When a professor says something was common in 600 BC, would that be the years 501 to 599? Does the count run backwards or what?

Yes, the count "runs backwards" for years followed by the "BC" designation. Because of the influence of the church on the development of the modern calendar, the era of Jesus is considered a "starting point," so anything before that is called "Before Christ" (BC) and the numbers get larger the further back you go. In your example, the years 501 to 599 are on our side of the "dividing line," and were somewhere in the neighborhood of 1500 years ago. (A year number which is not followed by "BC" is assumed to be "after the birth of Christ." Those years are sometimes marked AD (a Latin expression for "In the year of our lord" or CE, which means "in the common era.") Your teacher said 600 BC, so he means somewhere around 2600 years ago, much longer ago than the era your example describes.

It would be 600BC. Why don't you believe him? If it was before it would be 601 etc but if it were after it would be 599 and later.

idiot