# What are the best ways to prepare one's self for introductory classes in proofs, analysis, and modern algebra?

I'm a second-year college student, coming from a mathematical background that includes everything up to differential equations, linear algebra, and a survey discrete mathematics. How might I go about preparing myself for the standard undergraduate courses mentioned above?

Would it be a good idea to dive into more advanced texts (I see Rudin/Axler/Munkres suggested fairly often) and just work my way through them? Or would it more efficient to find material of a more intermediate difficulty? Any advice or suggestions would be greatly appreciated!

Another way to become more familiar with proof techniques is to read your previous texts over again (which definitely contain proofs) and focus heavily on the proofs therein. For example, real analysis is an extension of calculus on $\mathbb{R}$ to $\mathbb{R}^n$ and the like. Having a thorough understanding of calculus and the proofs therein will make the transition to real analysis much smoother as the ideas are similar but are more abstract.