I have regrettably little to say about the hookup culture, but on the subject of college mathematics instruction, I see George Leef has suggested that:
What schools should do is create a challenging course for non-majors that will (or at least can) give students a look into the way mathematicians think — their approach to problems. Taught well, such a course could really be mind-expanding, showing students the beauty of mathematical logic.
While I agree that it would be a good idea for college students to learn more math, I’m not sure this is the way to accomplish it. In general, I’m skeptical of college classes that purport to teach about a subject, rather than teaching the subject itself. If you shy away from details and specifics, there’s no way to be rigorous and nothing you can test on, so it ends up being one of those classes where if you just show up most of the time, you’ll get an A. (I majored in math myself; I don’t know if that makes me more or less qualified to hold an opinion on this question.)
This is particularly true in mathematics, where, outside of a few high-profile problems (like the four-color theorem) that can be easily grasped, it’s hard for most laymen to understand the subject matter except in a very fuzzy way, and even harder for most experts to describe it comprehensibly, let alone explain how mathematicians have approached it (though this is not true for a master like John Derbyshire or, presumably, the author of the article George links to). Most areas of mathematical research are so complicated and abstract that talking about them would be like trying to explain sex to a Martian: Unless you already understand the point of it all, there’s no way to make it sound interesting.
If I were designing a math requirement for college students, I would make everyone take a class in statistics. The basic concepts require no more than high-school algebra; they have many applications to real life (a knowledge of statistics will teach students more about how the world works than any political-science class); and best of all, the students can actually perform calculations and get results themselves — instead of studying the subject at arm’s length, and thereby absorbing the implicit message that math is too complicated for the average person to do.