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CS 205 Mathematical Methods for Robotics and Vision

Robotics and computer vision are interdisciplinary subjects at the intersection of engineering and computer science. By their nature, they deal with both computers and the physical world. Although the former are in the latter, the workings of computers are best described in the black-and-white vocabulary of discrete mathematics, which is foreign to most classical models of reality, quantum physics notwithstanding. This class surveys some of the key tools of applied math to be used at the interface of continuous and discrete. It is not on robotics or computer vision. These subjects evolve rapidly, but their mathematical foundations remain. Even if. | CS 205 Mathematical Methods for Robotics and Vision Carlo Tomasi Stanford University Fall 2000 2 Chapter 1 Introduction Robotics and computer vision are interdisciplinary subjects at the intersection of engineering and computer science. By their nature they deal with both computers and the physical world. Although the former are in the latter the workings of computers are best described in the black-and-white vocabulary of discrete mathematics which is foreign to most classical models of reality quantum physics notwithstanding. This class surveys some of the key tools of applied math to be used at the interface of continuous and discrete. It is not on robotics or computer vision. These subjects evolve rapidly but their mathematical foundations remain. Even if you will not pursue either field the mathematics that you learn in this class will not go wasted. To be sure applied mathematics is a discipline in itself and in many universities a separate department. Consequently this class can be a quick tour at best. It does not replace calculus or linear algebra which are assumed as prerequisites nor is it a comprehensive survey of applied mathematics. What is covered is a compromise between the time available and what is useful and fun to talk about. Even if in some cases you may have to wait until you take a robotics or vision class to fully appreciate the usefulness of a particular topic I hope that you will enjoy studying these subjects in their own right. 1.1 Who Should Take This Class The main goal of this class is to present a collection of mathematical tools for both understanding and solving problems in robotics and computer vision. Several classes at Stanford cover the topics presented in this class and do so in much greater detail. If you want to understand the full details of any one of the topics in the syllabus below you should take one or more of these other classes instead. If you want to understand how these tools are implemented numerically you should .