I went a little off the deep end a bunch of years ago learning geometric algebra. For a similar, but slightly different and cool take, check this out [0]. It's a take on multivectors, dyadics, and differential forms, which really shine in E&M. It's a shame this isn't taught to undergrads with linear algebra and vector calc.

[0] http://onlinelibrary.wiley.com/book/10.1002/0471723096