 (linear transformations, null space, range, matrices, invertibility and isomorphisms,
change-of-basis, dual spaces, applications to differential equations). You do not need to know about
the duals of infinite-dimensional vector spaces.
Material from Chapter 3 as described in
Section 4.4 (but you don't need to know how to prove any of these properties of determinants).
Sections 5.1, 5.2 and 5.4 (eigenvalues, eigenvectors, diagonalizability, invariant subspaces, the
Sections 7.1 and 7.2 (Jordan canonical form). You do not need to know anything about "dot
Sections 6.1 to 6.4 omitting pages 370-372, section 6.5 as far as the end of p383, and section 6.7
omitting the material on Polar Decomposition (inner product spaces, Gram-Schmidt, orthogonal
complements, adjoints, self-adjoint operators and their diagonalizability, Singular Value
Decomposition and pseudoinverse).
You should expect roughly half the exam to cover material that was assessed on the midterms, and half the
exam to concentrate on the material that we covered since the second midterm. A sample final is available
. The solution is
The sample second midterm is available