"Am I ready for Calculus"
"I'm not ready for Calculus"...
But seriously, forks.
Obviously there are many factors to consider. Are you planning on taking more math courses? If so, then they will probably be (a) Calculus, Differential Equations, Linear Algebra, and the like.
But then there's a much more abstract/pure/theoretical level of math... (b) analysis, topology, and algebra (to name a few). I doubt you have ever done any of this, and this is (so they tell me!) what many mathematicians - especially the non-applied/stats - do.
If you're going to stick to option (a), then those kind of books you mentioned will suffice.
For option (b), you need a backgroun in logic, set theory, and proofs.