I don't know yet of any Linear Algebra or Discrete Mathematics books in English (unless A.I. Kostrikin "Linear Algebra and Geometry" focusing on physics track counts, but this is incidental).

Linear algebra:

Gilbert Strang, Linear Algebra and its Applications for an applied/computational introduction. You can watch lectures from one of his classes, if you're into that. Halmos's Finite Dimensional Vector Spaces for more theory because Halmos. Sheldon Axler's Linear Algebra Done Right somewhere in between.

You do not want a single book about "discrete mathematics", they give too superficial a look at too many things that aren't really closely related. Instead

Logic and Set Theory: All introductory logic books suck. Dirk van Dalen's Logic and Structure is the best I'm aware of. Raymond Smullyan's Logical Labyrinths is more of an introduction for philosophers than mathematicians, but if you're interested in logic you want to get used to reading philosophers and computer scientists too. Halmos's Naive Set Theory because Halmos. Stephen Cole Kleene, Introduction to Metamathematics is too old to be a good introduction, but is a classic and still worth reading. Bourbaki's Theory of Sets, because everyone should read some Bourbaki.

Combinatorics: Peter Cameron, Combinatorics: Principals, Techniques and Algorithms emphasizes constructions, which are the fun part of combinatorics. van Lind and Wilson, A Course in Combinatorics for more counting. Concrete Mathematics for a humbling experience.

Graph Theory: Reinhard Diestel's Graph Theory. Free.

I would probably have to start calculus over again since it's been years. So that Pure Mathematics book seems to fit the bill, at least your description of it. I'll take a look at it. I suspect that I would do better at learning the subject if there was a class concurrently running. But cracking a book never hurt anyone.