There are some great books to build up some intuition and rigor in all branches of math, with no prior knowledge: * How to Prove It (Velleman) * Algebra; Trig

There are some great books to build up some intuition and rigor in all branches of math, with no prior knowledge: * How to Prove It (Velleman) * Algebra; Trigonometry; F&G; The Method of Coordinates (Gelfand) * Geometry (Kiselev) * Calculus Made Easy (Thompson) * How to Count without Counting (Niven) * Introduction to Probability Theory (Hoel) * The Little Schemer (Friedman) The proceed to more advanced texts like: * Naive Set Theory (Halmos) * Linear Algebra Done Right (Axler) * Geometry Revisited (Coxeter) * Infinitesimal Calculus (Keisler) * Concrete Mathematics (Graham) * Information Theory, Inference and Learning (MacKay) * SICP (Abelson)