Note that Stanford is on the quarter system, so it requires 180 quarter units to graduate (1 quarter unit = 2/3 semester unit, since a quarter is 2/3 as long as a semester).
26 units (14%) in math (including two math-for-CS courses in the CS department)
11 units (6%) in science (not CS)
13 units (7%) in engineering
43 units (24%) in CS
1 course (usually 4 units or 2%) in technology and society
The total for the CS major is 97 units, or 54% of the 180 units needed to graduate. (Looks like 4 is the most common credit unit value at Stanford, as it is at many other schools, but there are many 3 and 5 unit courses there.)
As a CS major too, I’m sure there are free spaces even if you are a CS major.
If logical reasoning (proofs) comes more naturally for you, I don’t think it is impossible.
Otherwise, Apostol’s book would have killed me with CS. I had lots of spare time and uhmm…I don’t think I attend a horrible school. It is ranked within the top 5 nationally in USNews ranking…
I been regularly taking 18 credits and it doesn’t seem to be a problem for me even when my other classes (notably math) are advanced classes… (and I had 2 part time jobs and friends)
That said, if you are a CS major, gl if you are planning to party all your 4 years.
I think that part will be a huge stretch unless you only do the bare minimums…