Motivation for discrete exterior calculus (DEC); de Rham complex; Simplicial complexes; Discrete differential forms; Discrete exterior derivative; Discrete wedge product; Leibniz (product) rule; Simplicial maps and naturality

Dual cell complex; Discrete Hodge star; Codifferential; Hodge-Laplace problems; Relationship with finite element exterior calculus and Whitney forms; Discrete contraction and Lie derivative

Exterior covariant derivative; Discrete vector bundles with connection; Discrete exterior covariant derivative; Discrete curvature; Discrete Bianchi identity. If there is time left then: Bernstein-Gelfand-Gelfand construction with application to elasticity complex