(1) First, the two courses of physics and chemistry are tied together as a composite element, and then all the other four elements are arranged. * * * and A22? A55=240 different arrangements;

(2) First arrange physics, chemistry and physical education to form four intervals, then insert Chinese, mathematics and English, and use A33? A34= 144 different arrangements;

(3) Full permutation comes first, because there are only two sequences in Chinese and English, so there are 12×A66=360 different permutations;

(4) It is divided into two categories: the first category, where mathematics ranks in the first category and all others rank, and the second category, where mathematics is not in the first category. The first category has four choices, and then the sixth category has four choices. Finally, in other categories, there are 55+4×4×A44=504 different permutations;