These links do not count as 1,000 links from 1,000 seperate website, since Google does recognize linking root domains.
The most important link to your website would be from the page with the highest page authority, which is almost always the home page.
I am not 100% sure, but I remember reading about a recent Google algorithm update that targets multiple links from one domain. Web design firms were affected, since they typcally sign the footer, which creates a link on every page of the website.
The subdomain, works similar to a subpage. Google will notice the root dominan, which is abc.edu.
I do not think you are at risk of a penalty or anything like that, but if you want to continue to increase your rankings, once you get a link from a domain, I would focus my efforts on getting another link from a separate root domain, instead of a link from a subpage or subdomain from the same root domain.