Applying to PhDs is hard! I did it twice. My first time round I got rejected from all fifteen places I applied to – heartbreaking. However, on my second attempt I got into my dream program. Attached below are my statements of purpose, CV and writing sample from my first (unsuccessful) and second (successful) application to Berkeley. Good luck to all of you applying.

Application Element	What Changed/Stayed the Same	Notes
Statement of Purpose	Thought more about research agenda, written better, including personal motivation	Everyone has different styles – for more unusual areas, I think the statement of purpose is more important than for more mainstream areas
Personal History Statement	Stayed the same
CV	Basically unchanged
GRE Scores	Stayed the same
Letters of Recommendation	These changed! More diverse letter writers who knew me better after I had worked with them for longer and discussed more intellectual ecoomicsy things
Writing Sample	Added three research proposals as well as my MSc Dissertation	I think adding the research proposals really helped!
Qualifications	I did a real analysis course