Hi,
I have a question about the amino acids we're supposed to
memorize.  The worksheet that Dr. G handed out conflicts with the
book.  Are cysteine and tyrosine polar or non-polar?

It's a good question - these sort of divisions aren't absolute. Cysteine and tyrosine are both marginal amino acids whose side chains can really go either way.

Cysteine, for example, is polar in the sense that it can form hydrogen bonds and exist perfectly happily in water. It is structurally very similar to a serine (a polar amino acid) except that the -SH group is not quite as good at forming H-binds as the -OH group. We most often find cysteines out on the surface of proteins, playing in the water. But, sometimes they are buried. So, all in all, I'd call cysteine a polar amino acid, albeit not a very good one.

Alternatively, while the -OH group of tyrosine is very good at making H-bonds (the characteristic of polar amino acids), the big greasy phenyl ring behind it is quite hydrophobic (i.e., non-polar) and dominates its interactions. So it's very common to find tyrosines buried away from water, though it needs someone other than water to make a H-bond with. But, sometimes they're out on the surface. So, all in all, I'd call tyrosine a hydrophobic amino acid, albeit one that dabbles with polar H-bonds.

Don't agonize over the fact different authors draw the line in different places - amino acids really have a spectrum of properties and the division between "polar" and "non-polar" is a convenient oversimplification.