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I was accepted under PhD program by a professor. How to write an email to thank him sincerely

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Dear Professor Smith,

With this letter, I want to express how much I appreciate your having accepted me into the PhD program. It means so much to me, and I'd like you to know how grateful I am for your support.


Your student,

Jack Roberts


If you want a longer letter, you could add something like the following:

I have learned so much from you, and you will always be a role model to me.


I don't know if you studied under this professor or not, but you could add some points to support why you are are so thankful for what s/he has done for you in his/her role in your life.