Shai Simonson is awesome (disclaimer: I'm a fan!), so if for whatever reason the above course doesn't work out for you, might I suggest his course?  ;-)
Note: quickly skimming the chapter outline, I think Shai's course covers up until chapter 15, maybe 16 out of 22.
On a lighter note:
All the previous chapters seem to connive to lead the unsuspecting reader to chapters 14 and 15, and then to section 15.7.
"So far we have shown that 3SAT is no harder than Quadratic Equations, Independent Set, Maximum Cut, and Longest Path. [...] It turns out we can reduce all three problems to 3SAT in one fell swoop."
Yeah, yeah. You think we don't know where you're going with this?
we need abstract higher order theoretical computer science
In that sense, theoretical computer science would be a sort of "applied" mathematics
But, maybe we can go even higher such that the material has zero pragmatic pay-off?
-- J. McCarthy circa. 1958
This is a wonderful resources for me, to see where the blanks in my knowledge of the field are.
I'll be definitely taking a look at this :p
I struggled with P/NP and that was in a 3rd year algorithms course.
Any 200 pages alternative?
Kidding, but there's a point: If you want to make it 1/3 shorter, and not lose any info, it has to be denser. That won't make it easier to read - probably the opposite, in fact.