This course is designed to teach students to meticulously craft logically sound mathematical arguments about a wide variety of basic mathematical concepts. These topics include sets, relations, functions, recurrence relations, graphs, and limits. In addition to direct proofs, students also learn to write proofs by contraposition, contradiction, and mathematical induction. Specifically, it is meant to prepare students for the rigorous reasoning required in higher level mathematics courses such as MATH 01340 Modern Algebra I and MATH 01330 Introduction to Real Analysis I.