How to deal with arrogant e-mail of a student

How to deal with this?

Dear [student],

Thank you for pointing this out.

[1 or 2 more sentences of explanation]

Sincerely, [your name].

What troubles me is the attitude, which I found it kind of offensive (but I might be wrong).

Maybe the email is offensive, or maybe the student just wrote an email from their phone. Maybe they are actively trying to be a jerk, or maybe they just don't know how to behave properly. Maybe they are just trying to be a troll. In all those cases, I have found the best way is just to not engage and write a neutral response that does not comment on the perceived rudeness.

• If it's just a regular student writing an email from the phone, this does not create a conflict out of thin air.
• If it's a jerk or troll, this does little to satisfy their hunger for drama.
• If it's a student without manners, well, you are not their parent - don't make it your job to educate them on proper email etiquette.

What I certainly would not recommend is "inviting" them into your office for some sort of explanation, just for writing a factually correct but unfriendly email. You are, again, at worst creating a conflict where there is none, and at best spending significant energy trying to educate a fellow adult on basics of etiquette.

But I feel that the student would create same issues in case some typo is found in the subsequent notes and make similar comments.

So what? If they have a real concern, address them. If they make things up to feel important, either ignore the email or tell them that you do not see the issue.

There are several things which are not mentioned in the email but which can be assumed when processing such a message:

• The student is actually trying to help everyone involved. Otherwise they wouldn't have bothered sending the correction.
• How did the student get to this stage? It seems likely that they first solved the exercise correctly, only to find that their solution didn't match the proposed one. They might then have proceeded to use much more time (not necessarily wasted because of their increased understanding, but they might not see it that way) on trying to match the proposed solution, only to finally realise that they were right all along. This can be a frustrating experience, involving disappointment, erosion of (mistaken) belief in the infallibility of teachers, lost time, and opportunity cost. They then get in a bad mood. Time might be of the essence to make sure others don't repeat the process, so they fire off the quickest message they can to get closure and fix it for others.
• On a completely different tack, they might be more used to text messages or the kind of ultra-condensed emails that are popular in certain work places. For example, I've seen people recommend acknowledging emails with a simple "Ack" or "Got it" in the subject line, with no body at all. They might simply be trying to avoid wasting your time with niceties.
• As a software developer, this is the sort of style that I have learned to expect (and hope for) in bug reports. If that was a bug report the only bad style would have been the word "obviously".

With that in mind, you basically have two options:

1. Respond in kind, since that might be what they expect. "Thank you", "will be fixed", etc. They will likely format future emails in the same way.
2. Respond using the format you want them to use in the future. This should be a good enough hint on its own of what you expect, but I wouldn't bet on it.

Another obvious option, which I would not recommend, is to directly chastise them for not conforming to expectations. They will probably never report issues like this again.

Also: Don't worry. This wasn't even a complaint, just a correction. This sort of thing is only a problem if it keeps happening to many of your assignments, and coming from many students.

Finally, to anyone assuming that the student is either rude or bragging:

1. Research indicates that humans are really bad at judging the tone of written messages (1, 2, 3).
2. Sending a private message to the lecturer is pretty much the least bragging/bad-mouthing way possible to ensure the issue is fixed. The lecturer is free to correct the mistake in any way they see fit, and to credit the student or not. Conversely, universities have plenty of public forums where the student could have posted a similar message, which could have been justified by it then being fixed for everyone ASAP, but which could be interpreted as bragging and/or criticising the lecturer. The student showed good judgment by handling it this way.

An arrogant sounding email does not mean that the person is arrogant. It is well-known that language and even the assumed personality in online communication differ from the real ones, sometimes very significantly (see e.g. internet troll and internet hero). There may be a bunch of other reasons why a person uses an offensive language without realising it, e.g. their first language may not be English. There is also a cultural dimension to it.

The bottom line suggestion is: don't form your opinion by reading email only. Ask student in for an office hour and explain the solution to them. You can offer advice about the communication style used in academia and also get to know the student better by seeing her/him in person.