How does an academic mathematician educate him/herself about job opportunities outside academia? One of the contradictions of being a math professor is that a big part of your job is to train people to do things which are quite different from what you do yourself professionally; this is especially true for undergrads, but to some measure also with grad students.
This is not particularly helpful when it comes to convincing students that they should major in mathematics; most mathematicians I know, myself included, are quite ignorant of what people will actually do if they get BAs in mathematics, and don't go to graduate school, or otherwise enter education, which is obviously something students will be very concerned about in these tough economic times.
Obviously, the correct response is to educate one's self on what the job opportunities are for people with BAs in math.  I'm mostly interested in the US context, but would be happy to hear about other countries as well.
The best resource I know is the AMS Early Career Profiles page.  This is a lot of links (some broken) to profiles of BA graduates in math that individual departments have put together.  There some other reasonable links on this website.  Is there anywhere else I should be looking?
 A: One thing that I think might be helpful is for professors to post information about their ex-graduate students' whereabouts on their web pages.  Often you will see that Student X is now an assistant professor at University Y, but I think it would also be interesting to know that Student X is now a jazz musician.  I do agree with could-not-log-in that there is not a strong correlation between majors and careers. Nevertheless it would be interesting to know what PhD graduates in algebraic number theory end up doing, and it would be convenient to access that information by visiting websites of algebraic number theory professors.  
A: Is it the job of an academic mathematician to be aware of all existing career possibilities?...
I think the following is more important: putting undergraduate (and graduate) students in contact with alumni who have recently graduated, and who are now pursuing a career outside academia. What P. Nielsen describes (a bi-weekly seminar with speakers explaining their successful careers) looks great. But it could be even more useful for the students to get to talk to people who graduated just a few years ago.
In the high-school in which I work, I've seen how they do it:
Once a year, they invite some of their alumni pupils to tell the other kids about their experience in the study that they chose... It should be possible to implement something similar at university.
The advantage is that alumni might be able to give a better guidance to the students, and answer questions such as:
• How do I go about applying for jobs?
• What are the concrete problems that I could encounter in my first 2-3 years after graduating?
•  How can I deal with them?
That's what the students need to know.
A: Use a recruiter.  An academic is unlikely to have the insight into the job market and connections that a professional recruiter will have.  
If you want to go into software development, realize that a math degree by itself gives you zero credibility as a programmer.  In fact, it may give you negative credibility.  When I moved from academia to industry, some potential employers assumed I was a bad programmer because I had a PhD.  
An advanced degree in math may persuade employers that you are smart.  But are you impractical and distracted by interesting tangents, or do you use your ability to solve practical problems?  You're probably not a mediocre programmer; you're more likely to be really bad or really good.  Realize that's what people are thinking and do what you can to show you're in the latter group. 
If employers think you will be a good programmer, they may be concerned about how long it will take you to come up to speed.  Do what you can to show that you've learned on your own.  Professional certification such as MCP may help.  (On the other hand, don't over-estimate the value of certification.  Most employers don't value certification nearly as much as experience, but if you have no experience, it's better than nothing.)
You might want to contribute to an open source project so you can point to real software you've written.
A: I majored in Math as an undergrad. My first job out of college was as a financial analyst performing multiple regression analysis of historical pricing and technical data with 5 other Math B.S. recipients. I eventually got a Masters in Systems Science & Mathematics and I ended up in Engineering. I now work with a Math Ph.D, an Engineering Ph.D., a Physics M.S. a Computer Science M.S., and several computer science B.S. people doing computer programming. I've known other Math B.S. people to end up as Statisticians and Actuaries.
