How to succeed in this course

For many students, this is your first college-level course in mathematics. In high school, you may have taken calculus courses that taught you to perform (sometimes rather involved) mechanical procedures for computing derivatives, integrals, and the like. About half of this course will be similar, except instead of computing integrals, you'll learn to solve systems of linear equations of various forms.

The other half of this course, however, will likely be more abstract in nature than anything you've seen before. You are at the Georgia Institute of Technology, after all — this is not high school any more. We will focus on conceptual ways of understanding equations and their solution sets. We will ask questions like, what is the dimension of a set of solutions? What are all ways we can write them down? Are there any properties of the matrices involved that we can exploit to describe the solution sets, without actually solving the equations in the first place? What kind of geometric questions can we associate to a system of linear equations?

For these reasons, the methods you used to approach your previous mathematics courses may not suffice any more. For instance:

Read on for more specific advice.