I am currently reading up on some algebraic topology\differential geometry and have reached the section on de Rham theory. This is my first encounter with such notions and I am a little confused by what is meant when one applies a boundary operator to a simplex. Conceptually, I know that it takes a n-simplex to its boundary n-1 simplex, ,but quantitatively I am confused by the actual formula. How does one add simplicies? Do you sum their respective coordinate values, or do the list of points ie. v0,v1,v2,v3 constitute an algebraic "object" which is to be thought of as a whole and not it's constituent points? I apologize if I am not making much sense here .