Do you know a basic reference to introduce an undergraduate student with more physical rather than mathematical background to De Rham cohomology? 


The Student (from a Bachelors program in material science) should work on a summer project aiming to understand some of the mathematics behind the quantum hall efect, explained with chern numbers. The student has previously helped on experiments with some materials relevant to the quantum hall efect. 


I do know the mathematical ellaborations on this ranging von Bellisard, Schulz-Baldes, collaborators and Connes'approach on the topic in the noncommutative geometry book. This will be certanily too advanced from the point of view of mathematics. 



Reference for de Rham cohomology for physicists
If you are familiar with some topological field theory, then the de Rham cohomology of $M$ can be viewed as the vector space of supersymmetric vacua in the $\sigma$-model associated to $M$. I think this was first noted by Prof. Witten in his work on sypersymmetry and Morse theory. You can look it up in the paragraph 4 of chapter 10 [here](http://www.claymath.org/library/monographs/cmim01c.pdf).


