In some other questions, it has been noted that for certain programs at Cambridge, such as Part III of the Mathematical Tripos, one will not have had sufficient faculty contact to obtain strong recommendation letters. Additionally, no courses will show up on your transcripts until the end-of-year examinations (is what I have gathered from the answers to the above questions).
Thus, I imagine attending Part III may not significantly strengthen an application. Does attending Part III, such as on a Churchill Scholarship, carry significantly more weight to a graduate admissions committee?
