I agree that getting things in the right order is important, but would argue that the order in which math is usually taken in the US is not the optimal one! I

I agree that getting things in the right order is important, but would argue that the order in which math is usually taken in the US is not the optimal one! I recently took calc-1,2,3 and linear algebra through my local community college, and then started working my way through a wonderful book on mathematical proofs:(http://www.amazon.com/Mathematical-Proofs-Transition-Advanced-Mathematics/dp/0321797094/ http://www.amazon.com/Mathematical-Proofs-Transition-Advance...), as preparation for working on higher level math. I would now argue that being able to understand and write proofs is a (the?) key mathematical skill to understanding what I would call 'real' (higher) math, and could be learnt by most students following high school algebra. My impression of the calculus series and linear algebra courses was an excessive focus on calculation, the math proof book was way more fun, surprising for a subject that is often thought to be too difficult for first year college students. For those who are intimidated by the idea of a book on proofs (like I used to be), an example from the third chapter: Theorem: Let x be an integer. Then x^2 is even if and only if x is even It seems so simple, and I think would be accessible to anyone who had completed high school algebra but I found that even having done those calculus and linear algebra courses, I had now idea how to go about actually PROVING this! The book however, goes through the thought process step by step, and teaching the skills needed to be able to understand the real math books like Rudin.