Advice on finding higher math classes?

It is not surprising that many universities allow non-matriculated students to attend (paying tuition) in classes where there is otherwise-unused space available after matriculated students have enrolled.

For example, you can see which upper division math classes at Berkeley have space, so that they could possibly be options for a non-matriculated student:

http://osoc.berkeley.edu/OSOC/osoc?p_term=SP&x=0&p_classif=U&p_deptname=–+Choose+a+Department+Name±-&p_presuf=–+Choose+a+Course+Prefix%2fSuffix±-&y=0&p_dept=math