[WallWextra]

I got started on "real" math with Spivak's Calculus. Some people start with Topology by Munkres, which is not a difficult book but is very abstract and rigorous so makes a good introduction. If you feel like you have ok calculus chops, maybe Real Mathematical Analysis by Charles Pugh. Other good books are Linear Algebra Done Right by Axler, or the linear algebra book by Friedberg, Insel, and Spence. Maybe even learn linear algebra first. It's so useful.

Do plenty of exercises in every chapter, and read carefully. Count on about an hour per page (no joke). Plenty of math courses have their problem sets published, so you can google a course which uses your chosen book and just do the exercises they were assigned.

If you don't feel comfortable with basic algebra and other high school math, there's Khan Academy, and some books sold to homeschoolers called Saxon Math.

If you haven't had a course in calculus before, maybe you should skim a more intuitive book before or alongside reading Spivak. I don't know of any firsthand, but I heard Calculus for the Practical Man is good. Scans are freely available online (actually, of all these books) and Feynman famously learned calculus from it when he was 12.

[alfiedotwtf]

OP wants it from first principles as their maths is "poor" . I don't think Spivak is a good choice to jump right into calculus.

If OP wanted a more softer approach, Spivak's Hitchhiker's Guide to Calculus is probably a better option first before going full Spivak.

[WallWextra]

I honestly couldn't tell what he meant, whether he had stumbled through calc 3 and gotten sick of memorizing arbitrary rules, or if he can't solve a quadratic.

I tried to include some good high-school level math resources.

[WallWextra]

There are also some very good books by Israel Gelfand, written for a high-school level. Titles are Algebra, Trigonometry, The Method of Coordinates, etc. All by Gelfand and one other author. Sort of unusual because they are basic books written by one of the greatest mathematicians of the 20th century.

[cma]

I'd start with Discrete Mathematics before Spivak. From what I remember, Spivak jumps in to constructing the reals out of set theory pretty quickly.

A discrete math text will drill you over a lot more basic proofs involving set theory that would help in understanding his construction.

[WallWextra]

Construction of the reals is in an appendix at the back. He starts with ordered field axioms.

Frankly there's something about the presentation in "discrete math" books that I find much more confusing and difficult than Spivak, which is just talking logically about numbers and their properties.

[sehr]

Do any of those resources actually cover math from 'first principles'?

[WallWextra]

Sure, right from the axioms.