Please refer to my statement of purpose, in which I explain in depth why I intend to do a degree at Harvard.

[alpacinou]

Is this correct and natural?

Please refer to my statement of purpose, in which I explain in depth why I intend to do a degree at Harvard University.

 

[Barque]

Use "desire" or "wish to". "Intend" sounds as if you're sure you'll be admitted.

 

[alpacinou]

What about the rest of it? Could others also comment, please?

 

[5jj]

Could others also comment, please?

I see no need.

 

[Tarheel]

Do we "do" degrees?

I might say:

I plan to go to Harvard, study XYZ and earn a degree in that subject.

 

[Holmes]

Is this correct and natural?

Please refer to my statement of purpose, in which I explain in depth why I intend to do a degree at Harvard University.

"Intend" feels a bit too forceful to me in this context. I assume you are writing to university administrators, who have the power to grant or deny you admission, regardless of your intention. I might change "intend" to "seek."

Also, I prefer "pursue a degree" to "do a degree" in this context, because it shows them that you do not take it to be a foregone conclusion that you will complete your degree there. In other contexts, "do a degree" works fine.

Please refer to my statement of purpose, in which I explain in depth why I seek to pursue a degree at Harvard University.

Years ago, I asked a former philosophy professor of mine, "Did you do your Ph.D. at Berkeley?" (I had just seen him at the U.C. Berkeley campus for a 50-years-of-teaching celebration of one of the philosophy professors there, now deceased.) To this day, I remember his exact response: "I did it at Harvard."