[pzhon]

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I'm going to be taking linear algebra over the winter intersession at my college this winter. Basically it is a semester divided by 3, so the class is accelerated. What can I do to prepare for the class itself?

-2nd year mathematics major

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There are several types of introductory linear algebra classes. Most of the advice people have given seems to assume you are getting one particular type which emphasizes simple but tedious calculations. Other types include introductions to rigorous proofs and introductions to numerical methods. That you are taking the class in the intersession increases the chance you are getting one of the latter two types. Hybrids are possible.

At some point in your studies as a mathematics major, the emphasis changes from being able to compute things and knowing what is true to handling abstract systems and being able to prove things. Some colleges make this change in a class on number theory, some in real analysis, some in abstract algebra, and some in linear algebra. If this class is taught as an introduction to proofs, it would be a big mistake to focus on the calculations during the class, even if it is easiest to test your ability to calculate things. Before the class, review determinants, matrix multiplication, and Cramer's Rule from high school algebra so these don't get in the way. During the class, spend extra time making sure you know exactly what the definitions are of the objects studied, what properties have been established, and how these were proved. In fact, I recommend keeping a separate notebook to record these (and no calculations).

If the class is taught as an introduction to applied mathematics, I recommend familiarizing yourself with the syntax of the computational system used in the class (perhaps Matlab, Maple, or Mathematica) or the programming language suggested.

If this is an ordinary class on linear algebra, buy lots of paper and some quality pens.