LINEAR ALGEBRA

Prerequisites & course information

Requisites: MATH 234 . Not open to students with credit for MATH 375 . Course Designation: Core GenEd - Natural Science & Wellness + Lab Breadth - Natural Science Level - Advanced L&S Credit - L&S Liberal Arts and Science Honors - Accelerated Honors (!) Repeatable for Credit: No Last Taught: Fall 2026 Learning Outcomes: 1. Recall and state the formal definitions of mathematical objects and their properties used in elementary linear algebra (e.g., dimension of a vector space, linear dependence of a set of vectors, etc.). Audience: Undergraduate 2. Use the standard methods and tools of mathematical argument in the context of linear algebra (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 is an eigenvector, etc.). Audience: Undergraduate 4. Recall and state standard theorems used in elementary linear algebra (e.g., symmetric matrices are diagonalizable, linear operators with non-trivial kernel are not invertible, etc.). Audience: Undergraduate 5. Verify the premises of standard theorems in elementary linear algebra in order to apply their conclusions in the context of longer arguments (e.g., that a given matrix has zero determinant and therefore has nullity larger than one, etc.). Audience: Undergraduate 6. Prove or disprove statements related to the definitions, properties, and theorems of elementary linear algebra using the techniques of mathematical argument. Audience: Undergraduate 7. Perform standard computations in the context of linear algebra (e.g., finding the rank of a matrix, computing the determinant of a square matrix, etc.). Audience: Undergraduate 8. Convey formal mathematical arguments in English using appropriate mathematical terminology and notation. Audience: Undergraduate Learning Outcomes: 1. Recall and state the formal definitions of mathematical objects and their properties used in elementary linear algebra (e.g., dimension of a vector space, linear dependence of a set of vectors, etc.). Audience: Undergraduate 2. Use the standard methods and tools of mathematical argument in the context of linear algebra (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 is an eigenvector, etc.). Audience: Undergraduate 4. Recall and state standard theorems used in elementary linear algebra (e.g., symmetric matrices are diagonalizable, linear operators with non-trivial kernel are not invertible, etc.). Audience: Undergraduate 5. Verify the premises of standard theorems in elementary linear algebra in order to apply their conclusions in the context of longer arguments (e.g., that a given matrix has zero determinant and therefore has nullity larger than one, etc.). Audience: Undergraduate 6. Prove or disprove statements related to the definitions, properties, and theorems of elementary linear algebra using the techniques of mathematical argument. Audience: Undergraduate 7. Perform standard computations in the context of linear algebra (e.g., finding the rank of a matrix, computing the determinant of a square matrix, etc.). Audience: Undergraduate 8. Convey formal mathematical arguments in English using appropriate mathematical terminology and notation. Audience: Undergraduate