>>15724202Introductory.
1. Lang's Basic Mathematics. Covers "Pre-Calculus" content like analytic geometry, what is a function, solving basic equations, and many of the most basic things you need to read more advanced Math books.
2. Calculus by Stewart. And in parallel some Matrix Algebra book, or Engineering level Linear Algebra which is about the same. (This is to have motivation for the next courses, it doesn't seem logical to me to proof shit you didn't even know was true. Mathematicians prove what has no counterexamples so far. Proofs are generally not a way to deduce results.)
Next is the filter.
3. You may do some Multivariable Calculus in the level engineers do, but learning it in theory is not really worth it. Just learn from Spivak Calculus how one variable calculus proofs usually go and try exercises. Or Abott's Understanding Analysis. In parallel read Stephen-Insel-Spencer's Linear Algebra for the theory of Linear Algebra, up to half the book. You can learn Ordinary Differential Equations without following all the proofs too. Theory of Differential Equations is too high level as of now.
4. Now read Baby Rudin (chapters 1 to 8 are what's worth in the book), after Spivak Calculus or Abott Analysis it should be not impossible as some make it out to be. Then keep reading Linear Algebra. After Spivak Calculus also Complex Variables would be easy, Pennisi Elements of complex variables is an underrated book that focus on analysis but to an approachable level for undergrads. You can also learn basic probability.
5. Measure theory and Topology are also normal in Math undergrads and the door to Modern Analysis.
Abstract Algebra is not useful for undergrad topics unless you start to tackle Number Theory, to which Complex Variables is also useful.
The extent to which it might be useful is to keep the self-esteem of students high giving them easy content lol.
Axiomatic Set Theory is a waste of time in general.
