[LeicesterCity]

Do you have a math reading list for an aspiring self-taught software engineer (assume I have no math background -- took calculus many years ago)? I was thinking of going from studying Calculus, then a book on proofs, then discrete math, then algorithms, maybe linear algebra too?

[impendia]

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.

[LeicesterCity]

Thank you for the response. Would reading Calculus to Epps then to some linear algebra & algorithms be most appropriate in a linear progression? Or would I be able to read some books concurrently?

[impendia]

Neither calculus nor Epp's book require any prereqs beyond high school algebra. Studying algorithms would definitely be easier if you'd gotten through Epp first.

For linear algebra, it depends heavily on your choice of book. To read Hefferon or (even more so) Axler, you'll want to have seen a fair amount of mathematical formalism, and read through some proofs. Knop is probably a good place to learn mathematical formalism; if you approach it with limited background it will be slow going but you'll learn a lot.