征求对方许可（ask for permission）时,要用May I...或 Can I...,但前者更正式,往往用于陌生人之间或者正式场合.相当于I want to...Do you permit me 显然,教授和学生是熟人关系.
另一场合：某人抱着一叠书一不小心掉到地上了,她的好朋友过来帮她说:"can i help you?" 这时用 "may I"就见外了.
另外：一个商店的老板见一小孩在翻动陈列架上的商品时会很严厉的说“May I HELP you?" 其意思是 "请不要乱翻"
Shall I ...用来征求对方意见（ask for opinion）,相当于Do you want me...
-I hear you've got a set of valuable Australian coins． ＿＿ I have a look﹖
-Yes,certainly．