In my course “Introduction to the algebraic topology” I’ve got the following exam problem:
Construct continuous map $S^1 \times S^1 \rightarrow S^2$, which degree is non-zero. Calculate the degree of this map.
I believe that my problem is understanding the concept of the degree. $S^1 \times S^1$ and $S^2$ are obviously orientable manifolds, so there top homology groups are isomorphaic to $\mathbb Z$. Any continuous map $f$ induces homomorphism of this groups $f_*$. By definition, degree of $f$ is just an image of $$ (generator) under $f_*$.
So I need some hints how degree can be calculated in practice, i.e. some examples.