This talk (the first of two) will be an exposition of B. Osserman's paper "Self Maps of P^1 with Prescribed Ramification in Characteristic p" where he considers the following problem: in positive characteristic, how many separable self-maps of P^1 are there with a specified tame ramification divisor? Unlike the case of characteristic zero, the answer need not be finite, and in low characteristics, certain pathologies occur. However, when the characteristic is large compared with the degree, there is a recursive formula expressing the answer for general points on P^1. I will explain the proof, which proceeds by translating the problem into a question about intersection of Schubert cycles, and then using a degeneration argument to reduce to the case of three ramification points.