It Happens To Everyone.
Everyone experiences rejection at some point. Whether you've been rejected once or a hundred times, it doesn't matter. Odds are someone else has faced similar rejection. There are over seven billion people on the planet, and billions of interactions between those people daily. Take comfort in that. You will grow from this pain, and learn to shrug it off.
There Are Other Fish In The Sea.
With over seven billion people on the planet there are many people to meet. Sure, that guy you finally got the guts to ask out to coffee may have shot you down, but there's always another guy to go after! There are about 17,000 students at UM. It's said that in a lifetime, you may form meaningful relationships with approximately 150 people on average. Considering the sheer magnitude of students attending UM, you've got plenty of other options than the people from your classes. You could also just stumble into a guy when buying lunch at the cafeteria, or over pints at The Rat! In a lifetime, if you really put yourself out there, you can meet many different kinds of people. Among all those, definitely a few potential romantic partners and great friends.
Low Risk - High Reward
Asking someone out is a low risk, high reward interaction. If you stumble into a cute girl and after a small chat feel she is someone you are interested in, just ask her if she'd like to grab coffee. Grabbing coffee is a very harmless, secure thing to ask someone. If they're not interested they'll say "no" or "maybe another time," and go on their way. Sure, it is rough at first, but realize that there are plenty nice, funny and cute people to stumble into at UM and even more people outside of that. If you ask someone out, and they say yes, awesome! You get to go on a date and begin developing a friendship with them. If you ask someone out, and they say no, it may not feel that great, but you're still alive! You have all your limbs attached and your plans for the day aren't affected. Don't let a good day turn into a bad one just because you were simply rejected. Not everyone you encounter is going to be into you, the same way you aren't into everyone you encounter.