To put it shortly, I never learned mathematics. I never learned the algorithms for multiplication and division, &c. (I had always just mentally scaled by powers of 10, making it unnecessary for me to ever learn algorithms for what was presented to me). I intend to remedy my lack of knowledge, and see how far I can go :) I wish for an abstract treatment of whatever I work on, or I will quickly become bored. (I'm a philosopher).
I wish to cover these topics first: http://en.wikipedia.org/wiki/Outline_of_arithmetic
For elementary algebra, I discovered the book Elements of Algebra by Euler, but have the feeling that a more comprehensive and abstract treatment exists, as much of the book seems to focus on just finding the answer.
I'm asking for recommendations on the most abstract and comprehensive coverage of arithmetic and elementary algebra. @_@
Sorry to ask such a noobish thing, but I am of the opinion that there is almost always a near-optimal or optimal way to approach something, and this is no exception. I need to learn these things before I can go onto trigonometry, then analysis, &c.