In the first lecture, we prove without measure theory a version of
Fatou's lemma for continuous functions on [0,1], using only
that the uniform limit of continuous functions is continuous, and that
every continuous function on [0,1] attains its maximum. The
proof depends on an eigenvector property of a certain family of
matrices, and can be adapted to prove a result on convergence in a
general Banach space. In the second talk, we show how a generalization of
the Hahn-Banach theorem due to Mazur and Orlicz can be used to prove a
classical minimax theorem, and we also show the connection between
minimax theorems and weak compactness in a Banach space. In the
remaining three talks, we define monotone and maximal monotone
multifunctions on a Banach space, and show how the minimax theorem can
be used to prove a number of results about these multifunctions.