I am trying to visualize the correct learning curve for mathematics. Currently I know a Calculus 1 and 2 and basic linear algebra. But as far as post-secondary math courses go, that is all I have taken. I want to advance my knowledge of mathematics to the point where I can look at math PhD research papers and appreciate them, because they currently look like foreign gibberish to me. I ultimately want to learn (to a respectable level of fluency) Vector Calculus, ODE, PDE, Set Theory, Group Theory, Real Analysis, Complex Analysis, Discrete Math, Abstract Algebra, Combinatorics, Dynamical Systems, Number Theory, Differential Geometry, Topology, Chaos Theory, Graph Theory, Category Theory, Order Theory, Measure Theory, & Fractal Geometry. I would also like to learn enough mathematics to understand and appreciate Quantum Field Theory. http://s12.postimg.org/gesxh6viz/Mathematics.jpg ^ Here is the rough copy of my flow chart thus far, what changes/suggestions would you make.