I recommend this book: http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192 http://www.amazon.com/Mathematics-Elementary-Approach-

I recommend this book: http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192 http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-... > Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. I find the book to be a great introduction to topics that are (actually) explored at the upper division level. The vast majority of what I've learned from lower division mathematics courses was a list of methods rather than understanding (which is understandable as it's really geared for engineers, who arguably care more about results rather than a deep understanding), with the exception of linear algebra and perhaps calculus 1.