APPLIED LINEAR ALGEBRA

Prerequisites & course information

Requisites: ( MATH 320 , 340 , 341 , 345 , or 375 ), graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate) Course Designation: Core GenEd - Natural Science & Wellness Breadth - Natural Science Level - Advanced L&S Credit - L&S Liberal Arts and Science Repeatable for Credit: No Last Taught: Spring 2026 Learning Outcomes: 1. Recall and state the formal definitions of the mathematical objects and their properties used in applied linear algebra (e.g., system of equations, matrices, linear transformations, inner product spaces, quadratic forms, etc.). Audience: Undergraduate 2. Use such definitions to argue that a mathematical object does or does not have the condition of being a particular type or having a particular property (e.g., system of equations has a solution, matrix has an LU factorization, linear transformation is invertible, etc.). Audience: Undergraduate 3. Recall and state the standard theorems of applied linear algebra. (e.g., Rank-Nullity theorem, Spectral theorem of normal operators, theorems leading to SVD and PCA methods, etc.). Moreover, apply these theorems to solve problems in applied linear algebra. Audience: Undergraduate 4. Construct mathematical arguments related to the above definitions, properties, and theorems, including the construction of examples and counterexamples. Moreover, the student will learn classical algorithms to solve scientific problems using linear algebra (e.g., Page rank, Recommendation systems, SVD and matrix completion, Least square and Gram Schmidt process, etc.). Audience: Undergraduate 5. Convey arguments in oral and written forms using English and appropriate mathematical terminology and notation, and justify the applicability of classical linear algebra based algorithms in science. Audience: Undergraduate Learning Outcomes: 1. Recall and state the formal definitions of the mathematical objects and their properties used in applied linear algebra (e.g., system of equations, matrices, linear transformations, inner product spaces, quadratic forms, etc.). Audience: Undergraduate 2. Use such definitions to argue that a mathematical object does or does not have the condition of being a particular type or having a particular property (e.g., system of equations has a solution, matrix has an LU factorization, linear transformation is invertible, etc.). Audience: Undergraduate 3. Recall and state the standard theorems of applied linear algebra. (e.g., Rank-Nullity theorem, Spectral theorem of normal operators, theorems leading to SVD and PCA methods, etc.). Moreover, apply these theorems to solve problems in applied linear algebra. Audience: Undergraduate 4. Construct mathematical arguments related to the above definitions, properties, and theorems, including the construction of examples and counterexamples. Moreover, the student will learn classical algorithms to solve scientific problems using linear algebra (e.g., Page rank, Recommendation systems, SVD and matrix completion, Least square and Gram Schmidt process, etc.). Audience: Undergraduate 5. Convey arguments in oral and written forms using English and appropriate mathematical terminology and notation, and justify the applicability of classical linear algebra based algorithms in science. Audience: Undergraduate