Is it possible to study Differentiable Manifolds from Lee's "Introduction to smooth manifolds" before studying classical differential geometry from DoCarmo's text or Kristopher Tapp's "Differential Geometry of Curves and Surfaces".
Right now I'm hearing two sides, with one saying that Differentiable Manifolds doesn't really tie in with Classical Differential Geometry and the other opposing side states that its necessary to understand Classical Differential Geometry to supposedly help with intuition.
In this case I'm wondering what side is right in terms of what course of action to take. Study Differentiable Manifolds first then go back to studying classical differential geometry or start in the other direction?
I currently understand Topology, Abstract Algebra, Real Analysis, Linear Algebra.