Schools are institutions in which students' course taking creates series of linked learning opportunities continually shaped by not only curricular structures but demographic and academic backgrounds. In contrast to a seven-step normative course sequence reflecting the conventional hierarchical structure of mathematics, analysis of more than 17,000 high school transcripts indicates that students followed remarkably diverse pathways through high school mathematics. Students from less socially and academically advantaged backgrounds were more likely to deviate from common course sequences, thus contributing to their not progressing as far through the mathematics curriculum by the end of high school. Modeling course enrollments as growth trajectories indicates that gaps in mathematics progress related to demographic and earlier educational differences widen most rapidly in the later years of high school. The implications of our findings for schools' course scheduling and monitoring of students' progress are discussed. (Contains 14 notes, 3 tables and 3 figures.)