I took 4555 as a first-year after taking only calc three and discrete structures. I had little prior experience with proofs. I took it with Prof. Weitsman, and he was great. The lecture only had nine people, and he would answer any question you asked him. There are proofs in the class, and the exams had proofs on them, but a large portion of it was applying what you learned to examples. You will definitely be fine without real analysis, but maybe brush up on proofs by induction and contradiction.