As mentioned in other answers, Thompson's Calculus Made Easy is an excellent informal book for calculus. Spivak and Apostol are nice at a much higher (rigorous and proof-based) level.
Most mainstream calculus books suck; they tend to hedge their bets between being advanced and proof-based on the one hand, and catering to students with a mediocre grasp of algebra on the other. Thomas' book is probably the best of this bunch.
Epp does proofs and discrete math, and a little bit of algorithms. The usual favorite for algorithms is Cormen et al.'s Introduction to algorithms, although I don't know it well.
For linear algebra, Axler (as someone else mentioned) is a very nice book. I really like Knop also (more beginner-friendly). Hefferon's Linear Algebra looks very nice, and is (legally!) free online. If you prefer a more applied/computational bent, try Strang.
Most mainstream calculus books suck; they tend to hedge their bets between being advanced and proof-based on the one hand, and catering to students with a mediocre grasp of algebra on the other. Thomas' book is probably the best of this bunch.
Epp does proofs and discrete math, and a little bit of algorithms. The usual favorite for algorithms is Cormen et al.'s Introduction to algorithms, although I don't know it well.
For linear algebra, Axler (as someone else mentioned) is a very nice book. I really like Knop also (more beginner-friendly). Hefferon's Linear Algebra looks very nice, and is (legally!) free online. If you prefer a more applied/computational bent, try Strang.