What job did you get with a degree in math?

It was a long six-year fight for me to get my undergraduate degree in Mathematics. Just having a degree in (pure) math made me more "employable" than others with less technical degrees or no degree. I think you should give earning a degree another try. Find a school that will help you earn a degree in a way that works for you. You could start with an Associate's Degree, which at least gives you some post-secondary credentials and is a smaller amount of work to commit to. Associates are also usually very affordable.

For self-study, the most important part of learning anything is practice. If you are reading a book that has exercises, do as many of them as you can stand, if not all of them. If you are working with a source that does not have exercises, make them up for yourself. Ask yourself questions about what you're reading and try to develop or find the answers. When learning to program, it is important to write programs. If you have a smart phone you can download the appropriate development tools for free for Android (I think) or $5 for iPhone and start writing silly apps that test your skills.

As you read and do exercises and practice, you will start to learn how to best read, exercise and practice. The process that works for you is one of the primary benefits of practice. Everyone's mind is different which is why we can't simply just tell each other things and have that work for everyone. Each of us must repeatedly work through examples of ideas to integrate those ideas into our own way of thinking. When you get stuck (when, not if) you can look in the book or go online. Anyone with enough motivation and dedication can teach themselves almost anything with the assistance of the Internet.

In addition: I have a friend who has been an actuary for 15+ years. He has a maxim that I believe is true: If you learn math, you can learn to program, but if you just learn to program, you still don't know math.

Just a few notes: You're YOUNG in the whole scheme of things, have already accumulated a significant number of undergraduate credits, and you are motivated. As I see it, you're not at all in a "bad" place to be, in terms of "making a go of it."

One suggestion: being employable is a good thing. So is doing what you love to do. Try to find an area of concentration that will satisfy both. But don't spread yourself too thin. You listed a whole host of possible directions. So do explore a bit, perhaps before re-enrolling in college, but try to hone in on area of concentration (e.g., major/minor) - that may combine a few areas of interest you've listed - but not too many that you don't develop depth and mastery of what you are learning.

Good luck!

It doesn't really look like anyone has answered your question, "What job did you get?", so I will attempt.

Also, some of the answers are from people who said they graduated a while ago.

Firstly, what country are you in? This probably makes quite a difference.

I graduated in Maths-Physics from the top university in my country (not where I am located now) two years ago, and got straight into a job as a derivatives trader (banker) in a big finance city on a very high salery.

Of the 23 people who graduated in my year, at least half went into working in some sort of banking/ actuary/ financial consulting etc. Our degree had no Stats or Probability classes, except for Statistical Mechanics (but this is not like a Stats or Probability course), and a very basic amount of computer programming.

Of those who graduated in Pure-Maths, of which there were about the same number, the numbers who went into financial type work are about the same.

The point being, from someone who recently graduated, once you have any degree in Maths (very broad!) people will want to pay you lots of money to make them lots more money in the world of high finance!

So I would not be too worried about it.

Just pick whichever you enjoy more, and whichever you feel that you will do best at.

To your final question, I should add that I never did any industry internships while in my undergrad (I found research ones far more fun, and far less stressful! re. the poor guy who dropped dead while interning in London last summer).

Many others in my class had done this, and it helped them they reckoned.

I was absolutely thrown in the deep end! I remember feeling very very very stupid for the first number of months (maybe I still do!), but you learn quickly, like anything else. It was not much different from moving from secondary school Maths to University Maths.

So again, you can rest assured that many of the other newbies around you in the office will be finding it tough too. It took some time before anyone would admit it to each other (if you think people are very compeditive in university, wait til you see what people will do when theres a promise of a big bonus at the end of the road!) but eventually everyone let on that they were in the same boat. The empolyer will know that you're fresh out of college, and won't be expecting you to run the place within two weeks! They are aware that it takes time.

As a final point, those who neither went into further study (another large fraction) nor finance and related areas, I think teaching was also a popular option. A few people did that, but I actually think the three that I am currently in contact with absolutely dispise it, and aren't getting paid very well for it, relative to finance. Something to bare in mind.