Two students at a Northern California university scrawled swastikas and other hate speech in residence halls, the campus president said Thursday.

The swastikas were found Tuesday at two separate dormitories that mostly house first-year students at San Jose State University.

Next to one of the swastikas was scrawled "Admit One Jew," President Mary Papazian said in a statement emailed to all students Thursday. She said police have identified the student responsible and "determined that this act, while bias-based, targeted no one in particular and is not by definition a hate crime."

The other swastika was drawn on a white board in a common area of another dormitory. The white board was described to police by the student responsible as a "joke board," said Papazian, adding that this incident remains under investigation and police were confident the two cases are not related.

A university spokeswoman, Pat Harris, said the school was considering sanctions against the students that could result in expulsion.

Officials didn't release the identities of the students involved to preserve student confidentiality, the statement said.

Papazian said she was disheartened and outraged by these "profoundly hurtful acts" but hoped the campus would learn from it.

"Together, we can use this difficult moment to grow and learn how to be a fully inclusive and welcoming community," she said in her statement.