Harvey Mudd’s Math 30G or 30B “Focus on mathematical reasoning, rigor and proof” and assume that the student has had calculus in high school. https://www.hmc.edu/mathematics/program/mathematics-course-descriptions/
Well, not exactly the same, but Reed math courses start with 111 (single variable calculus) followed by 112 (introduction to analysis). Reed considers AP calculus credit (5 on AB or 4 on BC) to be duplication of 111, so it is possible for a Reed frosh with calculus in high school to start in introduction to analysis. https://www.reed.edu/math/courses.html