My plan as an undergraduate was unequivocally to be a pure mathematician, working as an algebraist as a bigshot professor at a bigshot university. I'm graduating this month, and I didn't get into where I expected to get into. My letters were great and I'm published, but my GRE was bad and my grades were good but not perfect. My current plan, I guess, is to start a PhD program at my backup school, and then reapply to the better schools next year.
Reality is starting to hit, though, and I'm starting to think about "selling out." I would still love to work in algebra, but I'm not as in love with the Ivory Tower as I was a few years ago, and I don't want to give up my entire life for it. If the institution isn't going to let me do what I wanted to do, or if I'll never be as talented as I wanted to be, it isn't worth the sacrifice. In other words, I'd rather be a well paid-paid applied mathematician in industry than a poor, mediocre pure mathematician at a low end-end university.
The problem is it seems that most of the applied jobs out there are all about analysis / continuous mathematics, and I am firmly in the algebra / discrete camp. I really do not want to spend my life solving-solving fluid flow PDEs. I always hear about cryptography as an "applied algebra" job, but I'm not particularly crazy about working for the NSA or a telecom (plus crypto can't be the only option).
I read some of the answers from Can I use my powers for good? but it's not clear to me which of these suggestions value algebraic thinking. Many seem very quantitative, rather than structural - is it possible to avoid this in the industry? Also, I have a lot of debt from a long undergraduate career across several majors, so "how much" is unfortunately also a concern. I don't want to sell out cheap.
Are there applied math jobs in industry which focus on structural mathematics reminiscent of abstract algebra, earn an appreciably high salary, and aren't cryptography?
How would one best go about pursuing these jobs starting as a recent graduate / first year-year graduate student?