Optics is a part of physics. A lot of undergraduate physics courses do not ever get to it because it is usuall the last chapter in the text book.
Basically optics is how to numerically determine what will happen to light when passing through different medias. There can be a lot of formulas to memorize if you want to do optics that way, but there are ways around it. You can do almost any optics problem relating to ophthalmic lenses or mirrirs by what is called "surface-to-surface." Instead of memorizing the entire equation that took calculus to derive, just determine what will happen to light as it hits each surface of the media. That way all you really need to know is how to divide the media density over the linear distance or dioptric power.
The prof. at my school teaches us how to do every problem at least 3 ways: Surface-to-surface, formula, and just estimation. Most of our class can do most of an optics exam without a calculator because we know what "should" happen so only one answer makes sense. If you think about it, that is probably the best way because when doing an exam you are not going to pull out your calcualtor and figure out what lens you need, you need to know what lenses will do to light and apply that clinically.
But to answer your main question, optics involves calculus, linear algebra, trig, and geometry.
I hope that made sence, I think I may have just rambled.