Thus I'd say, in my limited exposure, this is an example of at least a handful of jobs a Math person could end up in with or without a graduate degree - engineering, programming, IT, statistics, actuary, or financial analysis. 
And to answer the question directly, all an academic mathematician has to do to educate him/herself about job opportunities outside academia is to post to a site like mathoverflow.net and get personal testimonies. QED
A: This answer is not so much about teaching others about carreer opportunities, but many universities offer coaching or training programs for this purpose. They are usually aimed (at least here) at PhD students or staff members though. Although they are not aimed specifically at mathematicians, I found such a program quite helpful (I recently followed a 2 day training). For one, it is important to find out your own qualities (and be able to convince others of this!). The interesting part is when you can get feedback from other participants, that come from a completely different field, to get useful suggestions for jobs that you might not have thought of. As mentioned by other people here already, it is not so much about the mathematics you learn, but more about the skills that you acquire that can be useful outside academia (an analytic mind, being able to see patterns emerge, etc.).
A: My experience, based on years in and out of academia, is that both students and professors vastly overestimate the connection between a major and a career. If you speak with successful professionals 20 years after their college graduation, you find that their majors are really kind of random. Among the people I talked with today, for instance, were a super-talented programmer who majored in English, a tech entrepreneur who majored in graphic design, and marketing executive who majored in philosophy.
I think the best advice for a student is to major in a subject that they'd enjoy studying for four years. That way they'll have a good time and find it easy to work hard! Note also that "enjoy studying" means the whole process, taking into account which subjects have inspiring professors and interesting fellow students.
A: As one of the previous posts reply pointed out, the B.A. in mathematics can lead to anything: from M.D. to M.B.A, to some kind of engineering or actuarial degree.  The really difficult question is how do you encourage your students that Ph.D. in mathematics might still be a good idea, even if they might not like teaching or unsure about their research skills.  Essentially, you have to tell them there is plenty of demand for mathematicians in the industry or the government (think NSA, CCR).  This is also suggested by this ranking, btw.  Unfortunately, in the past few years there has plenty of drum against going to grad school (see here, here, here, and somewhat less applicable but still strongly worded followup here). So how do you respond?  
My answer is trivial: start early.  While in graduate school, take advanced classes in CS, applied or numerical math, finance, or economics.  It is often easy to cross register at the business school, but very few people ever do this.  But you don't even have to do that - the lecturer might allow you to just audit the class.  If things work out, you succeed in mathematics and become a professor, you will know what to say.  But if things don't work out, you will know what to do...  
A: I agree with could-not-log-in:
From my experience outside of academia, if you apply for a job it is most important what you did the last five years. This means that if you manage to get a job and be successful for at least five years, the subject that you majored in becomes unimportant.
As for getting your first job: It will be very rare that there is any opportunity to apply anything you learned in academia in your job. You learned some probablitity and statistics? Well, try to get a job at an insurance company where you can apply this - but chances are that you will end up somewhere else where it's of no use. This applies to other professions as well, of course, not only to mathematicians. There are just too few jobs out there that need some specific mathematical knowledge. Don't tell your students that they should take classes in applied mathematics etc. It's far more important to work some hours a week outside of academia to gain experience about the workplace, the people and what's important to them.
So you should not look for jobs where some specific mathematical knowledge has to be applied, but for jobs where the secondary virtues and skills that mathematicians have are important:


