TRUlivin

Hi guys first time using the forum. So currently i am in my first year Computer Science at a small university Thompson Rivers University in Kamloops British Columbia. I am wondering if by attending a smaller university ( not that prestigues) if i am limiting my future job potential. For example from my knowledge, bigger companies such as Google (etc..) will hire from more prestigious universities such as University of British Columbia etc... Is this true? Or will i be able to achieve such after graduating from Thompson Rivers, i just don't want to be limiting my future job potentials because of my university. I know that to my knowledge the content taught between the universities is virtually the same. So i have been debating transferring to a University of British Columbia, or University of Victoria just for this prestigious factor. So from your guy's experience does attending a high ranked university really play a big role in the long run? Or am i stressing myself out for no reason? Any advice is much appreaciated, i have been really stressing this the last few weeks. Thanks in advance !