Geometric introduction to exterior algebra

Question

Could anyone point me to a geometric introduction to exterior algebra (meaning, one with a good number of figures and/or verbal descriptions of geometric objects in it)? Thanks!

Answer 1

Mathematical physicists see much of their work as an generalization of exterior algebra, so try:

• The geometry of physics by Theodore Frenkel.

A lot of this stuff was invented before good computer graphics, but Wikipedia has some neat figures as well:

Answer 2

Have a look at chapter 4 in Gravitation by Misner, Thorne and Wheeler. It describes differential forms and various operations on them in terms of the honeycomb constructions described by john in his answer taking electromagnetism as the main example.

Answer 3

On the Visualisation of Differential Forms

A Geometric Approach to Differential Forms

Teaching Electromagnetic Field Theory Using Differential Forms