Many mathematics department faculty are happy to take on undergraduate mentees for supervised reading/research projects. Some things to keep in mind:
Here is a list of faculty who encourage undergraduates to contact them.
Most faculty, even ones not listed, will welcome direct inquiries from students.
It helps to know the faculty member from a class or other academic context.
Don't be offended if you are turned down by a particular faculty member; many of them are very busy and may be advising many others already.