To extend the analysis of mathematics as the "critical filter" into actual college experience, the influence of high school and college mathematics on choice of majors and progress in the major during college was studied using data from 745 freshmen at Arizona State University. Attention was also directed to an expanded mathematics curricula that was designed to provide students the opportunity to remedy their mathematics deficiencies and to pursue math-based scientific or technical college majors and careers. Comparative data were included on: the level of gender segregation and the racial or ethnic distribution of college majors, the high school academic background of students in different majors, and changes in majors during the four years of study. Majors were grouped into seven discipline clusters, classified on the basis of the level of mathematics required. Structural-equation models for each of the seven discipline clusters showed the relationship of students' precollege mathematics background, mathematics course taking, grades, and progress in college majors. Findings include: 45% of students majoring in scientific/technical majors did not have trigonometry or fourth-year high school mathematics; and the majority of college students made some significant change from intended to actual majors during college. (SW)