It's the value of the equity (shares); market cap completely ignores debt.

Market cap is a good way to think about what the total value of a company's stock is, but a leveraged (indebted) company may have some of its "company value" "owned" by bondholders as well. EV is the total value, whereas MC is just the shareholders' part.

I feel like this shouldn't be a dumb question, but here it goes:

So, how come people are purchasing equity without paying any attention to debt?

I understand how different classes of shares may be equivalent in scenarios where a company is successful, but very different if it is failing. I also understand that the market has established a price for 0.01% of a company, and not necessarily a price for a much larger share.

Ha, I wonder what the students in that class thought when the instructors were "too dumb" to teach the consensus understanding in corporate finance.

That said, on Hacker News, subjects like company valuations seem to be discussed in terms that are more consistent with economics than what you typically hear from students of finance.