Please forgive the long setup but I think it is relevant to my question.
I am a third year Electrical Engineering student (before dismissing me a an engineer please read the rest of the question) and I am planning on doing graduate studies in Control Theory. I find it really brings together pure math and some sort of distant application which is enough for me. As such I've taken the usual engineering math courses (Calculus, Linear Algebra, Complex Analysis, Dynamical Systems, a whole ton of Fourier analysis, PDEs, Probabilities and such) where they proceeded to completely disregard any rigor. The only thing close to rigorous math that I actually did was in our Algorithms course which was fascinating (P=NP, Graphs, etc) and actually satisfyingly rigorous.
Anyways, I am now at a point where I want to strengthen my actual math knowledge and especially work towards a really good knowledge of Differential Geometry, Complex Analysis and Topology. As such I began studying the basics: real analysis with Chapman Pugh which I am really enjoying. However I would have appreciated some input on what you think is the best way to proceed from here.
My plan was next to do Topology with Munkres, Abstract Algebra with Dummit (perhaps not everything but at the very least a good coverage of group theory) and sometime after Smooth Manifolds by Lee and Papa Rudin. What do you think?