NUMERICAL LINEAR ALGEBRA

Prerequisites & course information

Requisites: ( MATH 320 , 340 , 341 , 345 , or 375 ) and ( COMP SCI 200 , 220 , 300 , 310 , or placement into COMP SCI 300 ), graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate) Course Designation: Core GenEd - Natural Science & Wellness + Lab Breadth - Natural Science Level - Advanced L&S Credit - L&S Liberal Arts and Science Grad 50% - Counts toward 50% graduate coursework requirement 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 numerical linear algebra (e.g., matrix norms, the condition number, diagonalizability, under- and over-determined linear systems, normal equations, pseudoinverse, etc.). Audience: Both Grad & Undergrad 2. Use different algorithms of numerical linear algebra in their appropriate settings (e.g., LU factorization, QR decomposition, Gram–Schmidt process, singular value decomposition, power method, Arnoldi iteration, etc.). Audience: Both Grad & Undergrad 3. State the main theoretical results in the field (e.g., error bounds on the numerical solution of linear systems, algorithm stability, Gershgorin circle theorem, eigenvalue sensitivity to perturbations, etc.). Audience: Both Grad & Undergrad 4. Describe the complexity of different algorithms and how this affects the choice of algorithm for a particular purpose. Apply general principles for the efficient computer implementation of numerical linear algebra. Audience: Both Grad & Undergrad 5. Convey arguments in oral and written forms using English and appropriate mathematical terminology, notation and grammar. Audience: Both Grad & Undergrad 6. Identify applications of course content in current areas of research. Audience: Graduate Learning Outcomes: 1. Recall and state the formal definitions of the mathematical objects and their properties used in numerical linear algebra (e.g., matrix norms, the condition number, diagonalizability, under- and over-determined linear systems, normal equations, pseudoinverse, etc.). Audience: Both Grad & Undergrad 2. Use different algorithms of numerical linear algebra in their appropriate settings (e.g., LU factorization, QR decomposition, Gram–Schmidt process, singular value decomposition, power method, Arnoldi iteration, etc.). Audience: Both Grad & Undergrad 3. State the main theoretical results in the field (e.g., error bounds on the numerical solution of linear systems, algorithm stability, Gershgorin circle theorem, eigenvalue sensitivity to perturbations, etc.). Audience: Both Grad & Undergrad 4. Describe the complexity of different algorithms and how this affects the choice of algorithm for a particular purpose. Apply general principles for the efficient computer implementation of numerical linear algebra. Audience: Both Grad & Undergrad 5. Convey arguments in oral and written forms using English and appropriate mathematical terminology, notation and grammar. Audience: Both Grad & Undergrad 6. Identify applications of course content in current areas of research. Audience: Graduate