Our next lecture will cover one of the basic tools we’ll use throughout the rest of the course: *exterior algebra*. The basic idea is to add a couple new operations to our usual list of vector operations (dot product, cross product, etc.) that make it easy to talk about *volumes* rather than just vectors. If you felt ok working with things like the cross product and the determinant in your linear algebra/vector calculus courses, this shouldn’t be too big of a leap. (If not, could be a good moment for a review!)

## 2 thoughts on “Lecture 3: Exterior Algebra”

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On slide 44/1 hour in, $\star(3v_1 \wedge v_2 \wedge v_3)$ should be 1/3 instead of 3 right?

I don’t think so; $\star(e_1 \wedge e_2 \wedge e_2) = 1$, so $\star(3e_1 \wedge e_2 \wedge e_2) = 3$.