Our expert says:
The sad truth about most people at work isn't that colleagues hate you, but that they actually don't care at all. Everybody makes mistakes - they show their quality by how they handle the mistakes. And you can tell the quality of an organization by the way they deal with an employees mistakes - they're supposed to respond with understanding, advice, and if necessary further job training to help you recover from the mistake and avoid repeating it.
You should be able to discuss these problems with the HR person or department, who should help to put things right.
You don't mention what specific sort of rumours have arisen, or why anyone would bother to do this, so its hard to advise more specifically about that.
Also, a job skill they never remember to teach or even demonstrate in university is Humility. I found early on I was often by far the cleverest person in the room, which is fine - but when they feel you are reminding them of that, they find that objectionable. There's an art in being humble, and letting others feel competent and included
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