I am applying for a Ph.D. in Mathematics in U.S. universities from India. The application process requires me to register people who can comment on my capability for research and recommend me for the graduate school. I have heard that since most applicants for (pure) mathematics Ph.D.s generally do not have publications to show, the recommendations are crucial in the selection process. Hence, I have three questions about selecting my recommenders wisely.
1) Do you feel that recommendations coming from a Professor carries more weightage than the ones coming from an Assistant Professor? My question is that, does the seniority of my recommender add any extra weight or credibility to the recommendation?
2) If a senior Professor gives me 'above average'(or 'good') recommendation while another Assistant Professor ( just two years on the job, not very famous but a very active and well cited researcher) gives me 'excellent' recommendation - which one do you think will support my application better?
3) Which recommendation should I prefer - from a person with whom I worked on a project for around a month, or , from someone who has taught me two courses over two semesters?