THE THEORY OF SINGLE VARIABLE CALCULUS

Prerequisites & course information

Requisites: MATH 234 or graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program Course Designation: Core GenEd - Natural Science & Wellness + Lab Breadth - Natural Science Level - Advanced L&S Credit - L&S Liberal Arts and Science Repeatable for Credit: No Last Taught: Fall 2026 Learning Outcomes: 1. Understand and use the standard methods and tools of mathematical argument (e.g direct and indirect methods, the construction of examples and counterexamples, induction arguments, first-order logic, set theory, and quantifiers). Audience: Undergraduate 2. Recall and state the formal definitions of mathematical objects (e.g. sets, functions, and graphs) and their properties used in calculus. Audience: Undergraduate 3. Distinguish if a mathematical construct does or does not have the condition of having a particular property formally (e.g. limits, continuity, differentiability, and integrability). Audience: Undergraduate 4. Recall and state standard calculus theorems (e.g. Intermediate Value Theorem, Mean Value Theorems, and Fundamental Theorem of Calculus), and recall arguments for these theorems and the underlying logic of their proofs. Audience: Undergraduate 5. Prove or disprove statements related to the definitions, properties, and theorems of calculus using the techniques of mathematical argument. Audience: Undergraduate 6. Write mathematical proofs and concepts in logical, reasonable, and concise ways. Audience: Undergraduate Learning Outcomes: 1. Understand and use the standard methods and tools of mathematical argument (e.g direct and indirect methods, the construction of examples and counterexamples, induction arguments, first-order logic, set theory, and quantifiers). Audience: Undergraduate 2. Recall and state the formal definitions of mathematical objects (e.g. sets, functions, and graphs) and their properties used in calculus. Audience: Undergraduate 3. Distinguish if a mathematical construct does or does not have the condition of having a particular property formally (e.g. limits, continuity, differentiability, and integrability). Audience: Undergraduate 4. Recall and state standard calculus theorems (e.g. Intermediate Value Theorem, Mean Value Theorems, and Fundamental Theorem of Calculus), and recall arguments for these theorems and the underlying logic of their proofs. Audience: Undergraduate 5. Prove or disprove statements related to the definitions, properties, and theorems of calculus using the techniques of mathematical argument. Audience: Undergraduate 6. Write mathematical proofs and concepts in logical, reasonable, and concise ways. Audience: Undergraduate