I recommend this book to anyone starting CS and wondering "why do I have to learn all this stuff?" "What good is data structures and algorithms?"
Read from a certain perspective, TAOCP is less a book about how to do things better (the focus of many CS courses), and more about "wow, who would have imagined ...". I think CS students might find their curricula more engaging if, rather than having a set of concepts to master, there were actually interesting puzzles to solve. Thus, I suggest reading TAOCP not as a text book, but more as a novel. Take a look at the parts that interest you (how many ways of sorting 10 numbers can you think of just using paper and pencil?). CS is a lot easier to learn as a process of surprising discovery, than as a set of barriers that must be overcome.