<p>I am considering attending the University of Rochester next year as a prospective math major. I am interested specifically in "pure" mathematics, and am interested in attending graduate school for it to hopefully someday be able to teach and/or do research at a university. Before asking any specific questions, I was wondering if anyone could give any anecdotal advise regarding the mathematics department there, specifically MTH 171-174 and the subsequent honors courses.</p>
<p>To clarify my situation before asking my main question, I am well aware of the jump between AP Calculus and abstract, proof-based math such as analysis. I took AP Calculus last year and, out of my own interest, supplemented it by reading through Spivak in my free time. This piqued my interest and I studied a cheap Dover book on introductory analysis afterwards (one which included metric spaces), followed by some discontinuous studies of subjects like linear algebra and multivariable calculus online. I tried to keep my study of analysis focused though, and recently purchased a copy of baby Rudin and have been slowly working my way through each chapter and exercise. </p>
<p>So in summary, I am familiar with proofs, especially analytic ones. I have a good grasp of epsilon-delta's and understand how they can be used beyond simple limits. This puts me in an uncertain situation, because on the one hand I lack formal instruction in these subjects, but on the other I am worried about starting my undergraduate education in a less-than-ideal position. </p>
<p>On this page, it suggests that there are cases in which certain students may start with 173, but I cannot find anything else. Does anyone know anything about this? If it is actually a thing, how feasible might it be for someone in a position like mine? Would it be a good decision to accelerate myself like this, or foolish to skip the formal instruction of 171-172?</p>
<p>Thank you in advance to anyone with any advice!</p>