Introductory Computer Science self-study

[petersburg]

Hey all. I'm a prospective computer science student who wants to get acquainted with some of the basic mathematical and theoretical concepts before I enter said program. I'm looking for books that will introduce me to some of the rigor involved with the introductory topics (namely algorithms and data structures, compiler theory), but will not drown me in a deluge of terse, academic-for-the-sake-of-academic language. If you have any suggestions, please share them.

 

Also, I have a couple of questions about the mathematical rigor of those introductory topics. What level of mathematical ability would be adequate to acquire at least a solid grasp? Do the mathematics make heavy use of advanced logic, calculus, set/graph theory, linear algebra, or a combination of them?

 

For the record, my highest level of math to date has been a course in advanced functions, precalculus if you will. Although I haven't taken a high school calculus course yet, will I be ill-prepared mathematically, even for those introductory topics?

[Pangloss]

Some schools may require high school calculus, but I believe in general it's assumed that you'll take calculus at the undergraduate level. You could look at it (taking it in high school) as a way of getting a leg up on the competition for admission -- the better you do at the most advanced courses, the more likely they are to want you on their roster.

 

Georgia Tech computer science program's undergraduate course requirements may be viewed at the link below. I linked these because if memory serves they're fairly typical. As you can see they have calculus listed, which means they're expecting most of their undergrads to take it. It looks like they make you take the first two Calc classes alongside engineering/science students, but the third one is explicitly for CS, and then a fourth class is on applied combinatorics (probably how to write algorithms that run against finite data structures).

 

http://www.cc.gatech.edu/future/undergraduates/bscs/corereq