Is knowing Linux required to learn Unix?

If you’re a UNIX user, all UNIX are pretty much the same.
If you’re a UNIX programmer, all UNIX are a little bit different.
If you’re a UNIX system admin, all UNIX are completely different!

— Bob Koehler
Hubble Space Telescope
Payload Flight Software Team

Strictly speaking Linux is a kernel and knowing it won't help that much when targeting Solaris. However, I guess by Linux you mean Gnu/Linux based distributions. In such case, Solaris and most of these operating systems share a lot of common or similar code, like Xorg, Gnome, most Gnu utilities, Java, OpenOffice, Apache, openssl, perl, python, sudo, firefox, thunderbird, the gimp, MySQL and plenty of other open source code.

The administration side is where you'll find some major differences between Solaris and Linuxes but you'll find a lot of differences too between various families of Gnu/Linux based OSes too.

No, they are similar but there is no dependencies between the two. So you can learn Solaris without knowing anything about Linux.

On the other hand, I don't think it's a bad thing to know a little bit about how the different versions of unix behave....

From the user perspective, all *nix like systems (Linux, Ubuntu, Red Hat, Sun/Solaris, AIX) are essentially the same. By this I mean that the commands a user uses most (vi, cat, more, cd, mkdir, rmdir, rm, cp, mv, man) are available and have mostly the same options.

If, however, you want to do system administration they are different; sometimes very different.

As for Unix courses, you'll have to check the course descriptions or ask your teachers.