I recognize that there are strong incentives to try to get good grades and that you are presented with opportunities to cheat. Remember that what you are here for is education, not grades. It does you no good to get a good grade by cheating. In the long run, your grades in this course are of little consequence, but your actions as a person are of great importance. They are what define who you are, not your grades.
Think of it this way: Would you go to a doctor who cheated her way through her medical exams? Would you go to a stockbroker who cheated to get his certification? Is that the kind of doctor or stockbroker you want to be? If you cheat here, what will that mean for you in the future? Your actions here will be with you the rest of your life; make sure they are actions you are willing to carry with you. Make them represent the kind of person you want to be.
I have a great deal of respect for someone who can admit that he does not know how to do something hard. I have no respect for someone who cheats to make it appear that he does. When students say they don't know how to do a problem, it makes me want to help them understand how; when students cheat in my class, it just makes me angry and want to stop helping them.
Take time now to consider what you think you should do if you are presented with an opportunity to cheat. Suppose you have been working on a problem set or take-home quiz for several hours, but can't get the last problem, and are running out of time. Your roommate has already done the problem, and you know his write up is in a notebook on his desk. What do you think you should do? Think about this now, when you aren't really under any pressure so that you know what you think is the right action before you are put in this position; you will not be able to think dispassionately about it at that time. Then, when you are in that situation, remember the decision you made now.
To those of you who resist the temptation to cheat, I say "Thank you, you're doing a great job. I appreciate it a lot, and am proud of you." To you others, I say "I'll see you in the Dean's office." You get to choose the path you'll take. Make it one you can live with.