The mathematics SSEA module is split into two tracks: one is a crash course in single variables calculus and the second is an introduction to linear algebra. Students who take the first track will likely enroll in Math 41 in the fall, whereas students in the second will likely enroll in Math 51.
In the 41 track I expect to cover most of the highlights in differential calculus. We will start by examining the tangent problem and use this as our motivation for exploring limits and defining derivatives. After this we will gain some proficiency in computing derivatives, and finish differential calculus by discussing some of the sweet applications of the theory. If we have time left over I will introduce the Jack Lemon to differentiation's Walter Mathau: integration. This track will be much like a high school calculus class, except that I hope to emphasize the concepts behind calculus as well as the computations. My goal is that you come away with a geometric and algebraic understanding of differentiation/integration, as I think this is the best way to understand calculus.
In the 51 track I hope to be able to introduce most of the concepts in an introductory linear alegebra course up to linear transformations. We begin by introducing vectors and the basic terminology which goes along with them. This will lead us naturally into considering the connection between linear algebra and systems of linear equations, which will in turn provide the tools to answer some geometric problems we're interested in. More than most high school math classes, students in 51 have a responsibility to know the definitions and theorems stated in class. Linear algebra is an entirely new language that many of you haven't yet seen, and the terminology we introduced is our common language.
The mathematics track is taught by Andrew Schultz. His office is in the basement of the math building, room 380-G. You can contact him by email at aschultz@stanford (of course, you'll want to append a '.edu'). He'll be around most days from about 10 til about 5, though he won't always be in his office at those times. He strongly encourages you to approach him with questions either by email, in his office, or after class or section. Learning mathematics is about struggling with problems, screwing up calculations, and eventually figuring out why the way you've been thinking about problems isn't the right way to solve them after all. He can help you move through this process with the minimal amount of pain and the maximal amount of reassurance, so use him as a resource.