TOPICS IN MULTI-VARIABLE CALCULUS AND LINEAR ALGEBRA

Prerequisites & course information

Requisites: Consent of Instructor 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. Identify the formal definitions of mathematical objects and their properties used in linear algebra and differential multivariable calculus (e.g., vector spaces, linear transformations, derivatives of multivariate functions, etc.). Audience: Undergraduate 2. Use the standard methods and tools of mathematical argument in the context of linear algebra and multivariate differential calculus (e.g., direct and indirect methods, the construction of examples and counterexamples, induction arguments, 1st order logic, set theory, quantifiers, etc.). Audience: Undergraduate 3. Verify if a mathematical construct does or does not have the condition of having a particular property (e.g., that a matrix is invertible, that a set is a vector subspace, that a vector valued function is differentiable, etc.). Audience: Undergraduate 4. Identify standard theorems in linear algebra and differential multivariate calculus and recall arguments for these theorems and the underlying logic of their proofs (e.g., symmetric matrices are diagonalizable, chain rule for multivariate functions, etc.). Audience: Undergraduate 5. Prove or disprove statements related to the definitions, properties, and theorems of linear algebra and differential multivariate calculus using the techniques of mathematical argument. Audience: Undergraduate 6. Perform standard computations in the context of linear algebra and differential multivariate calculus. Audience: Undergraduate 7. Write mathematical proofs and concepts in logical, reasonable, and concise ways. Audience: Undergraduate Learning Outcomes: 1. Identify the formal definitions of mathematical objects and their properties used in linear algebra and differential multivariable calculus (e.g., vector spaces, linear transformations, derivatives of multivariate functions, etc.). Audience: Undergraduate 2. Use the standard methods and tools of mathematical argument in the context of linear algebra and multivariate differential calculus (e.g., direct and indirect methods, the construction of examples and counterexamples, induction arguments, 1st order logic, set theory, quantifiers, etc.). Audience: Undergraduate 3. Verify if a mathematical construct does or does not have the condition of having a particular property (e.g., that a matrix is invertible, that a set is a vector subspace, that a vector valued function is differentiable, etc.). Audience: Undergraduate 4. Identify standard theorems in linear algebra and differential multivariate calculus and recall arguments for these theorems and the underlying logic of their proofs (e.g., symmetric matrices are diagonalizable, chain rule for multivariate functions, etc.). Audience: Undergraduate 5. Prove or disprove statements related to the definitions, properties, and theorems of linear algebra and differential multivariate calculus using the techniques of mathematical argument. Audience: Undergraduate 6. Perform standard computations in the context of linear algebra and differential multivariate calculus. Audience: Undergraduate 7. Write mathematical proofs and concepts in logical, reasonable, and concise ways. Audience: Undergraduate