I have been somewhat incorrectly convicted of copying another student's test, and the prospects of reversing this seem doubtful. My school's policy is somewhat more lenient here due to it being a first offense so they removed points on questions they think I cheated on and that this happened is kept on file, though it is not on my transcript. How would this affect my ability to get into top math graduate schools (assuming I am unable to successfully reverse this)? In particular, do many ask me to specify such things?
This is certainly not going to help your application for graduate school, and it can be fatal if it doesn't look like you've learned from it. I suspect the default position of most people is going to be against you, unfortunately.
- If you still have time (i.e. years till you graduate), make sure to show that you can put the incident behind you. Don't cheat in other classes, but get good grades in them anyway.
- If you don't have time, that's bad. You'll need to write a good explanation in your application.
- You will be asked about this. There's a box in many graduate applications asking if you've ever been involved in academic dishonesty situations. Don't omit this even if you've put the incident behind you, because if you do, you are not reporting full facts and if discovered any offer of admission can be rescinded even if you've already matriculated (see the statement you have to sign at the end of the application).
While it is impossible to say with complete accuracy, not knowing more, I doubt that it will affect you at all, provided that you act honestly and honorably in everyone's view in the remainder of your tenure. If that is the case, then, even if it is still considered an infraction, then it will also be considered an aberration. That is probably the reason for the nature of the policy in place.
Since the record being retained isn't public, the only way it would affect you in the future is if one of your recommenders mentions it. That is unlikely if you show yourself to be honest.
People make mistakes and other people recognize that. You don't actually need to have the record corrected to your satisfaction as long as your behavior is such that people in future want to write you great letters of recommendation.
But your goal is to be seen as a paragon so that your professors will look on the past as an out of character incident, even if they think that you really did cheat on one exam. Look to the future if you can't alter the past.
Has the matter been "expunged"?
- If so, then your university should not mention it (you may want to verify this) and you might legally/ethically be allowed to answer "no" when asked about this (you will definitely want to verify this as well, preferably with the new school(s) [anonymously] and in writing).
- If not, then you will have to mention it, and I agree with Allure's answer -- this will count against you, possibly in a major way -- all you can do is to address it very nicely in your SOP.