Characterizing introduction to proof courses: a survey of U.S. R1 and R2 course syllabi

Many tertiary institutions with mathematics programmes offer introduction to proof courses to ease mathematics students’ transition from primarily calculation-based courses like Calculus and differential equations to proof-centred courses like real analysis and number theory. However, unlike most tertiary mathematics courses, whose mathematical content is directly implied by their course titles, introduction to proof courses may vary substantively in terms of the mathematics content discussed. In this study, we document the variation in content of introduction to proof courses by examining recent syllabi and other relevant course documents from introduction to proof courses at 176 R1/R2 universities across the United States. Since there is a growing number of mathematics education studies on undergraduate introductory proof and proving emerging from the U.S., this broad sample of what content these introductory proof courses cover is illuminating for both U.S. proof researchers, who are likely unaware of what cross institution variation exists, as well as international proof researchers aiming to better contextualize the student populations studied in U.S. proof education research.