I know Berkeley has a slight edge in the "prestige" factor, but is this edge well-earned? Is there a significant difference in the quality of instruction and opportunities for research at these two institutions, particularly in the pure math department? Is there much difference in the level/ability of your peers? Would a degree from Berkeley (as opposed to UCLA) help alot in grad school admissions? I ask this because UCLA would be more convenient for me location-wise, but Berkeley is worth the loss of this convenience if its academics are better. This is for undergraduate, btw. Thanks.