Hi./P>

Your long question raises a number of issues which are probably too numerous to address properly in a single comment. I'm going to try to tackle your basic question. I believe you wished to know "What else can one do with a math degree other than go to graduate school?"

While I am not sure if the material is easily found on our website, the YMN has addressed this issue a number of times in the past. We often run panel discussions at the winter meetings where we invite mathematicians from industry to come and showcase their professions for the audience. I remember that we ran such an event a year ago in Atlanta. We often publish summaries of these discussions for our newsletter and this website.

Part of the answer depends upon your additional training. Someone working in the corporate world will usually need a more diverse skill set than someone in academia. For example, have you taken a programming course or two?

Anyway, here are some options to consider. Some involve a bit of extra study in the form of a master's degree, but others do not:

• Scientific Programming: Let's imagine that you have taken some applied math courses (probability, numerical analysis, linear algebra, discrete math, etc.) and are familiar with a current programming language (C++ or Java). You might consider going to work as a programmer in an industry that does modelling and simulations. Often in these situations, smart people are required who can understand the theory and implement it successfully.
• Actuarial Science: Again, we'll imagine that you are familiar with calculus, probability and statistics. With this training, you could take and pass the the first actuarial exam. If you do well, you could start a career as an actuary. I hear that it is quite lucrative. (OK! You won't be a millionaire.)
• Statistician: Go get a masters in statistics and work as a statistician. The amount of data requiring analysis by companies is staggering and continues to grow. I hear that, unlike mathematics, there is rarely difficulty finding work as a statistician.
• Operations Research: is a form of very applied mathematics. With a master's degree in operations research you are quite employable to tackle a company's problems involving routing, queues, and quality control.
• Government: Unless you have a strong anarchic anti-government streak (and a criminal record to accompany it), you might consider going to work for the government. A number of agencies employ mathematically-gifted individuals. If you don't have an advanced degree, the nature of your job may differ, but the specific lack of a Ph.D. probably won't matter. Some of these agencies are: National Security Agency (NSA), NASA, National Institutes of Standards and Technology (NIST), U.S. Census Bureau, and the National Institutes of Health (NIH). The list is based upon knowledge of mathematicians/physicists who work in each of these agencies and/or based upon seeing these agencies appear at local career fairs to recruit undergraduates. One thing to keep in mind is that if your job is of a "sensitive" nature, it may require U.S. citizenship, that you may lack.

I hope that this list has helped you to see some of the additional careers available to a mathematics major who chooses to stray from the "yellow brick road" of pure graduate study leading to a doctoral degree, followed by a university career including a tenured position. I also hope that other commentators (and editors) with more direct experience in these areas will be able to flesh out one or more of the careers that I've only mentioned in passing. I know that there are mathematicians in industry, or who have worked in industry, who read the posts on this website on a regular basis. Others are directly involved in math programs geared towards non-academic careers such as becoming an actuary or teaching mathematics in a high school.

I wish you the best as you grapple with that big question which often looms before a graduate of any kind: high school, college, masters, doctoral. "I'm finished and what will I do next for the REST OF MY LIFE?"

Dov ;-)