Algebraic geometry II - schemes and sheaves

In Lecture 3, we covered the following topics:

-Spec(R) as a topological space with its Zariski topology;

-examples;

-closure of a point in Spec(R) and geometric interpretation for it;

-Spec of quotient R/I and identification between Spec(R_f) and the principal open D(f);

-definition of the presheaf of regular functions on Spec(R),

-the stalks of the structure sheaf on Spec(R) (no proof);