The purpose of this chapter is to establish the geometric intuition that undergird the approach we take to this material throughout the course. In Section 1.1 we revisit some ideas from Linear Algebra and explore the connection between algebraic operations and geometric interpretations. This is not meant to serve as a review of Linear Algebra prerequisites, but as a warm up that centers the geometric intuition (A brief review of a few linear algebra topics may be found in Section A.1). In Section 1.2 we give some examples of problems we wish to address in this course and show how we may interpret them geometrically. In Section 1.3 we describe the geometric notions which will be most useful to us throughout the course, and give formal and intuitive descriptions of these ideas.
