Is it possible to not keep ios apps on your main computer?

I sync my iPhone and iPad with my MacBook. It appears that iTunes stores copies of all of my apps on my MacBook, even though I, for obvious reasons, can't actually use them there. The problem is that they take several gigabytes of space. Is there something I can do about this?

Make sure that app syncing is disabled between your Mac and iOS devices (which you can double-check in settings within iTunes when device is plugged in). Then go into Apps section of iTunes and delete all of the apps. With iCloud and iTunes Match I stopped syncing my iOS devices over a year ago and there is absolutely no need to have these apps backed up on your computer.

If you need help managing your syncing, see this article on Apple's Knowledge Base. You will essentially want to do the opposite of what it says.