How relevant do you think finite fields are for solving applied optimization problems? What proportion of a course do you think should be devoted to them?
Every ordered field has characteristic 0, so I don't think finite fields are likely to be terribly useful for solving optimization problems. But:
(0) There is way more to linear algebra than linear programming.
(1) A linear algebra course is not the right place for an extensive study of how to solve optimization problems anyway. That belongs in a real analysis course.
This is a graduate-level course in the department of computer and information science.
> Prerequisite(s): Undergraduate course in linear algebra, calculus
> The goal of this course is to provide firm foundations in linear algebra and optimization techniques that will enable students to analyze and solve problems arising in various areas of computer science, especially computer vision, robotics, machine learning, computer graphics, embedded systems, and market engineering and systems. The students will acquire a firm theoretical knowledge of these concepts and tools. They will also learn how to use these tools in practice by tackling various judiciously chosen projects (from computer vision, etc.). This course will serve as a basis to more advanced courses in computer vision, convex optimization, machine learning, robotics, computer graphics, embedded systems, and market engineering and systems.
