How can a master student get research opportunities? I'm an international student in a master program in applied math department in the United States. There are two ways that I have known in which the person like me can find the research opportunities:


Independent research: do it on your own. Is it common for most math students to do research in this way?
Research for the master thesis: As I know, the credits for the master program in applied math in my school are mainly for courses. You will not do research until you are writing thesis. 


What else opportunities can a math student like me have for doing research?
Find the hallway where your department's faculty have their offices.

Knock on the first door.

When the professor answers, say "Hi, I'm [name].  I'm a master's student, and I'm interested in doing research.  Do you have some time to talk?"

Repeat for the remaining doors.

(It also helps to have some idea what kind of research you want to do, and to do some background reading on the professors' research before you talk to them.  We like it when students say "I read your paper on X, and I have a few questions.")