<p>No college program would allow you to take those classes without first being introduced to proofs; generally the topics covered in Algebra are briefly touched on in such a proof based class (with most of the prepatory groundwork for analysis having come from Calculus). </p>
<p>Realistically, Algebra should be the only difficult class to transition to, since its unlikely that you will have seen much of the material ahead of time (unless you take Linear Algebra and Number Theory first - which you totally should; LA in particular is a pre-req for algebra at my campus). Analysis is far easier than Algebra, and if you’ve done calculus and learned how to approach a proof - you’ve got all the tools you need.</p>