Many mathematics graduate students focus on the thesis and don't learn a ton about what to do afterward. What will they do next?
In case you haven't noticed, the job market has been sh*tty for a while. For several years state funding cuts and dramatic losses in private endowments curtailed hiring. Now hiring is rebounding a bit, but people who took any job they could to stay in the game three years ago are looking to move up. Postdocs at research schools are still vulnerable to budget game-playing. The number of tenure-track positions has been declining steadily for years while the armies of contingent labor grow... just want to warn you all not to expect a smooth sail.
If you're geographically limited, the market gets even tougher because your competition pool remains international but you're not looking at as many colleges or universities. Good luck.
Many graduate students (or their silly advisors) look to jobs at small liberal arts colleges (SLACs) as a fallback from the research life that one should of course want. This is quite foolish: jobs at many SLACs are quite competitive. Not only do SLACs want people with a particular outlook and kind of preparation, but they now have a huge pool of very qualified applicants and they can afford to be picky. In general, the more prestigious the graduate school, the less likely a grad student is competitive for a tenure-track SLAC job. Why?
* Did you teach more than two classes a semester and show you could balance teaching with research?
* Did you ever teach your own classes, setting the syllabus, assigning homework, writing exams, and grading some chunk of this?
* Have you shown you looove undergrads through math club activities, outreach, or mentoring?
* Were you involved in innovations in pedagogy? Do you have experience teaching with technology, teaching through group work, teaching through inquiry, running a senior capstone course, teaching a writing course focused on proof? Can you talk about these experiences intelligently?
* Have you done any service work at your university or in the larger mathematical community?
Sure, none of these things are really prerequisites for the tenure-track job -- you'll get to do all of them eventually. You may turn out to be a stellar teacher who can balance teaching, service, a bit of research focusing on undergraduates, and Pi Day baking. That's not the point. The point is that you're competing against people who have done these things. Done them. They had nice postdocs in 2008 because they graduated in 2006, and in 2009 they took so-so tenure-track jobs, and now that the economy is easing they want to move on. It's easier to go with the sure bet and the extensive track record if you're hiring -- and who would blame the hiring committee for that?
Grad students: my list of questions above is not complete. If you want a SLAC job, read that list and add your own questions. A SLAC job is something to prepare for, not something to fall back on.