*

*analysing complex technical problems,

*finding convincing solutions, being very critical until a maximum of clarity is achieved,

*high frustration tolerance,

*being able to explain the results to the uninitiated,

*being able to learn complicated new stuff quickly on your own.
There are two areas that come to my mind that offer excellent job opportunities to mathematicians:


*

*all kinds of consulting,

*all kinds of engineering that need abstract thinking, the prototype being of course the software industry.
Example problem solving: Some engineers I know, when confronted with a problem, are used to sit down for a while until they come up with a solution. A mathematician will know that this does not always work, but that it will take time to brood, getting distracted, brooding again, until someday you get it. This is a crucial experience that gives mathematicians a head start. But it's the experience and knowledge how to tackle complicated problems, it's not the knowledge of specific topics in mathematics.
A: When I was helping set up my department's web site, I wanted to create a web page providing similar information. It was rather frustrating how little information is provided by the professional mathematical organizations such as the American Mathematical Society. Here is the page: Careers in Mathematics
ADDED: I would add that I recommend strongly that a math department try to stay in touch with its alumni (both undergraduate and graduate). You can't do better than learning from them what kinds of careers they are able to pursue with their degree in mathematics.
MORE: Another suggestion I have, if you're up for it, is to take advantage of your right to earn money doing something else one day a week and try to work as a consultant for a company. Not many companies look for mathematicians, but if you talk to lots of people (parents of your kids' classmates are a great way to meet non-academics), you might stumble onto something. What I've learned from working in the "real world" has been of immeasurable benefit to virtually every aspect of my life as an academic mathematician. The least is the ability to give convincing advice to students on what kind of careers they can pursue and what they need to know to succeed.
A: As an undergrad who has recently been looking for jobs I would make the following suggestions...
1) Learn to program! MOST of the jobs I've run into that require mathematicians/statisticians will eventually require learning one or more of Perl/Python/R/C++/SAS. I'm in the process of writing a book on the subject (programming for mathematicians, specifically in python)
2) Learn probability and statistics! I didn't do that directly and wish I had because I run into problems all the time for which probability and statistics knowledge would be useful.
3) Kind of coupled with 1, but learn Algorithms and Data Structures. If you never program than this isn't worth doing, but algorithms is math heavy and most companies that want to hire people to do algorithms expect a base knowledge, and basic knowledge of data structures is a MUST in that scenario)
4) Try applied classes! Other departments will not eat you! I promise... unless it's the department of cannibalism...
5) FINISH projects! Make sure whenever you get involved with a project that you push as hard as you can to get something finished and a "product" to show off.
6) Talk to professors outside of the department if they do something you think looks interesting. I don't mean to stress coding so much, but coding is something that everyone outside of CS departments (since coders are a dime a dozen there) needs, at least in the hard sciences and engineering.
7) For someone who doesn't plan on going into academia... internship >> summer classes. Search far and wide for these, they're extremely valuable and show that you can handle a work environment in addition to being able to handle an academic environment.
These are most relevant to undergrads, I haven't a clue what a grad student should do b/c I haven't gotten there yet!!
A: In terms of educating both professors and their students about what opportunities are available with a degree in mathematics, I think our department has done an outstanding job.
First, we have the website When Will I Use Math which discusses a number of career opportunities, salary potentials, and gives other useful information.  We have made it freely available to everyone; so you might take a look, or direct your students there.
Second, we have a bi-weekly seminar, in which we invite speakers from different industries to explain their careers.  One week we might have a financial analyst, another week we'll have a cryptographer, and the next week we'll have someone who researches the effects of nuclear stockpiles.  I'm surprised at some of the applications people find for their experience in mathematics.
Third, we are a bit more proactive, when mentoring undergraduates, in finding them jobs.  To aid us in knowing what is available, our department creates a list of companies looking for internships, etc...
I hope this helps.
A: You can use any job searching site and subscribe to vacancies which contain words "mathematics" "math" of whatever. 
In Russia I am subscribed on www.hh.ru  - I am getting about 10-20 vacancies everyday,
it is for free, absolutely most of them are not really related to math, but sometimes something related appears. But I guess in USA you will get much more vacancies where mathematicians are required or at least welcome.
I think http://www.monster.com/ 
is Okay for USA.
I am sorry if this rather trivial answer already has been posted - I looked answers and did not see one. Any way I think your question is very good.
A: Rather than look at lists someone else has compiled of "what can you do with a degree in X?", I would suggest that it's more useful to go directly to the source: search job boards and company websites for the work people do outside education.
A few places I think make sense to start:


*

*Principal business activity codes A list of business categories. As far as understanding work and career goes, I think it makes more sense to think in terms of industrial categories rather than academic departments.

*Large public companies – Large-cap public companies are not the only places to work but they do have big hiring budgets. Becoming familiar with what they want done is certainly good, if only partial, information about business.

*Job search – Pretend you are one of your students and ask yourself how you would go about finding a job. You may start searching with terms like "quantitative" skills and come to find a lot of unfamiliar terms representing what .

*relative composition of your country – Wikipedia has nice pictures for many countries of the relative size of imports and exports, which is related to but not the same as how many people are employed doing various things.

*View from the top – a set of interviews with CEO's


In my opinion the barrier to overcome is dividing the world according to academic department labels. (eg, thinking that $\textrm{management} = \textrm{psychology} \oplus \textrm{business}$) It takes time, but in principle it's not hard to apply a functor that repositions the topology (and adds new objects) according to the goals and methods of commercial businesses, whether that's Altria, TimeWarner, VeriSign, Tesoro, Cargill, or Airbus.
