df:
ID  sem  course
10  1    "math"
10  1    "phys"
10  1    "other"
10  2    "math"
10  2    "phys2"
10  2    "chem"
11  1    "other"
11  2    "math"

mylist=list(NA)
for in each ID {
   for j in each sem{
      check the element course=='math'{
          insert it into mylist (or do some other stuffs here)
 }}}

mylist
"math","math", "math"