mail to professor
Is there any grammatical mistakes in the following letter which I'm going to send to my professor? Does it need any amendments?
Dear professor XX;
Back to our previous conversation, you gave me the opportunity to write a conference paper by comparing the results of experiments E5 and E7 from the doctoral dissertation of Dr. YY.
As you are aware, I handed in a draft version of the paper within a week after your approval; however, at that time you ordered me to change some parts of the manuscript without exactly specifying them. After applying some changes, I've attached the revised script to this email.
I understand that you are busy these days, but please let me know if it needs any amendments at your earliest convenience.
sincerely;
ZZ
****P.S. : I really need this email to be overly formal and without any mistakes. So I would appreciate any suggestions to improve the above script toward "perfection" :)

Question

mail to professor
Is there any grammatical mistakes in the following letter which I'm going to send to my professor? Does it need any amendments?
Dear professor XX;
Back to our previous conversation, you gave me the opportunity to write a conference paper by comparing the results of experiments E5 and E7 from the doctoral dissertation of Dr. YY.
As you are aware, I handed in a draft version of the paper within a week after your approval; however, at that time you ordered me to change some parts of the manuscript without exactly specifying them. After applying some changes, I've attached the revised script to this email. 
I understand that you are busy these days, but please let me know if it needs any amendments at your earliest convenience. 
sincerely;
ZZ
****P.S. : I really need this email to be overly formal and without any  mistakes. So I would appreciate any suggestions to improve the above script toward "perfection" :)

Answer

It's fine. It strikes a respectful tone but is not overly formal. He knows you're not a native speaker, so he isn't looking for perfection in an email.

Answer

Yep, it's ok.
you can use https://app.grammarly.com/ for this kind of questions(you can install it as an extension if you are using Chrome)

Answer

'Regarding' is better than 'back to'.

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