The goal of this course is for students to become comfortable with abstraction, rigour, logic, and proofs. They will practice reading and understanding mathematical statements, analyzing definitions and properties, formulating conjectures and generalizations, providing and writing reasonable and precise arguments, writing and critiquing proofs. The instructor may use specific mathematical content, which could vary from year to year, to practice these skills. Students who take MAT135H1 and MAT136H1 and wish to take MAT237Y1 are required to take MAT138H1 prior to undertaking MAT237Y1. Students who are taking MAT137Y1 or MAT157Y1 and/or MAT240H1 and are interested in more preparation with logical arguments are encouraged to take MAT138H1 concurrently.