UAR 45MA: Mathematical Foundations for University Success, Building Strength for Calculus and Beyond

This course is designed to support students in making a successful transition to university-level mathematics at Stanford. Building on and enriching foundational prerequisite skills, the course prepares students for Calculus (Math 19) and for further study in mathematics and related STEM fields.

Students will strengthen their proficiency in precalculus mathematics with an emphasis on deep conceptual understanding, scaffolded problem-solving, and mathematical confidence. A central goal of the course is to help students develop the analytical skills necessary to succeed in Stanford mathematics courses and beyond.

Topics include algebraic reasoning, manipulation of expressions, functions and their representations, graphing, trigonometry, exponentials and logarithms, and an introduction to limits. Each concept is explored through multiple perspectives—algebraic, graphical, numerical, and analytical—so that students build a rich and connected understanding of the material.

Throughout the course, students engage actively in problem-solving, discussion, and collaborative exploration. We emphasize not only how mathematical techniques work, but why they work, helping students develop a deeper understanding that supports long-term success. The course also highlights applications of these ideas in fields such as physics, chemistry, engineering, and other STEM disciplines.

The course is delivered in a blended format, combining pre-class video lectures with live, interactive sessions. Students are expected to engage with instructional materials in advance so that class time can focus on deeper problem-solving, conceptual discussion, and student presentations. Students complete regular assignments and assessments and receive detailed, individualized feedback from instructors.

This course is intended primarily for students planning to enroll in Math 18 or 19, ideally in the fall quarter, but it will be valuable for any student preparing to take calculus during their first year at Stanford.