For first year math, you go through Elements almost entirely front-to-back. I have mixed feelings about the Great Books programs in general, but the Euclid class was remarkable. It tends not to be a math-heavy group of students, but even those who think they're bad at math can still follow (for the most part) the geometric proofs. It gave all of the students--those of us who were mathematically inclined and those who weren't--a shared vocabulary and methodology for talking about actual mathematics in a way that any of the other math classes I took later after transferring to another university would not have.
If anyone wants to go through them by yourself, do yourself a favor and get the Heath-annotated copies. Those annotations can be a life-saver when you get stuck.