university is universitas
perguruan tinggi is school for higher education. the degree is diferent and lower than from a university.
Perguruan tinggi and universitas itu sama dan sinonim.
Maybe you confuse it with "sekolah tinggi"?
What is a mathematics library?
A library with books about mathematics ?
A library for the mathematics students. The University of Sydney, where I worked in the main library, used to have many branch libraries, including a mathematics library.
"The university does not have a mathematics library"?